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Use
two-step procedure to select a simple random sample of EAI
employees. Click
on the datafile logo to reference the data.
The
input in the box below will not be graded, but may be reviewed and considered
by your instructor.
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According to Wine-Searcher, wine critics generally
use a wine-scoring scale to communicate their opinions on the relative quality
of wines. Wine scores range from to , with a score
of indicating a great wine, indicating an outstanding
wine, indicating a very good wine, indicating a good
wine, indicating a mediocre wine, and below indicating
that the wine is not recommended. Random ratings of a pinot noir recently
produced by a newly established vineyard in follow:
Excel File: data07-11.xlsx
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a. Develop
a point estimate of mean wine score for this pinot noir (to decimals).
b. Develop
a point estimate of the standard deviation for wine scores received by this
pinot noir (to decimals).
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In ,
the Pew Internet & American Life Project asked teens
aged to several questions about their attitudes toward
social media. The results showed that say social media makes them
feel more connected to what is going on in their friends'
lives; say social media helps them interact with a more diverse
group of people; and feel pressure to post content that will get a
lot of likes and comments. Round
your answers to four decimal places. a. Develop a point estimate of the proportion of teens
aged to who say social media makes them feel more
connected to what is going on in their friends' lives. b. Develop a point estimate of the proportion of teens
aged to who say social media helps them interact with a
more diverse group of people. c. Develop a point estimate of the proportion of teens
aged to who feel pressure to post content that will get
a lot of likes and comments.
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The
CPA Practice Advisor reports that the mean preparation fee
for federal income tax returns was . Use this price as the
population mean and assume the population standard deviation of preparation
fees is . Use z-table. Round
your answers to four decimal places. a. What is the probability that the mean price for a sample
of federal income tax returns is within of the
population mean? b. What is the probability that the mean price for a sample
of federal income tax returns is within of the
population mean? c. What is the probability that the mean price for a sample
of federal income tax returns is within of the
population mean? d. Which, if any, of the sample sizes in parts (a), (b), and (c) would
you recommend to have at least a probability that the sample mean
is within of the population mean?
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The
Food Marketing Institute shows that of households spend more
than per week on groceries. Assume the population proportion
is and a simple random sample of households will be
selected from the population. Use the z-table. a. Show the sampling distribution of , the sample proportion
of households spending more than per week on groceries. (to decimals) (to decimals) b. What is the probability that the sample proportion will be within of
the population proportion (to decimals)? c. Answer part (b) for a sample of households
(to decimals).
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A
simple random sample of items resulted in a sample mean of .
The population standard deviation is . a. Compute the confidence interval for the population
mean. Round your answers to one decimal place. b. Assume that the same sample mean was obtained from a sample
of items. Provide a confidence interval for the
population mean. Round your answers to two decimal places. c. What is the effect of a larger sample size on the interval estimate? Larger
sample provides a margin
of error.
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For
a t distribution with degrees of freedom, find
the area, or probability, in each region. a. To the right of (to 3 decimals) b. To the left of (to 2 decimals) c. To the left of (to 2 decimals) d. To the right of (to 2 decimals) e. Between and (to 2 decimals) f. Between and (to 2 decimals)
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Customers
arrive at a movie theater at the advertised movie time only to find that they
have to sit through several previews and prepreview ads before the movie
starts. Many complain that the time devoted to previews is too long. A
preliminary sample conducted by The Wall Street Journal showed
that the standard deviation of the amount of time devoted to previews was 4
minutes. Use that as a planning value for the standard deviation in answering
the following questions. Round your answer to next whole number. a. If we want to estimate the population mean time for previews at movie
theaters with a margin of error of seconds, what sample size
should be used? Assume confidence. b. If we want to estimate the population mean time for previews at movie
theaters with a margin of error of minute, what sample size should
be used? Assume confidence.
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Fewer
young people are driving. In , of people
under years old who were eligible had a driver's license.
Bloomberg reported that percentage had dropped to in .
Suppose these results are based on a random sample of people
under years old who were eligible to have a driver's license
in and again in . a. At confidence, what is the margin of error and the interval
estimate of the number of eligible people under years old who had
a driver's license in ? Margin
of error (to four decimal places) Interval
estimate to (to four decimal places) b. At confidence, what is the margin of error and the interval
estimate of the number of eligible people under years old who had
a driver's license in ? Margin
of error (to four decimal places) Interval
estimate to (to four decimal places) c. Is the margin of error the same in parts (a) and (b)? Why,
or why not?
