BA6933 Statistics Week 5 Quiz ( Chapter 11 & 12 )

 Consider the following hypothesis problem.

n = 30	H0: σ2 = 500
s2 = 625	Ha: σ2 ≠ 500

The test statistic equals

a. 24.00.

b. 36.25.

c. 23.20.

d. 37.50.

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b

The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. The test statistic is

a. 30.

b. 1.2.

c. 500.

d. 31.2.

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a

The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. The p-value for this test is

a. less than .10.

b. zero.

c. greater than .10.

d. .05.

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c

Based on the sample evidence below, we want to test the hypothesis that population A has a larger variance than population B.

	Sample A	Sample B
n	11	10
s2	12.1	5

The test statistic for this problem equals

a. 2.

b. 2.42.

c. 1.1.

d. .4132.

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b

The bottler of a certain soft drink claims their equipment to be accurate and that the variance of all filled bottles is .05 or less. The null hypothesis in a test to confirm the claim would be written as

a. H0: σ2 > .05.

b. H0: σ2 ≥ .05.

c. H0: σ2 < .05.

d. H0: σ2 ≤ .05.

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d

Consider the following hypothesis problem.

n = 23	s2 = 60	H0: σ2 ≤ 66
		Ha: σ2 > 66

If the test is to be performed at the .05 level of significance, the null hypothesis

a. should not be tested.

b. should be rejected.

c. should be revised.

d. should not be rejected.

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d

Consider the scenario where

The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the table is(are) _____.

a. 5.629

b. 5.629 and 26.119

c. 6.262 and 27.488

d. 27.488

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b

A sample of 61 observations yielded a sample standard deviation of 6. If we want to test H0: σ2 = 40, the test statistic is

a. 9.

b. 54.90.

c. 54.

d. 9.15.

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c

Given the sample information below, what test statistic should be used to determine whether the standard deviations are equal for two populations, prior to performing a hypothesis test for the equality of the population means?

a. F = 2.49, with numerator degrees of freedom = 29 and denominator degrees of freedom = 19

b. F = 0.40, with degrees of freedom = 19

c. t = 18.75, with degrees of freedom = 19

d. F = 1.58, with numerator degrees of freedom = 19 and denominator degrees of freedom = 29

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a

Consider the following sample information from Population A and Population B.

	Sample A	Sample B
n	24	16
s2	32	38

We want to test the hypothesis that the population variances are equal. The null hypothesis is to be tested at the 10% level of significance. The critical value from the F distribution table is

a. 2.24.

b. 2.11.

c. 2.29.

d. 2.13.

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d

The random variable for a chi-square distribution may assume

a. any value between -1 to 1.

b. any value greater than zero.

c. any value between -∞ to +∞.

d. any negative value.

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b

Consider the following hypothesis problem.

n = 14	H0: σ2 ≤ 410
s = 20	Ha: σ2 > 410

The test statistic equals

a. .63.

b. 13.33.

c. 13.68.

d. 12.68.

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d

The χ 2 value for a one-tailed (upper tail) hypothesis test at 95% confidence and a sample size of 20 is _____.

a. 10.851

b. 10.117

c. 30.144

d. 31.410

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c

The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. The p-value for this test is

a. zero.

b. .05.

c. less than .10.

d. greater than .10.

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d

The sampling distribution used when making inferences about a single population's variance is

a. a t distribution.

b. an F distribution.

c. a chi-square distribution.

d. a normal distribution.

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c

The sampling distribution of the ratio of independent sample variances extracted from two normal populations with equal variances is the

a. chi-square distribution.

b. normal distribution.

c. t distribution.

d. F distribution.

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d

Consider the following hypothesis problem.

n = 23	s2 = 60	H0: σ2 ≤ 66
		Ha: σ2 > 66

If the test is to be performed at the .05 level of significance, the null hypothesis

a. should not be tested.

b. should be rejected.

c. should not be rejected.

d. should be revised.

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c

We are interested in testing whether the variance of a population is significantly more than 625. The null hypothesis for this test is

a. H0: σ2 > 625.

b. H0: σ2 ≤ 625.

c. H0: σ2 ≥ 625.

d. H0: σ2 ≤ 25.

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b

A sample of 20 bottles of soda yielded a standard deviation of .25 ounce. A 95% confidence interval estimate of the variance for the population is _____.

a. .0361 to .1333

b. –.6378 to .6378

c. .0394 to .1174

d. .0023 to .0083

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a

To avoid the problem of not having access to tables of the F distribution when a one-tailed test is required and with F values given for the lower tail, let the

a. sample variance from the population with the smaller hypothesized variance be the numerator of the test statistic.

b. smaller sample variance be the numerator of the test statistic.

c. larger sample variance be the numerator of the test statistic.

d. sample variance from the population with the larger hypothesized variance be the numerator of the test statistic.

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a

To avoid the problem of not having access to tables of the F distribution when a one-tailed test is required and with F values given for the lower tail, let the

a. smaller sample variance be the numerator of the test statistic.

b. sample variance from the population with the smaller hypothesized variance be the numerator of the test statistic.

c. sample variance from the population with the larger hypothesized variance be the numerator of the test statistic.

d. larger sample variance be the numerator of the test statistic.

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b

The value of F.01 with 9 numerator and 20 denominator degrees of freedom is

a. 2.39.

b. 2.91.

c. 2.94.

d. 3.46.

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d

The chi-square value for a one-tailed (upper tail) hypothesis test at a 5% level of significance and a sample size of 25 is

a. 36.415.

b. 37.652.

c. 33.196.

d. 39.364.

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a

Which of the following rejection rules is proper?

a. Reject H0 if p-value ≥ α/2.

b. Reject H0 if F ≥ Fα.

c. Reject H0 if F ≤ Fα/2.

d. Reject H0 if p-value ≤ Fα.

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b

The manager of the service department of a local car dealership has noted that the service times of a sample of 15 new automobiles has a standard deviation of 4 minutes. A 95% confidence interval estimate for the variance of service times for all their new automobiles is

a. 8.576 to 39.794.

b. 9.46 to 34.09.

c. 2.144 to 9.948.

d. 2.93 to 6.31.

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a

χ2.975 = 8.231 indicates that

a. 97.5% of the chi-square values are less than 8.231.

b. 5% of the chi-square values are equal to 8.231.

c. 2.5% of the chi-square values are greater than 8.231.

d. 97.5% of the chi-square values are greater than 8.231.

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d

Consider the following hypothesis problem.

n = 30	H0: σ2 = 500
s2 = 625	Ha: σ2 ≠ 500

The test statistic equals

a. 36.25.

b. 37.50.

c. 23.20.

d. 24.00.

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a

Consider the following hypothesis problem.

n = 30	H0: σ2 = 500
s2 = 625	Ha: σ2 ≠ 500

At the 5% level of significance, the null hypothesis

a. should be revised.

b. should not be tested.

c. should be rejected.

d. should not be rejected.

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d

The value of F.05 with 8 numerator and 19 denominator degrees of freedom is

a. 2.48.

b. 3.63.

c. 2.96.

d. 2.58.

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a

The symbol used for the variance of the population is

a. σ2.

b. s2.

c. s.

d. σ.

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a

The sampling distribution of the quantity (n - 1)s2/σ2 is the

a. normal distribution.

b. chi-square distribution.

c. F distribution.

d. t distribution.

