BA6933 All Quize's Week 4 Chapter's( 10, 11, 12)

Today	Five Years Ago
x̄	84.00	86.00
σ 2	119.5	52
n	53	49
The point estimate for the difference between the means of the two populations (Today – Five Years Ago) is _____.
	-2.00
An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below.
Under Age 18	Over Age 18
n1 = 600	n2 = 500
Number of accidents = 228	Number of accidents = 145
	600	500	1100
	228	145	373
			0.339090909
A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. Final examination scores from a random sample of students enrolled today and from a random sample of students enrolled five years ago were selected. You are given the following information.
Today	Five Years Ago
x	83	89
σ2	79.5	122.5
n	53	49
The p-value for determining if there is a difference between the two population means
X	83	89
n	53	49
Var	79.5	122.5	1.5	2.5
	SE	2
	Test Statastic	-3
		0.001349898
	In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated.
	Company 1	Company 2
	n1 = 80	n2 = 60
	x̄1 = $10.80	x̄2 = $10.00
	σ1 = $2.00	σ2 = $1.50
	Refer to Exhibit 10-13. The test statistic has a value of _____.
		a. 1.96
		b. 1.645	x	10.8	10
		c. 2.7	n	80	60
		d. .80	var	4	2.25	0.05	0.0375
			Std	2	1.5
				SE	0.295803989
				Test Statastic	2.704493615
					0.996579571
	The following information was obtained from matched samples.
	Individual	Method 1	Method 2
	1	7	5
	2	5	9
	3	6	8
	4	7	7
	5	5	6
		6	7		-1
	Refer to Exhibit 10-5. The point estimate for the mean of the population of differences (Method 1 – Method 2) is _____.
		a. –1
		b. 2
		c. 0
		d. 1
	A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. Final examination scores from a random sample of students enrolled today and from a random sample of students enrolled five years ago were selected. You are given the following information.
		Today	Five Years Ago
	x̄	82	88
	σ 2	112.5	54
	n	45	36
	Refer to Exhibit 10-3. The standard error of x̄ 1 - x̄ 2 is _____.
		a. 4
		b. 12.9		x	82	88
		c. 9.3		n	45	36
		d. 2		var	112.5	54	2.5	1.5
				Std	79.5	122.5
					SE	2
					Test Statastic	-3
						0.00135
	In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated.
	Company 1	Company 2
	n1 = 90	n2 = 70
	x1 = $11.60	x2 = $11.00
	𝜎1 = $2.00	𝜎2 = $1.60
		x	11.7	11
	The p-value is _____.	n	90	70
		var	4	2.25	0.044444444	0.032143
		Std	2	1.5
			SE	0.276744108
			Test Statastic	2.529412474
				0.9943	0.8400
				-1.994287317
		x	45	42
		n	10	12
		var	85	90	8.5	7.5
		Std	2	1.5
			SE	4			Refer to Exhibit 10-4. The standard error of x̄1 - x̄2 is _____.
			Test Statastic	0.75
				0.7734	0.7803
				-1.773372648
	In order to determine whether or not there is a significant difference between the hourly wages of two companies, two independent random samples were selected and the following statistics were calculated.
		Company A	Company B
		Sample size	80	50
		Sample mean	$9.75	$9.25
		Population standard deviation	$1.00	$0.90
		x	9.75	9.25
		n	80	50
		var	85	90	1.0625	1.8
		Std	1	0.9
			SE	1.691892432
			Test Statastic	0.295527062
				0.6162	0.7311
				-1.616204359
	At a significance level of 0.05, the null hypothesis _____.
	The results of a recent poll on the preference of shoppers regarding two products are shown below.
	Product	Shoppers Surveyed	Shoppers Favoring
			This Product
	A	800	560
	B	900	612
	Refer to Exhibit 10-10. At 95% confidence, the margin of error is _____.			n				p	1-p				SE
		a. 52		800	560		n1	0.7	0.3		0.0002625	0.000504278	0.022456
		b. .044		900	612		n2	0.68	0.32		0.000241778
		c. .064											ME
		d. .0225										1.96	0.044014
	The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information. Assume the samples were selected randomly.
		Store's Card	Major Credit Card
	Sample size	64	49
	Sample mean	$120	$115
	Population standard deviation	$15	$7
					n	64	n2	49
					x1	120	x2	115
	At 95% confidence, the margin of error is _____.				std	15	std	7
		a. 1.96
		b. 4.16				3.515625		1
		c. 2.125					4.515625
		d. 5					2.125
						1.96	4.165
	The results of a recent poll on the preference of shoppers regarding two products are shown below.
	Product	Shoppers Surveyed	Shoppers Favoring
			This Product
	A	800	560
	B	900	612		n				p	1-p				SE
					800	560		n1	0.7	0.3		0.0002625	0.000504	0.022456
					900	612		n2	0.68	0.32		0.000241778
	Refer to Exhibit 10-10. The point estimate for the difference between the two population proportions in favor of this product (Product A – Product B) is _____.													ME
		a. 100						p1-p2	0.02				1.96	0.044014
		b. 52
		c. .02
		d. .44
	In order to estimate the difference between the average hourly wages of employees of two branches of a department store, two independent random samples were selected and the following statistics were calculated.
		Downtown Store	North Mall Store
	Sample size	36	30
	Sample mean	$12	$10
	Sample standard deviation	$3	$2
	A 95% interval estimate for the difference between the two population means (Downtown Store – North Mall Store) is _____.
		a. $0.79 to $3.21
		b. $0.97 to $3.03
		c. $1.38 to $2.62
		d. $0.76 to $3.24
			n	36	n2	30
			x1	12	x2	10
			std	3	std	2			Diff	2
				0.25		0.133333
					0.383333333				0.786487
					0.619139187
				1.96	1.213512807				3.213513
	The daily production rates for a random sample of workers before and after a training program are shown below.