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The
Centers for Disease Control and Prevention (CDC) defines a healthy sleep
duration to be at least seven hours per day. The CDC reports that the
percentage of people who report a healthy sleep duration varies by marital
status. The CDC also reports that in , of those who are
married report a healthy sleep duration; of those who have never
been married report a healthy sleep duration; and of those who are
divorced, widowed, or separated report a healthy sleep duration. The
file SleepHabits contains sample data on the sleeping habits
of people who have never been married that are consistent with the CDC’s
findings. Use these data to answer the following questions. Click on the
datafile logo to reference the data.
a. Develop a point estimate and a confidence interval for the
proportion of those who have never been married who report a healthy sleep
duration.
b. Develop a point estimate and a confidence interval for the
mean number of hours of sleep for those who have never been married.
c. For those who have never been married, estimate the number of
hours of sleep per day for those who report a healthy sleep duration
(to decimals).
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The
National Center for Education Statistics reported that of college
students work to pay for tuition and living expenses. Assume that a sample
of college students was used in the study. a. Provide a confidence interval for the population
proportion of college students who work to pay for tuition and living
expenses. (to decimals) , b. Provide a confidence interval for the population
proportion of college students who work to pay for tuition and living
expenses. (to decimals) , c. What happens to the margin of error as the confidence is
increased from to ? The
margin of error becomes
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The
manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill
for a weekend is or less. A member of the hotel's accounting staff
noticed that the total charges for guest bills have been increasing in recent
months. The accountant will use a sample of future weekend guest bills to
test the manager's claim. a. Which form of the hypotheses should be used to test the
manager's claim? b. When cannot be rejected, can we conclude that the
manager's claim is wrong? c. When can be rejected, can we conclude that the
manager's claim is wrong?
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A
production line operation is designed to fill cartons with laundry detergent
to a mean weight of ounces. A sample of cartons is periodically
selected and weighed to determine whether underfilling or overfilling is
occurring. If the sample data lead to a conclusion of underfilling or
overfilling, the production line will be shut down and adjusted to obtain
proper filling. a. Formulate the null and alternative hypotheses that will help in
deciding whether to shut down and adjust the production line. b. Comment on the conclusion when cannot be rejected. Is
there evidence that the production line is not operating properly? c. Comment on the conclusion when can be rejected. Can
we conclude that overfilling or underfilling exists?
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Carpetland
salespersons average per week in sales. Steve Contois, the firm's
vice president, proposes a compensation plan with new selling incentives.
Steve hopes that the results of a trial selling period will enable him to
conclude that the compensation plan increases the average sales per
salesperson. a. Develop the appropriate null and alternative hypotheses. b. What is the Type I error in this situation? In
this situation, a Type I error would occur if it was concluded that the new
compensation plan provides a population mean weekly sales when
in fact it does not. What
are the consequences of making this error? c. What is the Type II error in this situation? In
this situation, a Type II error would occur if it was concluded that the new
compensation plan provides a population mean weekly sales when
in fact it does not. What
are the consequences of making this error?
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Consider
the following hypothesis test: : : A
sample of is used and the population standard deviation is .
Use the critical value approach to state your conclusion for each of the
following sample results. Use . Note: In the following questions, if the correct option is
"Reject " select "option 1" . If "Do not
reject " is correct, then select "option 2". a. b. c.
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TextRequest
reports that adults years old send and receive texts
every day. Suppose we take a sample of year olds to see if their
mean number of daily texts differs from the mean for year olds
reported by TextRequest. a. Select the null hypothesis we should use to test whether the population
mean daily number of texts for year olds differs from the
population daily mean number of texts for year olds. 1. : 2. : 3. : Select
the alternative hypothesis we should use to test whether the population mean
daily number of texts for year olds differs from the population
daily mean number of texts for year olds. 1. : 2. : 3. : b. Suppose a sample of thirty year olds showed a sample mean
of texts per day. Assume a population standard deviation
of texts per day and compute the -value. Round your answer to
four decimal places. c. With as the level of significance, what is your conclusion? .
We conclude
that the population mean daily texts for year olds differs
significantly from the population mean of daily texts
for year olds. d. Repeat the preceding hypothesis test using the critical value
approach. The
critical value(s) is(are) . Can
it be concluded that the population mean differs from ?
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According
to the IRS, taxpayers calling the IRS in waited minutes
on average for an IRS telephone assister to answer. Do callers who use the
IRS help line early in the day have a shorter wait? Suppose a sample
of callers who placed their calls to the IRS in the
first minutes that the line is open during the day have a mean
waiting time of minutes before an IRS telephone assister answers.
Based on data from past years, you decide that it is reasonable to assume
that the standard deviation of waiting times is minutes. Using
these sample results, can you conclude that the waiting time for calls placed
during the first minutes the IRS help line is open each day is
significantly less than the overall mean waiting time of minutes?