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b

Which of the following is not a property of a chi-square distribution?

a. χ2 is skewed to the right.

b. The number of degrees of freedom defines the shape of the distribution of χ2.

c. χ2 can have both positive and negative values.

d. All of these choices are properties of the χ2 distribution.

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c

The χ 2 value for a one-tailed (upper tail) hypothesis test at 95% confidence and a sample size of 20 is _____.

a. 10.117

b. 10.851

c. 31.410

d. 30.144

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d

Which of the following rejection rules is proper?

a. Reject H0 if p-value ≥ α/2.

b. Reject H0 if p-value ≤ Fα.

c. Reject H0 if F ≤ Fα/2.

d. Reject H0 if F ≥ Fα.

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d

Consider the following hypothesis problem.

n = 23	s2 = 60	H0: σ2 ≤ 66
		Ha: σ2 > 66

If the test is to be performed at the 5% level, the critical value(s) from the chi-square distribution table is(are)

a. 12.338 and 33.924.

b. 12.338.

c. 33.924.

d. 10.982 and 36.781.

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c

A manufacturer of carpentry screws claims that its production machine is very accurate and that the standard deviation of the length of all screws produced is .08 mm or less. A sample of 30 screws showed a standard deviation of .10. The test statistic to test the manufacturer's claim is _____.

a. 18.56

b. 19.2

c. 45.31

d. 23.2

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c

The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. The test statistic is

a. 1.2.

b. 30.

c. 500.

d. 31.2.

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b

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

The number of intervals or categories used to test the hypothesis for this problem is

a. 10.

b. 4.

c. 6.

d. 5.

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c

A study was conducted to examine whether the proportion of females was the same for five groups (Groups A, B, C, D, and E). How many degrees of freedom would the χ2 test statistic have when testing the hypothesis that the proportions in each group are all equal?

a. 0.20

b. 4

c. 5

d. 1

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b

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

The calculated value for the test statistic equals

a. 6.

b. 1.67.

c. 2.

d. 0.

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c

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.

Do you support capital punishment?	Number of individuals
Yes	40
No	60
No Opinion	50

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The conclusion of the test at the 5% level of significance is that the

a. distribution is uniform.

b. distribution might have been normal.

c. null hypothesis cannot be rejected.

d. Marascuilo procedure is more applicable.

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a

The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is

a. A chi-square distribution is not used.

b. k – 1.

c. number of rows minus 1 times number of columns minus 1.

d. n – 1.

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c

A population where each of its element is assigned to one and only one of several classes or categories is a

a. Poisson population.

b. multinomial population.

c. binomial population.

d. normal population.

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b

The table below gives beverage preferences for random samples of teens and adults.

	Teens	Adults	Total
Coffee	50	200	250
Tea	100	150	250
Soft Drink	200	200	400
Other	50	50	100
	400	600	1000

We are asked to test for independence between age (i.e., adult and teen) and drink preferences. The expected number of adults who prefer coffee is

a. 200.

b. .25.

c. 150.

d. .33.

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c

The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.

Political Party	Support
Democrats	100
Republicans	120
Independents	80

We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. The expected frequency for each group is

a. .333.

b. .50.

c. 50.

d. 100.

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d

Marascuilo procedure is used to test for a significant difference between pairs of population

a. proportions.

b. variances.

c. means.

d. standard deviations.

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a

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.

Freshmen	83
Sophomores	68
Juniors	85
Seniors	64

We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. At a .05 level of significance, the null hypothesis

a. cannot be tested.

b. should not be rejected.

c. was designed wrong.

d. should be rejected.

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b

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

The calculated value for the test statistic equals

a. 1.67.

b. 0.

c. 6.

d. 2.

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d

Two hundred randomly selected people were asked to state their primary source for news about current events: (1) Television, (2) Radio, (3) Internet, or (4) Other. We wish to determine whether the percent distribution of responses is 10%, 30%, 50%, and 10% for news sources 1 through 4, respectively. What is the null hypothesis?

a. H0: p = .50

b. H0: the proportions are not all equal.

c. H0: p1= .10, p2 = .30, p3 = .50, p4 = .10

d. H0: p1 = .25, p2 = .25, p3 = .25, p4 = .25

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c

The test for goodness of fit

a. is always an upper tail test.

b. is always a lower tail test.

c. can be a lower or an upper tail test.

d. is always a two-tailed test.

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a

The table below gives beverage preferences for random samples of teens and adults.

	Teens	Adults	Total
Coffee	50	200	250
Tea	100	150	250
Soft Drink	200	200	400
Other	50	50	100
	400	600	1000

We are asked to test for independence between age (i.e., adult and teen) and drink preferences. The test statistic for this test of independence is

a. 62.5.

b. 0.

c. 82.5.

d. 8.4.

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a

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. The expected frequency for the Business College is

a. 90.

b. .35.

c. 105.

d. .3.

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c

An important application of the chi-square distribution is

a. testing for goodness of fit.

b. testing for the independence of two categorical variables.

c. making inferences about a single population variance.

d. All of these alternatives are correct.

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d

A population where each of its element is assigned to one and only one of several classes or categories is a

a. multinomial population.

b. Poisson population.

c. normal population.

d. binomial population.

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a

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.

Do you support capital punishment?	Number of individuals
Yes	40
No	60
No Opinion	50

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The conclusion of the test at the 5% level of significance is that the

a. distribution is uniform.

b. null hypothesis cannot be rejected.

c. Marascuilo procedure is more applicable.

d. distribution might have been normal.

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a

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. This problem is an example of a

a. z test for proportions.

b. test for independence.

c. multinomial population.

d. Marascuilo procedure.

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c

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.

Freshmen	83
Sophomores	68
Juniors	85
Seniors	64

We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. The expected frequency of seniors is

a. 68.

b. 60.

c. 64.

d. 20%.

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b

The owner of a car wash wants to see if the arrival rate of cars follows a Poisson distribution. In order to test the assumption of a Poisson distribution, a random sample of 150 ten-minute intervals was taken. You are given the following observed frequencies:

Number of Cars Arriving in a 10-Minute Interval	Frequency
0	3
1	10
2	15
3	23
4	30
5	24
6	20
7	13
8	8
9 or more	4
	150

The calculated value for the test statistic equals

a. 1.72.

b. .18.

c. 3.11.

d. 2.89.

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d

Which of the following Chi-Square tests can be used to determine if a data set follows a Normal distribution?

a. Chi Square Test of Association

b. Chi-Square Test of Homogeneity

c. Chi-Square Goodness of Fit

d. Chi-Square Test of Equality of Three or More Population Proportions

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c

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.

Do you support capital punishment?	Number of individuals
Yes	40
No	60
No Opinion	50

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The conclusion of the test at the 5% level of significance is that the

a. Marascuilo procedure is more applicable.

b. distribution might have been normal.

c. distribution is uniform.

d. null hypothesis cannot be rejected.

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c

The table below gives beverage preferences for random samples of teens and adults.

	Teens	Adults	Total
Coffee	50	200	250
Tea	100	150	250
Soft Drink	200	200	400
Other	50	50	100
	400	600	1000

We are asked to test for independence between age (i.e., adult and teen) and drink preferences. The expected number of adults who prefer coffee is

a. .33.

b. 200.

c. .25.

d. 150.

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d

Marascuilo procedure is used to test for a significant difference between pairs of population

a. variances.

b. standard deviations.

c. means.

d. proportions.