	Worker	Before	After
	1	20	22
	2	25	23
	3	27	27
	4	23	20
	5	22	25
	6	20	19
	7	17	18
		22	22
	Refer to Exhibit 10-2. The point estimate for the mean of the population of difference is
			n	64	n2	49
			x1	120	x2	110
			std	3	std	2			Diff	10
				0.140625		0.081633
					0.222257653				9.075973
					0.471442099
				1.96	0.924026515				10.92403
			n				p	1-p				SE
			600	222		n1	0.37	0.63		0.000389	0.0007733	0.027808272
			500	130		n2	0.26	0.74		0.000385
												ME
						p1-p2	0.11				1.96	0.054504213
							3.9556575
						Pvalue	1.0000	0.8413
							-1.9999618
				Inner City Store	Suburban Store
			Sample Size	36	49
			Sampe Mean	40	35
			Stdev	9	10
	the point estimate of the difference between the mean ages of the two populations is x1 - x2			5
	Using 95% confidence and za/2 5 z.025 5 1.96			1.96
	Standard Error			2.071428571
			Mean Error	4.06		Confidence Interval
						0.94	9.06
			Test Statistic	2.413793103
				Inner City Store	Suburban Store
			Sample Size	30	40
			Sampe Mean	82	78
			Stdev	10	10
	the point estimate of the difference between the mean ages of the two populations is x1 - x2			4
	Using 95% confidence and za/2 5 z.025 5 1.96			1.96
	Standard Error			2.415229458
			Mean Error	4.733849737		Confidence Interval
						-0.73385	8.7338497
			Test Statistic	1.656157342
			Pvalue	0.95115502
				0.04884498	As it is in upper tail
			As it is two tail test	0.0977
	Independent			Inner City Store	Suburban Store			S1^2	S2^2
			Sample Size	28	22			22500	15625
			Sampe Mean	1025	910			803.5714	710.2273		645727.0408	504422.7789
			Stdev	150	125			1513.799			27	21
	the point estimate of the difference between the mean ages of the two populations is x1 - x2			115				2291587			0.037037037	0.047619048
	Using 95% confidence and Ta/2 5 t.025			2.012		Signification	95%				23915.81633	24020.13233
	Standard Error			38.90756612			5%	0.025			47935.94866
			Mean Error	78.27		Confidence Interval				DF=	47.8
						36.7	193.27193
			Test Statistic	2.955723307
			Pvalue	0.997567803
				0.002432197	As it is in upper tail
			As it is two tail test	0.0049
	Worker	time	Time	Caclulating d	di-d	(di-d)^2
	1	6	5.4	0.6	0.3	0.09
	2	5	5.2	-0.2	-0.5	0.25
	3	7	6.5	0.5	0.2	0.04
	4	6.2	5.9	0.3	0	0
	5	6	6	0	-0.3	0.09
	6	6.4	5.8	0.6	0.3	0.09		ud=	0	We get this from hypothesis
			d=	0.3		0.56
						5
						0.112
					Sd =	0.334664		Confidence Interval				DF=	5.0
					Mean Error	0.1366		-0.05	0.65
	Using 95% confidence and Ta/2 5 t.025					2.571		Signification	95%
						0.35			5%	0.025
					test Stattistic	2.20
					Pvalue	0.960242
						0.039758	As it is in upper tail
					As it is two tail test	0.0795
	Proportion			Inner City Store	Suburban Store			p(1-p)	p(1-p)
			Sample Size	250	300			0.1204	0.0819
			Errors	35	27			0.000482	0.000273
			P	0.14	0.09			0.000755			0.004
			1-P	0.86	0.91						0.003333333
			Stdev	150	125			0.02747			0.007333333
	the point estimate of the difference between the mean ages of the two populations is x1 - x2			0.05				0.045184
			Pooled Estimator	0.112727273	1-p	0.887273
	Using 95% confidence and Za/2 5 t.025			1.645		Signification	90%
	Standard Error			0.027469984			10%	0.05
				0.027470		Confidence Interval
			Mean Error	0.045184102		0.005	0.095
			Test Statistic	1.846189281
			Pvalue	0.967567637
				0.032432363	As it is in upper tail
			As it is two tail test	0.0649
	Proportion			Inner City Store	Suburban Store			p(1-p)	p(1-p)
			Sample Size	700	800			0.16	0.1771
			Errors	560	616			0.000229	0.000221
			P	0.8	0.77			0.00045			0.001428571
			1-P	0.2	0.23						0.00125
			Stdev	150	125			0.021212			0.002678571
	the point estimate of the difference between the mean ages of the two populations is x1 - x2			0.03				0.041575
			Pooled Estimator	0.784	1-p	0.216
	Using 95% confidence and Za/2 5 t.025			1.960		Signification	95%
	Standard Error			0.021211941			5%	0.025
			Mean Error	0.041575		Confidence Interval
						-0.012	0.072
			Test Statistic	1.408590425
			Pvalue	0.920521844
				0.079478156	As it is in upper tail
			As it is two tail test	0.1590
	Proportion			Inner City Store	Suburban Store			p(1-p)	p(1-p)
			Sample Size	700	800			0.2491	0.25
			Errors	329	400			0.000356	0.000313
			P	0.47	0.5			0.000668			0.001428571
			1-P	0.53	0.5						0.00125
			Stdev	150	125			0.025853			0.002678571
	the point estimate of the difference between the mean ages of the two populations is x1 - x2			-0.03				0.05067
			Pooled Estimator	0.486	1-p	0.514
	Using 95% confidence and Za/2 5 t.025			1.960		Signification	95%
	Standard Error			0.025852604			5%	0.025
			Mean Error	0.050670		Confidence Interval
						-0.081	0.021
			Test Statistic	-1.159764857
			Pvalue	0.123072278
				0.876927722	As it is in upper tail
			As it is two tail test	1.7539
				Inner City Store	Suburban Store
			Sample Size	14	16
			Sampe Mean	47	44
			Stdev	7.937253933	13.56465997
				63	184