Use . State
the hypotheses. What
is the -value (to decimals)? Can
you conclude that callers who use the IRS help-line early in the day have a
shorter wait?
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Consider
the following hypothesis test: : : A
sample of provided a sample mean and a sample standard
deviation . a. Compute the value of the test statistic
(to decimals). b. Use the distribution table (Table 2 in Appendix B) to compute a range for the -value. c. At , what is your conclusion? . d. What is the rejection rule using the critical value?
(Use .) Reject if is the
critical value of (to decimals). Can
you conclude that the population mean is greater than ?
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Consider
the following hypothesis test: : : A
sample of is used. Identify the -value and state your
conclusion for each of the following sample results. Use . a. With and , the -value is b. With and , the -value is c. With and , the -value is
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On
its municipal website, the city of Tulsa states that the rate it charges
per CCF of residential water is . How do the residential
water rates of other U.S. public utilities compare to Tulsa's rate? The
file ResidentialWater contains the rate per CCF
of residential water for randomly selected U.S. cities. Click
on the datafile logo to reference the data.
a. Formulate hypotheses that can be used to determine whether the
population mean rate per CCF of residential water charged by U.S.
public utilities differs from the rate charged by Tulsa. Choose
the correct null hypothesis: 1. : 2. : 3. : Choose
the correct alternative hypothesis: 1. : 2. : 3. : b. What is the -value for your hypothesis test in part (a)? Round
your answer to four decimal places. c. At , can your null hypothesis be rejected? What is your
conclusion? the
null hypothesis. The mean rate per CCF of residential water
throughout the U.S. significantly
from the rate per CCF of residential water in Tulsa. d. Repeat the preceding hypothesis test using the critical value
approach. The
critical value(s) is(are) . = (to decimals), the
null hypothesis.
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In ,
RAND Corporation researchers found that of all individuals
ages to are adequately prepared financially for
retirement. Many financial planners have expressed concern that a smaller
percentage of those in this age group who did not complete high school are
adequately prepared financially for retirement. a. Develop appropriate hypotheses such that rejection of will
support the conclusion that the proportion of those who are adequately
prepared financially for retirement is smaller for people in
the age group who did not complete high school than it is for the
population of the age group. : : b. In a random sample of people from the age group
who did not complete high school, were not prepared financially
for retirement. What is the -value for your hypothesis test
(to decimals)? If your answer is zero, enter "0". c. At , what is your conclusion? We that
the percentage of year old individuals who are adequately prepared
financially for retirement is smaller for those who did not complete high
school.
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Eagle
Outfitters is a chain of stores specializing in outdoor apparel and camping
gear. They are considering a promotion that involves mailing discount coupons
to all its credit card customers. This promotion will be considered a success
if more than of those receiving the coupons use them. Before going
national with the promotion, coupons were sent to a sample
of credit card customers. Click
on the datafile logo to reference the data.
a. Develop hypotheses that can be used to test whether the
population proportion of those who will use the coupons is sufficient to go
national. : b. The file Eagle contains the sample data.
Develop a point estimate of the population proportion
(to decimals). c. Use to conduct your hypothesis test. Should Eagle go
national with the promotion?
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At
Western University the historical mean of scholarship examination scores for
freshman applications is . A historical population standard
deviation is assumed known. Each year, the assistant dean uses a sample
of applications to determine whether the mean examination score for the new
freshman applications has changed. a. State the hypotheses. b. What is the confidence interval estimate of the
population mean examination score if a sample of applications
provided a sample mean of (to the nearest whole number)? c. Use the confidence interval to conduct a hypothesis test.
Using , can the assistant dean conclude that the mean examination score
for the new freshman applications has changed? d. What is the -value (to decimals)? (Use Table 1
from Appendix B.)
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According
to the National Association of Realtors, it took an average of three weeks to
sell a home in . Data for the sale of randomly selected homes
sold in Greene County, Ohio, in showed a sample mean
of weeks with a sample standard deviation of weeks.
Conduct a hypothesis test to determine whether the number of weeks until a
house sold in Greene County differed from the national average in .
Round your answer to four decimal places. -value
= Use for
the level of significance, and state your conclusion.
I.
Reject . There is a
statistically significant difference between the national average time to
sell a home and the mean time to sell a home in Greene County.
II.
Reject . There is not a
statistically significant difference between the national average time to
sell a home and the mean time to sell a home in Greene County.
III.
Do not reject . There is a
statistically significant difference between the national average time to
sell a home and the mean time to sell a home in Greene County.
IV.
Do not reject . There is not a
statistically significant difference between the national average time to
sell a home and the mean time to sell a home in Greene County. Choose
the correct option.
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