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d

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

The number of intervals or categories used to test the hypothesis for this problem is

a. 5.

b. 6.

c. 10.

d. 4.

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b

With respect to the number of categories, k, when would a multinomial experiment be identical to a binomial experiment?

a. k = 1

b. k = 2

c. k = 3

d. k = 4

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b

An important application of the chi-square distribution is

a. testing for goodness of fit.

b. testing for the independence of two categorical variables.

c. making inferences about a single population variance.

d. All of these alternatives are correct.

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d

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. The calculated value for the test statistic equals

a. .01.

b. 4.38.

c. .75.

d. 4.29.

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d

The sampling distribution for a goodness of fit test is the

a. t distribution.

b. chi-square distribution.

c. normal distribution.

d. Poisson distribution.

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b

The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.

Political Party	Support
Democrats	100
Republicans	120
Independents	80

We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. The calculated value for the test statistic equals

a. 2.

b. 0.

c. 8.

d. 4.

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c

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals

a. 9.348.

b. 5.991.

c. 7.378.

d. 7.815.

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b

If there are three or more populations, then it is

a. impossible to test for equality of the three population proportions, because chi-square tests deal with only two populations.

b. possible to test for equality of three or more population proportions.

c. reasonable to test for equality of multiple population proportions using chi-square lower tail tests.

d. customary to use a t distribution to test for equality of the three population proportions.

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b

The table below gives beverage preferences for random samples of teens and adults.

	Teens	Adults	Total
Coffee	50	200	250
Tea	100	150	250
Soft Drink	200	200	400
Other	50	50	100
	400	600	1000

We are asked to test for independence between age (i.e., adult and teen) and drink preferences. The test statistic for this test of independence is

a. 0.

b. 62.5.

c. 82.5.

d. 8.4.

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b

The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.

Political Party	Support
Democrats	100
Republicans	120
Independents	80

We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. The number of degrees of freedom associated with this problem is

a. 299.

b. 300.

c. 2.

d. 3.

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c

The test for goodness of fit

a. is always a two-tailed test.

b. is always an upper tail test.

c. is always a lower tail test.

d. can be a lower or an upper tail test.

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b

Which function in Excel is used to perform a test of independence?

a. CHISQ.TEST

b. T.TEST

c. NORM.S.DIST

d. Z.TEST

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a

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

The calculated value for the test statistic equals

a. 0.

b. 2.

c. 1.67.

d. 6.

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b

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

The number of intervals or categories used to test the hypothesis for this problem is

a. 10.

b. 6.

c. 5.

d. 4.

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b

A manufacturer of carpentry screws claims that its production machine is very accurate and that the standard deviation of the length of all screws produced is .08 mm or less. A sample of 30 screws showed a standard deviation of .10. The test statistic to test the manufacturer's claim is _____.

a. 18.56

b. 19.2

c. 45.31

d. 23.2

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c

We are interested in testing to see if the variance of a population is less than 7. The correct null hypothesis is

a. σ2 ≥ 49.

b. σ < 49.

c. σ < 7.

d. σ2 ≥ 7.

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d

The symbol used for the variance of the sample is

a. s2.

b. σ.

c. σ2.

d. s.

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a

The value of F.05 with 8 numerator and 19 denominator degrees of freedom is

a. 2.48.

b. 2.58.

c. 2.96.

d. 3.63.

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a

Which of the following has an F distribution?

a.

b.

c.

d.

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b

A researcher would like to test the hypothesis that population B has a smaller variance than population A, using a 5% level of significance for the hypothesis test. What is the critical value from the F distribution table?

a. 2.39

b. 2.84

c. 2.22

d. 1.96

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c

The 95% confidence interval estimate of a population variance when a sample variance of 324 is obtained from a sample of 81 items is

a. 16.42 to 194.35.

b. 243.086 to 453.520.

c. 254.419 to 429.203.

d. 14.14 to 174.94.

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b

We are interested in testing whether the variance of a population is significantly more than 625. The null hypothesis for this test is

a. H0: σ2 ≤ 625.

b. H0: σ2 > 625.

c. H0: σ2 ≤ 25.

d. H0: σ2 ≥ 625.

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a

For a sample size of 21 at 95% confidence, the chi-square values needed for interval estimation are

a. 10.283 and 35.479.

b. 2.700 and 19.023.

c. 8.260 and 37.566.

d. 9.591 and 34.170.

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d

The producer of a certain medicine claims that their bottling equipment is very accurate and that the standard deviation of all their filled bottles is .1 ounces or less. A sample of 20 bottles showed a standard deviation of .11 ounces. The test statistic to test the claim is

a. 2.3.

b. 22.99.

c. 4.85.

d. 24.2.

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b

The critical value of F using α = .05 when there is a sample size of 21 for the sample with the smaller variance, and there is a sample size of 9 for the sample with the larger sample variance is

a. 2.10.

b. 2.45.

c. 2.94.

d. 2.37.

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b

The chi-square value for a one-tailed (lower tail) test when the level of significance is .1 and the sample size is 15 is

a. 23.685.

b. 7.790.

c. 21.064.

d. 6.571.

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b

Consider the following hypothesis problem.

n = 30	H0: σ2 = 500
s2 = 625	Ha: σ2 ≠ 500

The test statistic equals

a. 37.50.

b. 23.20.

c. 24.00.

d. 36.25.

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d

A sample of 41 observations yielded a sample standard deviation of 5. If we want to test H0: σ2 = 20, the test statistic is

a. 100.75.

b. 51.25.

c. 50.

d. 10.

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c

The value of F.05 with 8 numerator and 19 denominator degrees of freedom is

a. 2.48.

b. 2.96.

c. 3.63.

d. 2.58.

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a

χ2.975 = 8.231 indicates that

a. 2.5% of the chi-square values are greater than 8.231.

b. 97.5% of the chi-square values are greater than 8.231.

c. 5% of the chi-square values are equal to 8.231.

d. 97.5% of the chi-square values are less than 8.231.

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b

Consider the following sample information from Population A and Population B.

	Sample A	Sample B
n	24	16
s2	32	38

We want to test the hypothesis that the population variances are equal. The test statistic for this problem equals

a. 1.19.

b. 1.50.

c. .84.

d. .67.

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a

Given the sample information below, what test statistic should be used to determine whether the standard deviations are equal for two populations, prior to performing a hypothesis test for the equality of the population means?

a. t = 18.75, with degrees of freedom = 19

b. F = 1.58, with numerator degrees of freedom = 19 and denominator degrees of freedom = 29

c. F = 2.49, with numerator degrees of freedom = 29 and denominator degrees of freedom = 19

d. F = 0.40, with degrees of freedom = 19

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c

Consider the following hypothesis problem.

n = 23	s2 = 60	H0: σ2 ≤ 66
		Ha: σ2 > 66

The p-value is

a. between .05 and .10.

b. less than .025.

c. between .025 and .05.

d. greater than .10.

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d

The sampling distribution used when making inferences about a single population's variance is

a. a normal distribution.

b. a t distribution.

c. a chi-square distribution.

d. an F distribution.

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c

The value of F.01 with 9 numerator and 20 denominator degrees of freedom is

a. 2.91.

b. 2.94.

c. 2.39.

d. 3.46.