	the point estimate of the difference between the mean ages of the two populations is x1 - x2			3
	Using 95% confidence and za/2 5 z.025 5 1.96			1.960		Signification	95%
	Standard Error			4			5%	0.025
			Mean Error	7.839855938		Confidence Interval
						-4.83986	10.839856
			Test Statistic	0.75
			Pvalue	0.773372648
				0.226627352	As it is in upper tail
			As it is two tail test	0.4533
	Independent			Inner City Store	Suburban Store			S1^2	S2^2
			Sample Size	14	16			63	184
			Sampe Mean	47	44			4.5	11.5		20.25	132.25
			Stdev	7.937253933	13.56465997			16			13	15
				63	184
	the point estimate of the difference between the mean ages of the two populations is x1 - x2			3				256			0.076923077	0.066666667
	Using 95% confidence and Ta/2 5 t.025			2.064		Signification	95%				1.557692308	8.816666667
	Standard Error			4			5%	0.025			10.37435897
			Mean Error	8.26		Confidence Interval				DF=	24.7
						-5.3	11.256
			Test Statistic	0.75
			Pvalue	0.769727818
				0.230272182	As it is in upper tail
			As it is two tail test	0.4605
				Inner City Store	Suburban Store
			Sample Size	64	49
			Sampe Mean	140	125
			Stdev	10	8
				63	184
	the point estimate of the difference between the mean ages of the two populations is x1 - x2			15
	Using 95% confidence and za/2 5 z.025 5 1.96			1.960		Signification	95%
	Standard Error			1.693700814			5%	0.025
			Mean Error	3.32		Confidence Interval
						11.68041	18.319593
			Test Statistic	8.856345744
			Pvalue	1
				0	As it is in upper tail
			As it is two tail test	0.0000
	Independent			Inner City Store	Suburban Store			S1^2	S2^2
			Sample Size	64	49			100	64
			Sampe Mean	140	125			1.5625	1.306122		2.44140625	1.705955852
			Stdev	10	8			2.868622			63	48
				63	184
	the point estimate of the difference between the mean ages of the two populations is x1 - x2			15				8.228995			0.015873016	0.020833333
	Using 95% confidence and Ta/2 5 t.025			1.982		Signification	95%				0.03875248	0.035540747
	Standard Error			1.693700814			5%	0.025			0.074293227
			Mean Error	3.36		Confidence Interval				DF=	110.8
						11.6	18.357
			Test Statistic	8.856345744
			Pvalue	1
				8.10463E-15	As it is in upper tail
			As it is two tail test	0.0000
	Independent simple random samples are selected to test the difference between the means of two populations whose standard deviations are not known. We are unwilling to assume that the population variances are equal. The sample sizes are n1 = 24 and n2 = 32. The correct distribution to use is the t distribution with how many degrees of freedom?
		24
		32
	DF	54
				Inner City Store	Suburban Store
			Sample Size	64	25
			Sampe Mean	46	44
			Stdev	11.3137085	7.745966692
				128	60
	the point estimate of the difference between the mean ages of the two populations is x1 - x2			2
	Using 95% confidence and za/2 5 z.025 5 1.96			1.960		Signification	95%
	Standard Error			2.097617696			5%	0.025
			Mean Error	4.11		Confidence Interval
						-2.11126	6.1112551
			Test Statistic	0.953462589
			Pvalue	0.829822129
				0.170177871	As it is in upper tail
			As it is two tail test	0.3404
	Individual	Method 1	Method 2
	1	8	6
	2	6	10
	3	4	10
	4	9	9
	5	3	5
		6	8
	point estimate	-2
	Worker	Before	After
	1	20	22
	2	25	23
	3	27	27
	4	23	20
	5	22	25
	6	20	19
	7	17	18
		22	22
	point estimate	0
	Refer to Exhibit 10-2. The point estimate for the mean of the population of difference is
				Inner City Store	Suburban Store
			Sample Size	64	36
			Sampe Mean	44	41
			Stdev	11.3137085	8.485281374
				128	72
	the point estimate of the difference between the mean ages of the two populations is x1 - x2			3
	Using 95% confidence and za/2 5 z.025 5 1.96			1.960		Signification	95%
	Standard Error			2			5%	0.025
			Mean Error	3.92		Confidence Interval
						-0.91993	6.919928
			Test Statistic	1.5
			Pvalue	0.933192799
				0.066807201	As it is in upper tail
			As it is two tail test	0.1336
				Inner City Store	Suburban Store
			Sample Size	45	36
			Sampe Mean	82	88
			Stdev	10.60660172	7.348469228
				112.5	54
	the point estimate of the difference between the mean ages of the two populations is x1 - x2			-6
	Using 95% confidence and za/2 5 z.025 5 1.96			1.960		Signification	95%
	Standard Error			2			5%	0.025
			Mean Error	3.92		Confidence Interval
						-9.91993	-2.080072
			Test Statistic	-3
			Pvalue	0.001349898
				0.998650102	As it is in upper tail
			As it is two tail test	1.9973
	Independent			Inner City Store	Suburban Store			S1^2	S2^2
			Sample Size	64	49			100	64
			Sampe Mean	140	125			1.5625	1.306122		2.44140625	1.705955852
			Stdev	10	8			2.868622			63	48
				63	184
	the point estimate of the difference between the mean ages of the two populations is x1 - x2			15				8.228995			0.015873016	0.020833333
	Using 95% confidence and Ta/2 5 t.025			1.982		Signification	95%				0.03875248	0.035540747
	Standard Error			1.693700814			5%	0.025			0.074293227
			Mean Error	3.36		Confidence Interval				DF=	110.8
						11.6	18.357
			Test Statistic	8.856345744
			Pvalue	1
				8.10463E-15	As it is in upper tail
			As it is two tail test	0.0000
	Independent			Inner City Store	Suburban Store			S1^2	S2^2
			Sample Size	90	70			9	6.76
			Sampe Mean	12.9	12			0.1	0.096571		0.01	0.009326041
			Stdev	3	2.6			0.196571			89	69
				63	184
	the point estimate of the difference between the mean ages of the two populations is x1 - x2			0.9				0.03864			0.011235955	0.014492754
	Using 95% confidence and Ta/2 5 t.025			1.975		Signification	95%				0.00011236	0.00013516
	Standard Error			0.443363766			5%	0.025			0.00024752
			Mean Error	0.88		Confidence Interval				DF=	156.1
						0.0	1.776
			Test Statistic	2.029935845
			Pvalue	0.977968823
				0.022031177	As it is in upper tail
			As it is two tail test	0.0441
				Inner City Store	Suburban Store
			Sample Size	90	70
			Sampe Mean	12.9	12
			Stdev	3	2.6
				112.5	54
	the point estimate of the difference between the mean ages of the two populations is x1 - x2			0.9
	Using 95% confidence and za/2 5 z.025 5 1.96			1.960		Signification	95%
	Standard Error			0.443363766			5%	0.025
			Mean Error	0.87		Confidence Interval
						0.031023	1.768977
			Test Statistic	2.029935845
			Pvalue	0.97881847
				0.02118153	As it is in upper tail
			As it is two tail test	0.0424
	Worker	time	Time	Caclulating d	di-d	(di-d)^2
	1	18	20	-2	-2.3	5.29
	2	23	21	2	1.7	2.89
	3	25	25	0	-0.3	0.09
	4	21	18	3	2.7	7.29
	5	20	23	-3	-3.3	10.89
	6	18	17	1	0.7	0.49		ud=	0	We get this from hypothesis
	7	15	16	-1	-1.3	1.69
			d=	0		28.63
						6
						4.771667
					Sd =	2.184414		Confidence Interval				DF=	6.0
					Mean Error	0.8918		-2.18	2.18
	Using 95% confidence and Ta/2 5 t.025					2.447		Signification	95%
						2.18			5%	0.025
					test Stattistic	0.00
					Pvalue	0.5
						0.5	As it is in upper tail
					As it is two tail test	1.0000
	Proportion			Inner City Store	Suburban Store			p(1-p)	p(1-p)
			Sample Size	700	800			0.2475	0.25
			Errors	315	400			0.000354	0.000313
			P	0.45	0.5			0.000666			0.001428571
			1-P	0.55	0.5						0.00125
			Stdev	150	125			0.025808			0.002678571
	the point estimate of the difference between the mean ages of the two populations is x1 - x2			-0.05				0.050583
			Pooled Estimator	0.476666667	1-p	0.523333
	Using 95% confidence and Za/2 5 t.025			1.960		Signification	95%
	Standard Error			0.02580836			5%	0.025
			Mean Error	0.050583		Confidence Interval
						-0.101	0.001
			Test Statistic	-1.934290942
			Pvalue	0.026538683
				0.973461317	As it is in upper tail
			As it is two tail test	1.9469
	Independent			Inner City Store	Suburban Store			S1^2	S2^2
			Sample Size	64	25			128	50
			Sampe Mean	49	42			2	2		4	4
			Stdev	11.3137085	7.071067812			4			63	24
				128	50
	the point estimate of the difference between the mean ages of the two populations is x1 - x2			7				16			0.015873016	0.041666667
	Using 95% confidence and Ta/2 5 t.025			1.995		Signification	95%				0.063492063	0.166666667
	Standard Error			2			5%	0.025			0.23015873
			Mean Error	3.99		Confidence Interval				DF=	69.5
						3.0	10.990
			Test Statistic	3.5
			Pvalue	0.999590125
				0.000409875	As it is in upper tail
			As it is two tail test	0.0008
	Worker	time	Time	Caclulating d	di-d	(di-d)^2
	1	5	6	-1	-1.3	1.69
	2	3	7	-4	-4.3	18.49
	3	8	7	1	0.7	0.49
	4	8	8	0	-0.3	0.09
	5	6	7	-1	-1.3	1.69
			d=	-1		22.45
						4
						5.6125
					Sd =	2.369072		Confidence Interval				DF=	4.0
					Mean Error	1.0595		-3.94	1.94
	Using 95% confidence and Ta/2 5 t.025					2.776		Signification	95%
						2.94			5%	0.025
					test Stattistic	-0.94
					Pvalue	0.199343
						0.800657	As it is in upper tail
					As it is two tail test	1.6013
				Inner City Store	Suburban Store
			Sample Size	49	25
			Sampe Mean	46	43
			Stdev	9.899494937	7.071067812
				98	50
	the point estimate of the difference between the mean ages of the two populations is x1 - x2			3
	Using 95% confidence and za/2 5 z.025 5 1.96			1.960		Signification	95%
	Standard Error			2			5%	0.025
			Mean Error	3.92		Confidence Interval
						-0.91993	6.919928
			Test Statistic	1.5
			Pvalue	0.933192799
				0.066807201	As it is in upper tail
			As it is two tail test	0.1336
	Worker	time	Time	Caclulating d	di-d	(di-d)^2
	1	21	23	-2	-2.3	5.29
	2	26	24	2	1.7	2.89
	3	28	28	0	-0.3	0.09
	4	24	21	3	2.7	7.29
	5	23	26	-3	-3.3	10.89
	6	21	20	1	0.7	0.49		ud=	0	We get this from hypothesis
	7	18	19	-1	-1.3	1.69
			d=	0		28.63
						6
						4.771667
					Sd =	2.184414		Confidence Interval				DF=	6.0
					Mean Error	0.8918		-2.18	2.18
	Using 95% confidence and Ta/2 5 t.025					2.447		Signification	95%
						2.18			5%	0.025
					test Stattistic	0.00
					Pvalue	0.5
						0.5	As it is in upper tail
					As it is two tail test	1.0000
	Proportion			Inner City Store	Suburban Store			p(1-p)	p(1-p)
			Sample Size	700	800			0.24	0.2451