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d

Which of the following is not a property of a chi-square distribution?

a. χ2 is skewed to the right.

b. The number of degrees of freedom defines the shape of the distribution of χ2.

c. χ2 can have both positive and negative values.

d. All of these choices are properties of the χ2 distribution.

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c

A sample of 41 observations yielded a sample standard deviation of 5. If we want to test H0: σ2 = 20, the test statistic is

a. 10.

b. 51.25.

c. 50.

d. 100.75.

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c

Which of the following rejection rules is proper?

a. Reject H0 if p-value ≥ α/2.

b. Reject H0 if F ≥ Fα.

c. Reject H0 if F ≤ Fα/2.

d. Reject H0 if p-value ≤ Fα.

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b

In practice, the most frequently encountered hypothesis test about a population variance is a

a. one-tailed test, with rejection region in the lower tail.

b. two-tailed test, with equal-size rejection regions.

c. two-tailed test, with unequal-size rejection regions.

d. one-tailed test, with rejection region in the upper tail.

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d

What is the null hypothesis for testing whether the variance of a population differs from 2.5?

a.

b.

c.

d.

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b

The critical value of F using α = .05 when there is a sample size of 21 for the sample with the smaller variance, and there is a sample size of 9 for the sample with the larger sample variance is

a. 2.45.

b. 2.10.

c. 2.94.

d. 2.37.

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a

Consider the following hypothesis problem.

n = 30	H0: σ2 = 500
s2 = 625	Ha: σ2 ≠ 500

The test statistic equals

a. 24.00.

b. 23.20.

c. 37.50.

d. 36.25.

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d

What is the critical value of F for a one-tailed test at the α=.10 level, when there is a sample size of 8 for the sample with the smaller variance and a sample size of 11 for the sample with the larger sample variance?

a. 2.70

b. 2.41

c. 1.65

d. 3.64

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a

We are interested in testing to see if the variance of a population is less than 7. The correct null hypothesis is

a. σ2 ≥ 49.

b. σ2 ≥ 7.

c. σ < 7.

d. σ < 49.

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b

Which of the following has a chi-square distribution?

a. (n - 1)s/σ.

b. (n - 1)s2/σ2.

c. (n - 1)σ2/s2.

d. (n - 1)σ/s.

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b

Consider the following hypothesis problem.

n = 23	s2 = 60	H0: σ2 ≤ 66
		Ha: σ2 > 66

The p-value is

a. greater than .10.

b. between .05 and .10.

c. between .025 and .05.

d. less than .025.

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Solution

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a

The 95% confidence interval estimate of a population variance when a sample variance of 324 is obtained from a sample of 81 items is

a. 16.42 to 194.35.

b. 254.419 to 429.203.

c. 14.14 to 174.94.

d. 243.086 to 453.520.

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d

The value of F.01 with 9 numerator and 20 denominator degrees of freedom is

a. 2.91.

b. 3.46.

c. 2.39.

d. 2.94.

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b

To avoid the problem of not having access to tables of the F distribution when a one-tailed test is required and with F values given for the lower tail, let the

a. sample variance from the population with the smaller hypothesized variance be the numerator of the test statistic.

b. smaller sample variance be the numerator of the test statistic.

c. larger sample variance be the numerator of the test statistic.

d. sample variance from the population with the larger hypothesized variance be the numerator of the test statistic.

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a

The value of F.05 with 8 numerator and 19 denominator degrees of freedom is

a. 2.58.

b. 2.48.

c. 2.96.

d. 3.63.

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b

The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. At the .05 level of significance, the null hypothesis

a. should not be tested.

b. should not be rejected.

c. should be rejected.

d. should be revised.

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b

A manufacturer of carpentry screws claims that its production machine is very accurate and that the standard deviation of the length of all screws produced is .08 mm or less. A sample of 30 screws showed a standard deviation of .10. The test statistic to test the manufacturer's claim is _____.

a. 19.2

b. 45.31

c. 23.2

d. 18.56

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b

A sample of 21 observations yielded a sample variance of 16. If we want to test H0: σ2 = 16, the test statistic is

a. 50.

b. 5.

c. 21.

d. 20.

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d

A sample of 28 elements is selected to estimate a 95% confidence interval for the variance of the population. The chi-square values to be used for this interval estimation are

a. 15.308 and 44.461.

b. 11.808 and 49.645.

c. 16.151 and 40.113.

d. 14.573 and 43.195.

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d

The producer of a certain medicine claims that their bottling equipment is very accurate and that the standard deviation of all their filled bottles is .1 ounces or less. A sample of 20 bottles showed a standard deviation of .11 ounces. The test statistic to test the claim is

a. 2.3.

b. 4.85.

c. 22.99.

d. 24.2.

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c

A sample of 21 observations yielded a sample variance of 16. If we want to test H0: σ2 = 16, the test statistic is

a. 20.

b. 50.

c. 21.

d. 5.

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a

To avoid the problem of not having access to Tables of F distribution when F values are needed for the lower tail, the numerator of the test statistic for a two-tailed test should be the one with

a. the larger sample size.

b. the larger sample variance.

c. the smaller sample variance.

d. the smaller sample size.

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b

Consider the following sample information from Population A and Population B.

	Sample A	Sample B
n	24	16
s2	32	38

We want to test the hypothesis that the population variances are equal. The test statistic for this problem equals

a. 1.19.

b. 1.50.

c. .67.

d. .84.

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Solution

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a

In practice, the most frequently encountered hypothesis test about a population variance is a

a. one-tailed test, with rejection region in the upper tail.

b. one-tailed test, with rejection region in the lower tail.

c. two-tailed test, with unequal-size rejection regions.

d. two-tailed test, with equal-size rejection regions.

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a

A sample of 21 elements is selected to estimate a 90% confidence interval for the variance of the population. The chi-square value(s) to be used for this interval estimation is(are)

a. 12.443 and 28.412.

b. 10.851 and 31.410.

c. 31.410.

d. 12.443.

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b

Consider the following hypothesis problem.

n = 14	H0: σ2 ≤ 410
s = 20	Ha: σ2 > 410

The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the chi-square distribution table is(are)

a. 5.009 and 24.736.

b. 5.629 and 26.119.

c. 23.685.

d. 22.362.

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d

onsider the scenario where

The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the table is(are) _____.

a. 6.262 and 27.488

b. 27.488

c. 5.629 and 26.119

d. 5.629

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c

A sample of 60 items from population 1 has a sample variance of 8 while a sample of 40 items from population 2 has a sample variance of 10. If we want to test whether the variances of the two populations are equal, the test statistic will have a value of

a. 1.56.

b. .8.

c. 1.25.

d. 1.5.

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c

The manager of the service department of a local car dealership has noted that the service times of a sample of 30 new automobiles has a standard deviation of 6 minutes. A 95% confidence interval estimate for the standard deviation of the service times (in minutes) for all their new automobiles is

a. 4.778 to 8.066.

b. 22.833 to 65.059.

c. 16.047 to 45.722.

d. 2.93 to 6.31.

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a

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.

Freshmen	83
Sophomores	68
Juniors	85
Seniors	64

We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. The calculated value for the test statistic equals

a. 1.66.

b. .65.

c. .54.

d. 6.66.