			Errors	420	456			0.000343	0.000306
			P	0.6	0.57			0.000649			0.001428571
			1-P	0.4	0.43						0.00125
			Stdev	150	125			0.02548			0.002678571
	the point estimate of the difference between the mean ages of the two populations is x1 - x2			0.03				0.04994
			Pooled Estimator	0.584	1-p	0.416
	Using 95% confidence and Za/2 5 t.025			1.960		Signification	95%
	Standard Error			0.025480034			5%	0.025
			Mean Error	0.049940		Confidence Interval
						-0.020	0.080
			Test Statistic	1.176024988
			Pvalue	0.880207555
				0.119792445	As it is in upper tail
			As it is two tail test	0.2396
				Inner City Store	Suburban Store
			Sample Size	80	60
			Sampe Mean	10.8	10
			Stdev	2	1.5
				98	50
	the point estimate of the difference between the mean ages of the two populations is x1 - x2			0.8
	Using 95% confidence and za/2 5 z.025 5 1.96			1.960		Signification	95%
	Standard Error			0.295803989			5%	0.025
			Mean Error	0.58		Confidence Interval
						0.220235	1.3797652
			Test Statistic	2.704493615
			Pvalue	0.996579571
				0.003420429	As it is in upper tail
			As it is two tail test	0.0068
	Independent			Inner City Store	Suburban Store			S1^2	S2^2
			Sample Size	80	60			4	2.25
			Sampe Mean	10.8	10			0.05	0.0375		0.0025	0.00140625
			Stdev	2	1.5			0.0875			79	59
				128	50
	the point estimate of the difference between the mean ages of the two populations is x1 - x2			0.8				0.007656			0.012658228	0.016949153
	Using 95% confidence and Ta/2 5 t.025			1.977		Signification	95%				3.16456E-05	2.38347E-05
	Standard Error			0.295803989			5%	0.025			5.54803E-05
			Mean Error	0.58		Confidence Interval				DF=	138.0
						0.2	1.385
			Test Statistic	2.704493615
			Pvalue	0.996145526
				0.003854474	As it is in upper tail
			As it is two tail test	0.0077
	Proportion			Inner City Store	Suburban Store			p(1-p)	p(1-p)
			Sample Size	600	500			0.2356	0.1659
			Errors	228	105			0.000393	0.000332
			P	0.38	0.21			0.000724			0.001666667
			1-P	0.62	0.79						0.002
			Stdev	150	125			0.026916			0.003666667
	the point estimate of the difference between the mean ages of the two populations is x1 - x2			0.17				0.052754
			Pooled Estimator	0.302727273	1-p	0.697273
	Using 95% confidence and Za/2 5 t.025			1.960		Signification	95%
	Standard Error			0.026915918			5%	0.025
			Mean Error	0.052754		Confidence Interval
						0.117	0.223
			Test Statistic	6.110631473
			Pvalue	1
				4.96188E-10	As it is in upper tail
			As it is two tail test	0.0000

  

		Sample Size(n)	30
		Significance	95%
			5%
		Sig1	0.025	0.975	45.72229		Interval Estimate
		Sig2	0.975	0.025	16.04707		102.7508	292.7637
		DF	29
		Confidence Coefficient	95%
		Standard Deviation(S)
		Sample variance(S^2)	162
		Variance from Hypotheis	100
		test Statistic[X^2]	46.98
		P value[Lower Tail]	0.98129563
		P value[upper Tail]	0.01870437
		P value[two Tail]	0.03740875
		0.05	5
		0.95
			11.0704977
		S1^2	120		n1	41		Df1	40
		S2^2	80		n2	31		Df2	30
		F =	1.5
		P-value	0.12564168
			0.87435832
		P-value	0.2513
		Sample Size(n)	23
		Significance	95%
			5%		Critical
		Sig1	0.025	0.975	36.78071		Interval Estimate
		Sig2	0.975	0.025	10.98232		35.88838	120.1932
		DF	22
		Confidence Coefficient	95%
		Standard Deviation(S)
		Sample variance(S^2)	60
		Variance from Hypotheis	66
		test Statistic[X^2]	20.00
		P value[Lower Tail]	0.41696025
		P value[upper Tail]	0.58303975
		P value[two Tail]	0.8339205
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 its new automobiles is _____.
		Sample Size(n)	15
		Significance	95%
			5%		Critical
		Sig1	0.025	0.975	26.11895		Interval Estimate
		Sig2	0.975	0.025	5.628726		8.576149	39.79586
		DF	14
		Confidence Coefficient	95%
		Standard Deviation(S)	4
		Sample variance(S^2)	16
		Variance from Hypotheis	66
		test Statistic[X^2]	3.39
		P value[Lower Tail]	0.00185659
		P value[upper Tail]	0.99814341
		P value[two Tail]	0.00371318
	The contents of a sample of 26 cans of apple juice showed a standard deviation of 0.06 ounce. We are interested in testing to determine whether the variance of the population is significantly more than .003.
	The null hypothesis is _____.
		Sample Size(n)	26
		Significance	95%
			5%		Critical
		Sig1	0.025	0.975	40.64647		Interval Estimate
		Sig2	0.975	0.025	13.11972		0.002214	0.00686
		DF	25
		Confidence Coefficient	95%
		Standard Deviation(S)	0.06
		Sample variance(S^2)	0.0036
		Variance from Hypotheis	0.003
		test Statistic[X^2]	30.00
		P value[Lower Tail]	0.775711
		P value[upper Tail]	0.224289
		P value[two Tail]	0.44857801
	The value of F0.01 with 9 numerator and 20 denominator degrees of freedom is _____.
		numerator	6
		Denominator	22
		F =	0.01
		P-value	3.76
													Exhibit 11-6
		S1^2	32		n1	26		Df1	25					Sample A	Sample B
		S2^2	38		n2	16		Df2	15				s 2	32	38
													n	24	16
		F =	0.84210526		Sifnificance =	0.05							We want to test the hypothesis that the population variances are equal.
													The null hypothesis _____.
		P-value	0.65854878		Fcritical	2.279729								a. should be rejected
			0.34145122											b. should be revised
		P-value	1.3171											c. should be retested
														d. should not be rejected
The producer of a certain medicine claims that its bottling equipment is very accurate and that the standard deviation of all its filled bottles is 0.1 ounce or less. A sample of 20 bottles showed a standard deviation of .11. The test statistic to test the claim is _____.
		Sample Size(n)	11
		Significance	95%
			5%		Critical
		Sig1	0.025	0.975	20.48318		Interval Estimate
		Sig2	0.975	0.025	3.246973		13.66975	86.23417
		DF	10
		Confidence Coefficient	95%
		Standard Deviation(S)	0.11
		Sample variance(S^2)	28
			0.1
		Variance from Hypotheis	0.01
		test Statistic[X^2]	28000.00
		P value[Lower Tail]	1
		P value[upper Tail]	0
		P value[two Tail]	0
		Sample Size(n)	26
		Significance	95%
			5%		Critical
		Sig1	0.025	0.975	40.64647		Interval Estimate
		Sig2	0.975	0.025	13.11972		0.002214	0.00686
		DF	25
		Confidence Coefficient	95%
		Standard Deviation(S)	0.06
		Sample variance(S^2)	0.0036
			0.1
		Variance from Hypotheis	0.003
		test Statistic[X^2]	30.00
		P value[Lower Tail]	0.775711
		P value[upper Tail]	0.224289
		P value[two Tail]	0.44857801
	The critical value of F for an upper tail test at a 0.05 significance level 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 _____.
		S1^2	32		n1	9		Df1	8
		S2^2	38		n2	21		Df2	20
		F =	0.84210526		Sifnificance =	0.05
		P-value	0.57764797		Fcritical	2.447064
			0.42235203
		P-value	1.1553
		Sample Size(n)	11
		Significance	95%
			5%		Critical
		Sig1	0.025	0.975	20.48318		Interval Estimate						Consider the following.
		Sig2	0.975	0.025	3.246973		195.2822	1231.917
		DF	10										n = 11	H0: σ2 ≤ 425
		Confidence Coefficient	95%										s = 20	Ha: σ2 > 425
		Standard Deviation(S)	20
		Sample variance(S^2)	400
			0.1										The test statistic for this problem equals
		Variance from Hypotheis	425
		test Statistic[X^2]	9.41
		P value[Lower Tail]	0.50647853
		P value[upper Tail]	0.49352147
		P value[two Tail]	0.98704294
	Last year, the standard deviation of the ages of the students at a univeristy was 1.97 years. Recently, a sample of 10 students had a standard deviation of 2.3 years. We are interested in testing to see if there has been a significant change in the standard deviation of the ages of the students at this university.
	The test statistic is _____.
		Sample Size(n)	10
		Significance	95%
			5%		Critical
		Sig1	0.025	0.975	19.02277		Interval Estimate
		Sig2	0.975	0.025	2.700389		2.50279	17.63079
		DF	9
		Confidence Coefficient	95%
		Standard Deviation(S)	2.3
		Sample variance(S^2)	5.29
			1.97
		Variance from Hypotheis	3.8809
		test Statistic[X^2]	12.27
		P value[Lower Tail]	0.80136895
		P value[upper Tail]	0.19863105
		P value[two Tail]	0.3972621
	In a hypothesis test about two population variances, the test statistic F is computed as _____.
		a. σ12/σ22
		b. 1/ (s12/s22)
		c. s12/s22
		d. 1/(σ12/σ22)
		Sample Size(n)	23
		Significance	95%
			5%		Critical									Exhibit 11-8
		Sig1	0.025	0.975	36.78071		Interval Estimate
		Sig2	0.975	0.025	10.98232		35.88838	120.1932						n = 23	H 0: σ 2 ≥ 66
		DF	22											s 2 = 60	H a: σ 2 < 66
		Confidence Coefficient	95%
		Standard Deviation(S)												At a 5% level of significance, the critical value(s) from the table is(are) _____.
		Sample variance(S^2)	60												a. 12.3380
															b. 43.7729
		Variance from Hypotheis	66												c. 33.9244
															d. 10.9823 and 36.7897
		test Statistic[X^2]	20.00
		P value[Lower Tail]	0.41696025
		P value[upper Tail]	0.58303975
		P value[two Tail]	0.8339205
	The producer of a certain bottling equipment claims that the variance of all its filled bottles is 0.026 or less. A sample of 31 bottles showed a standard deviation of 0.2. The p-value for the test is _____.
		Sample Size(n)	30
		Significance	95%
			5%		Critical
		Sig1	0.025	0.975	45.72229		Interval Estimate
		Sig2	0.975	0.025	16.04707		0.025371	0.072287
		DF	29
		Confidence Coefficient	95%
		Standard Deviation(S)	0.2
		Sample variance(S^2)	0.04
		Variance from Hypotheis	0.027
		test Statistic[X^2]	42.96
		P value[Lower Tail]	0.95411143
		P value[upper Tail]	0.04588857
		P value[two Tail]	0.09177713
	A random sample of 26 charge sales showed a sample standard deviation of $46. A 90% confidence interval estimate of the population standard deviation is _____.
		Sample Size(n)	35
		Significance	90%
			10%		Critical
		Sig1	0.05	0.95	48.60237		Interval Estimate							Consider the following.
		Sig2	0.95	0.05	21.66428		308.5035	692.107
		DF	34											n = 35	H0: σ2 = 350
		Confidence Coefficient	90%											s2 = 441	Ha: σ2 ≠ 350
		Standard Deviation(S)	46
		Sample variance(S^2)	441
														The test statistic for this problem equals _____.