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a

The owner of a car wash wants to see if the arrival rate of cars follows a Poisson distribution. In order to test the assumption of a Poisson distribution, a random sample of 150 ten-minute intervals was taken. You are given the following observed frequencies:

Number of Cars Arriving in a 10-Minute Interval	Frequency
0	3
1	10
2	15
3	23
4	30
5	24
6	20
7	13
8	8
9 or more	4
	150

The p-value is

a. between .05 and .1.

b. greater than .1.

c. between .025 and .05.

d. less than .01.

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b

Which of the following Chi-Square tests can be used to determine if a data set follows a Normal distribution?

a. Chi-Square Goodness of Fit

b. Chi Square Test of Association

c. Chi-Square Test of Equality of Three or More Population Proportions

d. Chi-Square Test of Homogeneity

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a

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.

Freshmen	83
Sophomores	68
Juniors	85
Seniors	64

We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. The expected number of freshmen is

a. 83.

b. 90.

c. 30.

d. 10.

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b

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

The calculated value for the test statistic equals

a. 6.

b. 2.

c. 1.67.

d. 0.

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b

The test for goodness of fit

a. is always an upper tail test.

b. is always a two-tailed test.

c. is always a lower tail test.

d. can be a lower or an upper tail test.

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a

The degrees of freedom for a table with 6 rows and 3 columns is

a. 10.

b. 18.

c. 15.

d. 6.

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a

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. This problem is an example of a

a. z test for proportions.

b. multinomial population.

c. Marascuilo procedure.

d. test for independence.

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b

The number of degrees of freedom associated with the chi-square distribution in a test of independence is

a. number of sample items minus 1.

b. number of populations minus 1.

c. number of populations minus number of estimated parameters minus 1.

d. number of rows minus 1 times number of columns minus 1.

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d

The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.

Political Party	Support
Democrats	100
Republicans	120
Independents	80

We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. The expected frequency for each group is

a. .333.

b. 50.

c. .50.

d. 100.

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d

The table below gives beverage preferences for random samples of teens and adults.

	Teens	Adults	Total
Coffee	50	200	250
Tea	100	150	250
Soft Drink	200	200	400
Other	50	50	100
	400	600	1000

We are asked to test for independence between age (i.e., adult and teen) and drink preferences. With a .05 level of significance, the critical value for the test is

a. 15.507.

b. 7.815.

c. 14.067.

d. 5.991.

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b

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.

Freshmen	83
Sophomores	68
Juniors	85
Seniors	64

We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. The expected number of freshmen is

a. 30.

b. 83.

c. 90.

d. 10.

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c

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

The calculated value for the test statistic equals

a. 1.67.

b. 2.

c. 6.

d. 0.

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b

In order not to violate the requirements necessary to use the chi-square distribution for testing equality of three or more population proportions, each expected frequency in a goodness of fit test must be

a. no more than 5.

b. at least 5.

c. less than 2.

d. at least 10.

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b

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.

Do you support capital punishment?	Number of individuals
Yes	40
No	60
No Opinion	50

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The expected frequency for each group is

a. .333.

b. .50.

c. 1/3.

d. 50.

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d

If the sample size is n = 75, what are the degrees of freedom for the appropriate chi-square distribution when testing for independence of two variables each with three categories?

a. 74

b. 4

c. 2

d. 69

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c

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals

a. 7.815.

b. 5.991.

c. 7.378.

d. 9.348.

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Solution

Correct Response

b

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.

Freshmen	83
Sophomores	68
Juniors	85
Seniors	64

We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. At a .05 level of significance, the null hypothesis

a. was designed wrong.

b. should not be rejected.

c. cannot be tested.

d. should be rejected.

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b

The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.

Political Party	Support
Democrats	100
Republicans	120
Independents	80

We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. The expected frequency for each group is

a. .333.

b. 50.

c. 100.

d. .50.

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c

A random sample of 550 physicians was selected and classified according to the type of practice they operate and whether or not their practice was full (meaning, not accepting new patients). The counts are given in the table below.

The test statistic for a test of independence is χ2 = 34.893. What is the p-value for this test?

a. p = .004

b. p = .0025

c. p = .05

d. p < .0001

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d

An important application of the chi-square distribution is

a. making inferences about a single population variance.

b. testing for the independence of two categorical variables.

c. testing for goodness of fit.

d. All of these alternatives are correct.

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d

How many degrees of freedom does the chi-square test statistic for a goodness of fit have when there are 10 categories?

a. 7

b. 62

c. 9

d. 74

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c

The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.

Political Party	Support
Democrats	100
Republicans	120
Independents	80

We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. The expected frequency for each group is

a. .50.

b. .333.

c. 100.

d. 50.

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Solution

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c

The table below gives beverage preferences for random samples of teens and adults.

	Teens	Adults	Total
Coffee	50	200	250
Tea	100	150	250
Soft Drink	200	200	400
Other	50	50	100
	400	600	1000

We are asked to test for independence between age (i.e., adult and teen) and drink preferences. The expected number of adults who prefer coffee is

a. 150.

b. .25.

c. .33.

d. 200.

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a

The table below gives beverage preferences for random samples of teens and adults.

	Teens	Adults	Total
Coffee	50	200	250
Tea	100	150	250
Soft Drink	200	200	400
Other	50	50	100
	400	600	1000

We are asked to test for independence between age (i.e., adult and teen) and drink preferences. The test statistic for this test of independence is

a. 0.

b. 8.4.

c. 82.5.

d. 62.5.

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Solution

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d

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. This problem is an example of a

a. z test for proportions.

b. test for independence.

c. Marascuilo procedure.

d. multinomial population.

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d

The degrees of freedom for a data table with 10 rows and 11 columns is

a. 90.

b. 21.

c. 100.

d. 110.

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a

If there are three or more populations, then it is

a. impossible to test for equality of the three population proportions, because chi-square tests deal with only two populations.

b. customary to use a t distribution to test for equality of the three population proportions.

c. reasonable to test for equality of multiple population proportions using chi-square lower tail tests.

d. possible to test for equality of three or more population proportions.

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d

The owner of a car wash wants to see if the arrival rate of cars follows a Poisson distribution. In order to test the assumption of a Poisson distribution, a random sample of 150 ten-minute intervals was taken. You are given the following observed frequencies:

Number of Cars Arriving in a 10-Minute Interval	Frequency
0	3
1	10
2	15
3	23
4	30
5	24
6	20
7	13
8	8
9 or more	4
	150

The calculated value for the test statistic equals

a. 1.72.

b. 3.11.

c. .18.

d. 2.89.

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Solution

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d

The owner of a car wash wants to see if the arrival rate of cars follows a Poisson distribution. In order to test the assumption of a Poisson distribution, a random sample of 150 ten-minute intervals was taken. You are given the following observed frequencies:

Number of Cars Arriving in a 10-Minute Interval	Frequency
0	3
1	10
2	15
3	23
4	30
5	24
6	20
7	13
8	8
9 or more	4
	150

The p-value is

a. less than .01.

b. between .025 and .05.

c. greater than .1.

d. between .05 and .1.

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c

If there are three or more populations, then it is

a. possible to test for equality of three or more population proportions.

b. impossible to test for equality of the three population proportions, because chi-square tests deal with only two populations.

c. customary to use a t distribution to test for equality of the three population proportions.

d. reasonable to test for equality of multiple population proportions using chi-square lower tail tests.

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a

The degrees of freedom for a table with 6 rows and 3 columns is

a. 10.

b. 6.

c. 15.

d. 18.

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a

In order not to violate the requirements necessary to use the chi-square distribution for testing equality of three or more population proportions, each expected frequency in a goodness of fit test must be

a. at least 5.

b. no more than 5.

c. at least 10.

d. less than 2.

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Solution

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a

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.

Do you support capital punishment?	Number of individuals
Yes	40
No	60
No Opinion	50

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The calculated value for the test statistic equals

a. 2.

b. 20.

c. -2.

d. 4.

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d

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.

Freshmen	83
Sophomores	68
Juniors	85
Seniors	64

We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. The p-value is

a. between .05 and .1.

b. less than .005.

c. between .025 and .05.

d. greater than .1.

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d

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

At the 5% level of significance, the conclusion of the test is that the

a. data does not follow a normal distribution.

b. sample data is incorrect.

c. null hypothesis cannot be rejected.

d. sample data has no probability distribution.

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c

Which function in Excel is used to perform a test of independence?

a. Z.TEST

b. CHISQ.TEST

c. T.TEST

d. NORM.S.DIST

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Solution

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b

A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a

a. probability test.

b. comparison test.

c. goodness of fit test.

d. normality test.

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Solution

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c

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. This problem is an example of a

a. multinomial population.

b. test for independence.

c. Marascuilo procedure.

d. z test for proportions.

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a

The number of categorical outcomes per trial for a multinomial probability distribution is

a. four or more.

b. two or more.

c. three or more.

d. five or more.

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c

If there are three or more populations, then it is

a. reasonable to test for equality of multiple population proportions using chi-square lower tail tests.

b. impossible to test for equality of the three population proportions, because chi-square tests deal with only two populations.

c. possible to test for equality of three or more population proportions.

d. customary to use a t distribution to test for equality of the three population proportions.

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c

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.

Do you support capital punishment?	Number of individuals
Yes	40
No	60
No Opinion	50

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The expected frequency for each group is

a. 1/3.

b. .50.

c. 50.

d. .333.

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c

The properties of a multinomial experiment include all of the following except

a. the experiment consists of a sequence of n identical trials.

b. the probability of each outcome can change from trial to trial.

c. the trials are independent.

d. three or more outcomes are possible on each trial.

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b

In order not to violate the requirements necessary to use the chi-square distribution for testing equality of three or more population proportions, each expected frequency in a goodness of fit test must be

a. less than 2.

b. at least 10.

c. no more than 5.

d. at least 5.

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d

A random sample of 100 high school students was surveyed regarding their favorite subject. The following counts were obtained:

The researcher conducted a test to determine whether the proportion of students was equal for all four subjects. What is the value of the test statistic?

a. 25

b. 6

c. 0

d. –4

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b

The test statistic for goodness of fit has a chi-square distribution with k - 1 degrees of freedom provided that the expected frequencies for all categories are

a. 5 or more.

b. 10 or more.

c. 2k.

d. k or more.

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Solution

Correct Response

a

The table below gives beverage preferences for random samples of teens and adults.

	Teens	Adults	Total
Coffee	50	200	250
Tea	100	150	250
Soft Drink	200	200	400
Other	50	50	100
	400	600	1000

We are asked to test for independence between age (i.e., adult and teen) and drink preferences. With a .05 level of significance, the critical value for the test is

a. 5.991.

b. 15.507.

c. 14.067.

d. 7.815.

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Solution

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d

Marascuilo procedure is used to test for a significant difference between pairs of population

a. proportions.

b. means.

c. variances.

d. standard deviations.

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Solution

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a

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.

Do you support capital punishment?	Number of individuals
Yes	40
No	60
No Opinion	50

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The conclusion of the test at the 5% level of significance is that the

a. Marascuilo procedure is more applicable.

b. distribution is uniform.

c. distribution might have been normal.

d. null hypothesis cannot be rejected.

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Solution

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b

The owner of a car wash wants to see if the arrival rate of cars follows a Poisson distribution. In order to test the assumption of a Poisson distribution, a random sample of 150 ten-minute intervals was taken. You are given the following observed frequencies:

Number of Cars Arriving in a 10-Minute Interval	Frequency
0	3
1	10
2	15
3	23
4	30
5	24
6	20
7	13
8	8
9 or more	4
	150

The p-value is

a. between .05 and .1.

b. between .025 and .05.

c. less than .01.

d. greater than .1.

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Solution

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d

Given the sample information below, what test statistic should be used to determine whether the standard deviations are equal for two populations, prior to performing a hypothesis test for the equality of the population means?

a. t = 18.75, with degrees of freedom = 19

b. F = 0.40, with degrees of freedom = 19

c. F = 1.58, with numerator degrees of freedom = 19 and denominator degrees of freedom = 29

d. F = 2.49, with numerator degrees of freedom = 29 and denominator degrees of freedom = 19

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d

A sample of 41 observations yielded a sample standard deviation of 5. If we want to test H0: σ2 = 20, the test statistic is

a. 50.

b. 100.75.

c. 51.25.

d. 10.

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Solution

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a

In practice, the most frequently encountered hypothesis test about a population variance is a

a. one-tailed test, with rejection region in the upper tail.

b. two-tailed test, with equal-size rejection regions.

c. two-tailed test, with unequal-size rejection regions.

d. one-tailed test, with rejection region in the lower tail.

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a

A sample of 21 observations yielded a sample variance of 16. If we want to test H0: σ2 = 16, the test statistic is

a. 21.

b. 5.

c. 50.

d. 20.

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d

Consider the following hypothesis problem.

n = 14	H0: σ2 ≤ 410
s = 20	Ha: σ2 > 410

At the 5% level of significance, the null hypothesis

a. should not be rejected.

b. should be revised.

c. should be rejected.

d. should not be tested.

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Solution

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a

The sampling distribution of the ratio of independent sample variances extracted from two normal populations with equal variances is the

a. chi-square distribution.

b. normal distribution.

c. F distribution.

d. t distribution.

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c

The sampling distribution of the ratio of independent sample variances extracted from two normal populations with equal variances is the

a. chi-square distribution.

b. normal distribution.

c. F distribution.

d. t distribution.

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c

We are interested in testing whether the variance of a population is significantly more than 625. The null hypothesis for this test is

a. H0: σ2 ≥ 625.

b. H0: σ2 ≤ 625.

c. H0: σ2 ≤ 25.

d. H0: σ2 > 625.

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b

Which of the following has an F distribution?

a. s1/s2.

b. (n - 1)s1/s2.

c. (n - 1)s/σ.

d. s12/s22.

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d

Which of the following has an F distribution?

a. s1/s2.

b. (n - 1)s1/s2.

c. (n - 1)s/σ.

d. s12/s22.

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Solution

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d

The table below gives beverage preferences for random samples of teens and adults.

	Teens	Adults	Total
Coffee	50	200	250
Tea	100	150	250
Soft Drink	200	200	400
Other	50	50	100
	400	600	1000

We are asked to test for independence between age (i.e., adult and teen) and drink preferences. The expected number of adults who prefer coffee is

a. .33.

b. 150.

c. .25.

d. 200.

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Solution

Correct Response

b

A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a

a. goodness of fit test.

b. normality test.

c. comparison test.

d. probability test.

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Solution

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a

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.

Freshmen	83
Sophomores	68
Juniors	85
Seniors	64

We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. The calculated value for the test statistic equals

a. .54.

b. 6.66.

c. .65.

d. 1.66.

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Solution

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d

The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.