		Variance from Hypotheis	350												a. 42.8
															b. 27.0
		test Statistic[X^2]	42.84												c. 20
															d. 38.2
		P value[Lower Tail]	0.85778086
		P value[upper Tail]	0.14221914
		P value[two Tail]	0.28443828
		Sample Size(n)	26
		Significance	95%
			5%		Critical
		Sig1	0.025	0.975	40.64647		Interval Estimate
		Sig2	0.975	0.025	13.11972		0.002214	0.00686
		DF	25
		Confidence Coefficient	95%
		Standard Deviation(S)	0.06
		Sample variance(S^2)	0.0036
		Variance from Hypotheis	0.003
		test Statistic[X^2]	30.00
		P value[Lower Tail]	0.775711
		P value[upper Tail]	0.224289
		P value[two Tail]	0.44857801
	Last year, the standard deviation of the ages of the students at UA was 1.81 years. Recently, a sample of 10 students had a standard deviation of 2.1 years. We are interested in testing to see if there has been a significant change in the standard deviation of the ages of the students at UA.
		Sample Size(n)	10
		Significance	95%
			5%		Critical
		Sig1	0.025	0.975	19.02277		Interval Estimate
		Sig2	0.975	0.025	2.700389		2.086447	14.69788
		DF	9
		Confidence Coefficient	95%
		Standard Deviation(S)	2.1
		Sample variance(S^2)	4.41
			1.81
		Variance from Hypotheis	3.2761
		test Statistic[X^2]	12.12
		P value[Lower Tail]	0.79309727
		P value[upper Tail]	0.20690273
		P value[two Tail]	0.41380545
	The sampling distribution used when making inferences about a single population's variance is a(n) _____ distribution.
		a. χ2
		b. F
		c. t
		d. normal
		Sample Size(n)	16
		Significance	95%
			5%		Critical
		Sig1	0.025	0.975	27.48839		Interval Estimate
		Sig2	0.975	0.025	6.262138		264.1115	1159.348					Consider the following.
		DF	15
		Confidence Coefficient	95%										n = 16	s = 22	H0: σ2 ≤ 584
		Standard Deviation(S)	22												Ha: σ2 > 584
		Sample variance(S^2)	484
			1.81
		Variance from Hypotheis	584										The test statistic for this problem equals _____.
														a. 0.57
		test Statistic[X^2]	12.43											b. 13.66
														c. 18.10
		P value[Lower Tail]	0.35388271											d. 12.43
		P value[upper Tail]	0.64611729
		P value[two Tail]	0.70776541
		S1^2	30		n1	18		Df1	17
		S2^2	32		n2	12		Df2	11
		F =	0.9375		Sifnificance =	0.05
		P-value	0.56180299		Fcritical	2.6851
			0.43819701
		P-value	1.1236
	A random sample of 33 charge sales showed a sample standard deviation of $48. A 90% confidence interval estimate of the population standard deviation is _____.
		Sample Size(n)	33
		Significance	90%
			10%		Critical
		Sig1	0.05	0.95	46.19426		Interval Estimate
		Sig2	0.95	0.05	20.07191		1596.042	3673.192
		DF	32
		Confidence Coefficient	90%
		Standard Deviation(S)	48
		Sample variance(S^2)	2304
			1.81
		Variance from Hypotheis	584
		test Statistic[X^2]	126.25
		P value[Lower Tail]	1
		P value[upper Tail]	3.868E-13
		P value[two Tail]	7.736E-13
	Last year, the standard deviation of the ages of the students at a univeristy was 1.97 years. Recently, a sample of 10 students had a standard deviation of 2.3 years. We are interested in testing to see if there has been a significant change in the standard deviation of the ages of the students at this university.
	The test statistic is _____.
		Sample Size(n)	10
		Significance	90%
			10%		Critical
		Sig1	0.05	0.95	16.91898		Interval Estimate
		Sig2	0.95	0.05	3.325113		2.814	14.31831
		DF	9
		Confidence Coefficient	90%
		Standard Deviation(S)	2.3
		Sample variance(S^2)	5.29
			1.97
		Variance from Hypotheis	3.8809
		test Statistic[X^2]	12.27
		P value[Lower Tail]	0.80136895
		P value[upper Tail]	0.19863105
		P value[two Tail]	0.3972621
		Sample Size(n)	12
		Significance	90%
			10%		Critical
		Sig1	0.05	0.95	19.67514		Interval Estimate						Consider the following.
		Sig2	0.95	0.05	4.574813		223.6325	961.7879
		DF	11										n = 12	H0: σ2 ≤ 430
		Confidence Coefficient	90%										s = 20	Ha: σ2 > 430
		Standard Deviation(S)	20
		Sample variance(S^2)	400
			1.97										The test statistic for this problem equals _____.
		Variance from Hypotheis	430											a. 11.16
														b. 11.83
		test Statistic[X^2]	10.23											c. 10.23
														d. 0.51
		P value[Lower Tail]	0.49040222
		P value[upper Tail]	0.50959778
		P value[two Tail]	0.98080443
	The sampling distribution of the ratio of two independent sample variances taken from normal populations with equal variances is a(n) _____ distribution.
		a. t
		b. χ2
		c. normal
		d. F
	The 99% confidence interval estimate for a population variance when a sample standard deviation of 11 is obtained from a sample of 10 items is _____.
		Sample Size(n)	10
		Significance	99%
			1%		Critical
		Sig1	0.005	0.995	23.58935		Interval Estimate
		Sig2	0.995	0.005	1.734933		46.1649	627.69
		DF	9
		Confidence Coefficient	99%
		Standard Deviation(S)	11
		Sample variance(S^2)	121
			1.97
		Variance from Hypotheis	430
		test Statistic[X^2]	2.53
		P value[Lower Tail]	0.02000497
		P value[upper Tail]	0.97999503
		P value[two Tail]	0.04000994
	Last year, the standard deviation of the ages of the students at UA was 1.81 years. Recently, a sample of 10 students had a standard deviation of 2.1 years. We are interested in testing to see if there has been a significant change in the standard deviation of the ages of the students at UA.
	The test statistic is _____.
		Sample Size(n)	10
		Significance	95%
			5%		Critical
		Sig1	0.025	0.975	19.02277		Interval Estimate
		Sig2	0.975	0.025	2.700389		2.086447	14.69788
		DF	9
		Confidence Coefficient	95%
		Standard Deviation(S)	2.1
		Sample variance(S^2)	4.41
			1.81
		Variance from Hypotheis	3.2761
		test Statistic[X^2]	12.12
		P value[Lower Tail]	0.79309727
		P value[upper Tail]	0.20690273
		P value[two Tail]	0.41380545
	A sample of 28 elements is selected to estimate a 95% confidence interval for the variance of the population. The χ2 values to be used for this interval estimation are _____.
		Sample Size(n)	28
		Significance	95%
			5%		Critical
		Sig1	0.025	0.975	43.19451		Interval Estimate
		Sig2	0.975	0.025	14.57338		2.7566	8.170375
		DF	27
		Confidence Coefficient	95%
		Standard Deviation(S)	2.1
		Sample variance(S^2)	4.41
			1.81
		Variance from Hypotheis	3.2761
		test Statistic[X^2]	36.35
		P value[Lower Tail]	0.89204351
		P value[upper Tail]	0.10795649
		P value[two Tail]	0.21591298
	We are interested in testing whether the variance of a population is significantly less than 1.44. The null hypothesis for this test is _____.
		Sample Size(n)	28
		Significance	95%
			5%		Critical
		Sig1	0.025	0.975	43.19451		Interval Estimate
		Sig2	0.975	0.025	14.57338		2.7566	8.170375
		DF	27
		Confidence Coefficient	95%
		Standard Deviation(S)	2.1
		Sample variance(S^2)	4.41
			1.81
		Variance from Hypotheis	3.2761
		test Statistic[X^2]	36.35
		P value[Lower Tail]	0.89204351
		P value[upper Tail]	0.10795649
		P value[two Tail]	0.21591298
		S1^2	22		n1	10		Df1	9
		S2^2	25		n2	8		Df2	7
		F =	0.88		Sifnificance =	0.05
		P-value	0.58097589		Fcritical	3.676675
			0.41902411
		P-value	1.1620
		Sample Size(n)	14
		Significance	95%
			5%		Critical
		Sig1	0.025	0.975	24.7356		Interval Estimate						Exhibit 11-5
		Sig2	0.975	0.025	5.008751		210.2233	1038.183
		DF	13										n = 14	H0: σ2 ≤ 410
		Confidence Coefficient	95%										s = 20	Ha: σ2 > 410
		Standard Deviation(S)	20
		Sample variance(S^2)	400										The test statistic for this problem equals _____.
			1.81											a. 13.33
		Variance from Hypotheis	410											b. 12.68
														c. .63
		test Statistic[X^2]	12.68											d. 13.66
		P value[Lower Tail]	0.52740924
		P value[upper Tail]	0.47259076
		P value[two Tail]	0.94518152
													Consider the following.
		S1^2	24		n1	27		Df1	26
		S2^2	27		n2	12		Df2	11					Sample A	Sample B
													s2	24	27
		F =	0.88888889		Sifnificance =	0.05							n	14	12
		P-value	0.61763023		Fcritical	2.594296
			0.38236977										We want to test the hypothesis that population B has a smaller variance than population A.
		P-value	1.2353
													The test statistic for this problem equals _____.
														a. 1.13
														b. 1.17
														c. 0.86
	The value of F0.01 with 6 numerator and 22 denominator degrees of freedom is _____.													d. 0.89
		numerator	6
		Denominator	22
		F =	0.01
		P-value	3.76
		S1^2	22		n1	10		Df1	9					Sample A	Sample B
		S2^2	25		n2	8		Df2	7				s2	22	25
													n	10	8
		F =	0.88		Sifnificance =	0.05
													We want to test the hypothesis that population B has a smaller variance than population A.
		P-value	0.58097589		Fcritical	3.676675
			0.41902411										The test statistic for this problem equals _____.
		P-value	1.1620
	A sample of 20 cans of tomato juice showed a standard deviation of 0.4 ounce. A 95% confidence interval estimate of the variance for the population is _____.
		Sample Size(n)	20
		Significance	95%
			5%		Critical
		Sig1	0.025	0.975	32.85233		Interval Estimate
		Sig2	0.975	0.025	8.906516		0.092535	0.341323
		DF	19
		Confidence Coefficient	95%
		Standard Deviation(S)	0.4
		Sample variance(S^2)	0.16
			1.81
		Variance from Hypotheis	3.2761
		test Statistic[X^2]	0.93
		P value[Lower Tail]	3.9385E-10
		P value[upper Tail]	1
		P value[two Tail]	7.8771E-10
		Sample Size(n)	27
		Significance	90%										Consider the following.
			10%		Critical
		Sig1	0.05	0.95	38.88514		Interval Estimate						n = 27	H0: σ2 = 650
		Sig2	0.95	0.05	15.37916		451.9979	1142.846					s2 = 676	Ha: σ2 ≠ 650
		DF	26
		Confidence Coefficient	90%
		Standard Deviation(S)	46										The test statistic for this problem equal
		Sample variance(S^2)	676
		Variance from Hypotheis	650
		test Statistic[X^2]	27.0
		P value[Lower Tail]	0.59276209
		P value[upper Tail]	0.40723791
		P value[two Tail]	0.81447583
	The value of F0.05 with 9 numerator and 15 denominator degrees of freedom is _____.
		numerator	9
		Denominator	15
		F =	0.05
		P-value	2.59