Political Party	Support
Democrats	100
Republicans	120
Independents	80

We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. The number of degrees of freedom associated with this problem is

a. 299.

b. 300.

c. 3.

d. 2.

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d

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. The expected frequency for the Business College is

a. .3.

b. 90.

c. .35.

d. 105.

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Solution

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d

Which function in Excel is used to perform a test of independence?

a. T.TEST

b. Z.TEST

c. NORM.S.DIST

d. CHISQ.TEST

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Solution

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d

An important application of the chi-square distribution is

a. making inferences about a single population variance.

b. testing for goodness of fit.

c. testing for the independence of two categorical variables.

d. All of these alternatives are correct.

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d

How many degrees of freedom does the chi-square test statistic for a goodness of fit have when there are 10 categories?

a. 62

b. 7

c. 9

d. 74

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c

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.

Freshmen	83
Sophomores	68
Juniors	85
Seniors	64

We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. The p-value is

a. between .025 and .05.

b. less than .005.

c. greater than .1.

d. between .05 and .1.

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c

The 99% confidence interval estimate for a population variance when a sample standard deviation of 12 is obtained from a sample of 10 items is

a. 4.589 to 62.253.

b. 54.941 to 746.974.

c. 62.042 to 562.895.

d. 46.538 to 422.171.

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b

A sample of 41 observations yielded a sample standard deviation of 5. If we want to test H0: σ2 = 20, the test statistic is

a. 50.

b. 10.

c. 51.25.

d. 100.75.

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Solution

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a

The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. At the .05 level of significance, the null hypothesis

a. should be revised.

b. should not be rejected.

c. should be rejected.

d. should not be tested.

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Solution

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b

We are interested in testing whether the variance of a population is significantly less than 1.44. The null hypothesis for this test is

a. H0: σ2 < 1.44.

b. H0: σ < 1.20.

c. H0: σ2 ≥ 1.44.

d. H0: s2 ≥ 1.44.

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c

The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. The p-value for this test is

a. less than .10.

b. zero.

c. .05.

d. greater than .10.

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Solution

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d

The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. The p-value for this test is

a. less than .10.

b. zero.

c. .05.

d. greater than .10.

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Solution

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d

Consider the following sample information from Population A and Population B.

	Sample A	Sample B
n	24	16
s2	32	38

We want to test the hypothesis that the population variances are equal. The null hypothesis is to be tested at the 10% level of significance. The critical value from the F distribution table is

a. 2.11.

b. 2.29.

c. 2.13.

d. 2.24.

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c

Which of the following rejection rules is proper?

a. Reject H0 if p-value ≥ α/2.

b. Reject H0 if F ≤ Fα/2.

c. Reject H0 if p-value ≤ Fα.

d. Reject H0 if F ≥ Fα.

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d

Which of the following rejection rules is proper?

a. Reject H0 if p-value ≥ α/2.

b. Reject H0 if F ≤ Fα/2.

c. Reject H0 if p-value ≤ Fα.

d. Reject H0 if F ≥ Fα.

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d

Which of the following rejection rules is proper?

a. Reject H0 if p-value ≥ α/2.

b. Reject H0 if F ≤ Fα/2.

c. Reject H0 if p-value ≤ Fα.

d. Reject H0 if F ≥ Fα.

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d

Which of the following is not a property of a chi-square distribution?

a. χ2 is skewed to the right.

b. The number of degrees of freedom defines the shape of the distribution of χ2.

c. χ2 can have both positive and negative values.

d. All of these choices are properties of the χ2 distribution.

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c

χ2.975 = 8.231 indicates that

a. 97.5% of the chi-square values are less than 8.231.

b. 5% of the chi-square values are equal to 8.231.

c. 97.5% of the chi-square values are greater than 8.231.

d. 2.5% of the chi-square values are greater than 8.231.

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c

The 95% confidence interval estimate of a population variance when a sample variance of 324 is obtained from a sample of 81 items is

a. 254.419 to 429.203.

b. 16.42 to 194.35.

c. 14.14 to 174.94.

d. 243.086 to 453.520.

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d

We are interested in testing to see if the variance of a population is less than 7. The correct null hypothesis is

a. σ2 ≥ 7.

b. σ < 7.

c. σ < 49.

d. σ2 ≥ 49.

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a

The chi-square value for a one-tailed (upper tail) hypothesis test at a 5% level of significance and a sample size of 25 is

a. 36.415.

b. 39.364.

c. 37.652.

d. 33.196.

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Solution

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a

There is a .90 probability of obtaining a χ2 value such that

a. χ2.90 < χ2 < χ2.10

b. χ2.05 < χ2 < χ2.95

c. χ2.10 ≤ χ2 ≤ χ2.90

d. χ2.95 ≤ χ2 ≤ χ2.05

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Solution

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d

Consider the following sample information from Population A and Population B.

	Sample A	Sample B
n	24	16
s2	32	38

We want to test the hypothesis that the population variances are equal. At the 10% level of significance, the null hypothesis

a. should be revised.

b. should be rejected.

c. should not be tested.

d. should not be rejected.

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Solution

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d

Consider the following hypothesis problem.

n = 14	H0: σ2 ≤ 410
s = 20	Ha: σ2 > 410

The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the chi-square distribution table is(are)

a. 23.685.

b. 22.362.

c. 5.009 and 24.736.

d. 5.629 and 26.119.

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Solution

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b

Consider the following hypothesis problem.

n = 14	H0: σ2 ≤ 410
s = 20	Ha: σ2 > 410

The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the chi-square distribution table is(are)

a. 23.685.

b. 22.362.

c. 5.009 and 24.736.

d. 5.629 and 26.119.

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Solution

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b

Consider the following hypothesis problem.

n = 14	H0: σ2 ≤ 410
s = 20	Ha: σ2 > 410

The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the chi-square distribution table is(are)

a. 23.685.

b. 22.362.

c. 5.009 and 24.736.

d. 5.629 and 26.119.

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Solution

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b

A sample of 21 observations yielded a sample variance of 16. If we want to test H0: σ2 = 16, the test statistic is

a. 5.

b. 50.

c. 21.

d. 20.

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Solution

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d

The manager of the service department of a local car dealership has noted that the service times of a sample of 15 new automobiles has a standard deviation of 4 minutes. A 95% confidence interval estimate for the variance of service times for all their new automobiles is

a. 8.576 to 39.794.

b. 2.144 to 9.948.

c. 2.93 to 6.31.

d. 9.46 to 34.09.

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Solution

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a

We are interested in testing whether the variance of a population is significantly less than 1.44. The null hypothesis for this test is

a. H0: σ < 1.20.

b. H0: s2 ≥ 1.44.

c. H0: σ2 < 1.44.

d. H0: σ2 ≥ 1.44.

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Solution

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d

The χ 2 value for a one-tailed (upper tail) hypothesis test at 95% confidence and a sample size of 20 is _____.

a. 31.410

b. 10.851

c. 10.117

d. 30.144

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Solution

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d

Consider the following hypothesis problem.

n = 30	H0: σ2 = 500
s2 = 625	Ha: σ2 ≠ 500

At the 5% level of significance, the null hypothesis

a. should not be tested.

b. should be rejected.

c. should not be rejected.

d. should be revised.

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c

What is the critical value of F for a one-tailed test at the α=.10 level, when there is a sample size of 8 for the sample with the smaller variance and a sample size of 11 for the sample with the larger sample variance?

a. 1.65

b. 3.64

c. 2.70

d. 2.41

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c

What is the null hypothesis for testing whether the variance of a population differs from 2.5?

a.

b.

c.

d.

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Solution

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a

What is the null hypothesis for testing whether the variance of a population differs from 2.5?

a.

b.

c.

d.

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Solution

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a

What is the null hypothesis for testing whether the variance of a population differs from 2.5?

a.

b.

c.

d.

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Solution

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a

What is the null hypothesis for testing whether the variance of a population differs from 2.5?

a.

b.

c.

d.

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a

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

At the 5% level of significance, the conclusion of the test is that the

a. sample data has no probability distribution.

b. null hypothesis cannot be rejected.

c. data does not follow a normal distribution.

d. sample data is incorrect.

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b

A random sample of 550 physicians was selected and classified according to the type of practice they operate and whether or not their practice was full (meaning, not accepting new patients). The counts are given in the table below.

The test statistic for a test of independence is χ2 = 34.893. What is the p-value for this test?

a. p = .05

b. p = .0025

c. p < .0001

d. p = .004

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c

A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a

a. comparison test.

b. normality test.

c. goodness of fit test.

d. probability test.

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c

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

The calculated value for the test statistic equals

a. 2.

b. 6.

c. 1.67.

d. 0.

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a

How many degrees of freedom does the chi-square test statistic for a goodness of fit have when there are 10 categories?

a. 62

b. 9

c. 74

d. 7

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b

A population where each of its element is assigned to one and only one of several classes or categories is a

a. normal population.

b. multinomial population.

c. binomial population.

d. Poisson population.

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b

The owner of a car wash wants to see if the arrival rate of cars follows a Poisson distribution. In order to test the assumption of a Poisson distribution, a random sample of 150 ten-minute intervals was taken. You are given the following observed frequencies:

Number of Cars Arriving in a 10-Minute Interval	Frequency
0	3
1	10
2	15
3	23
4	30
5	24
6	20
7	13
8	8
9 or more	4
	150

The calculated value for the test statistic equals

a. .18.

b. 2.89.

c. 3.11.

d. 1.72.

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b

If there are three or more populations, then it is

a. possible to test for equality of three or more population proportions.

b. impossible to test for equality of the three population proportions, because chi-square tests deal with only two populations.

c. reasonable to test for equality of multiple population proportions using chi-square lower tail tests.

d. customary to use a t distribution to test for equality of the three population proportions.

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a

The table below gives beverage preferences for random samples of teens and adults.

	Teens	Adults	Total
Coffee	50	200	250
Tea	100	150	250
Soft Drink	200	200	400
Other	50	50	100
	400	600	1000

We are asked to test for independence between age (i.e., adult and teen) and drink preferences. The expected number of adults who prefer coffee is

a. 200.

b. .25.

c. .33.

d. 150.

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d

The table below gives beverage preferences for random samples of teens and adults.

	Teens	Adults	Total
Coffee	50	200	250
Tea	100	150	250
Soft Drink	200	200	400
Other	50	50	100
	400	600	1000

We are asked to test for independence between age (i.e., adult and teen) and drink preferences. The expected number of adults who prefer coffee is

a. 200.

b. .25.

c. .33.

d. 150.

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d

Two hundred randomly selected people were asked to state their primary source for news about current events: (1) Television, (2) Radio, (3) Internet, or (4) Other. We wish to determine whether the percent distribution of responses is 10%, 30%, 50%, and 10% for news sources 1 through 4, respectively. What is the null hypothesis?

a. H0: the proportions are not all equal.

b. H0: p1= .10, p2 = .30, p3 = .50, p4 = .10

c. H0: p1 = .25, p2 = .25, p3 = .25, p4 = .25

d. H0: p = .50

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b

The test for goodness of fit

a. can be a lower or an upper tail test.

b. is always a lower tail test.

c. is always an upper tail test.

d. is always a two-tailed test.

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c

A random sample of 100 high school students was surveyed regarding their favorite subject. The following counts were obtained:

The researcher conducted a test to determine whether the proportion of students was equal for all four subjects. What is the value of the test statistic?

a. 0

b. –4

c. 25

d. 6

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d

If the sample size is n = 75, what are the degrees of freedom for the appropriate chi-square distribution when testing for independence of two variables each with three categories?

a. 74

b. 2

c. 4

d. 69

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b

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.

Freshmen	83
Sophomores	68
Juniors	85
Seniors	64

We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. At a .05 level of significance, the null hypothesis

a. should not be rejected.

b. should be rejected.

c. was designed wrong.

d. cannot be tested.

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a

The number of categorical outcomes per trial for a multinomial probability distribution is

a. three or more.

b. two or more.

c. five or more.

d. four or more.

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a

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals

a. 9.348.

b. 7.378.

c. 7.815.

d. 5.991.

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d

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. The calculated value for the test statistic equals

a. .01.

b. .75.

c. 4.38.

d. 4.29.

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d

The properties of a multinomial experiment include all of the following except

a. the experiment consists of a sequence of n identical trials.

b. the trials are independent.

c. three or more outcomes are possible on each trial.

d. the probability of each outcome can change from trial to trial.

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d

The properties of a multinomial experiment include all of the following except

a. the experiment consists of a sequence of n identical trials.

b. the trials are independent.

c. three or more outcomes are possible on each trial.

d. the probability of each outcome can change from trial to trial.

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d

The properties of a multinomial experiment include all of the following except

a. the experiment consists of a sequence of n identical trials.

b. the trials are independent.

c. three or more outcomes are possible on each trial.

d. the probability of each outcome can change from trial to trial.

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d

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. The expected frequency for the Business College is

a. 105.

b. 90.

c. .3.

d. .35.

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a

How many degrees of freedom does the chi-square test statistic for a goodness of fit have when there are 10 categories?

a. 62

b. 74

c. 7

d. 9

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d

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

The number of intervals or categories used to test the hypothesis for this problem is

a. 10.

b. 6.

c. 5.

d. 4.

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b

The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.

Political Party	Support
Democrats	100
Republicans	120
Independents	80

We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. The calculated value for the test statistic equals

a. 8.

b. 0.

c. 2.

d. 4.

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a

The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.

Political Party	Support
Democrats	100
Republicans	120
Independents	80

We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. The expected frequency for each group is

a. .333.

b. .50.

c. 50.

d. 100.

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d

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.

Do you support capital punishment?	Number of individuals
Yes	40
No	60
No Opinion	50

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The conclusion of the test at the 5% level of significance is that the

a. distribution might have been normal.

b. null hypothesis cannot be rejected.

c. Marascuilo procedure is more applicable.

d. distribution is uniform.

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d

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.

Do you support capital punishment?	Number of individuals
Yes	40
No	60
No Opinion	50

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The p-value is

a. less than .01.

b. between .05 and .1.

c. between .01 and .05.

d. larger than .1.

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d

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.

Do you support capital punishment?	Number of individuals
Yes	40
No	60
No Opinion	50

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The p-value is

a. less than .01.

b. between .05 and .1.

c. between .01 and .05.

d. larger than .1.

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d

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.

Do you support capital punishment?	Number of individuals
Yes	40
No	60
No Opinion	50

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The p-value is

a. less than .01.

b. between .05 and .1.

c. between .01 and .05.

d. larger than .1.

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d