Solved: Comparing Two Variances In Exercises 1926, (a) identify the claim and state H0

Explain how to find the critical value for an F@test.

List five properties of the F@distribution.

List the three conditions that must be met in order to use a two-sample F@test.

Explain how to determine the values of d.f.N and d.f.D when performing a two-sample F@test

In Exercises 58, find the critical F@value for a right-tailed test using the level of significance a and degrees of freedom d.f.N and d.f.D. = 0.05, d.f.N = 9, d.f.D = 16

In Exercises 58, find the critical F@value for a right-tailed test using the level of significance a and degrees of freedom d.f.N and d.f.D.a = 0.01, d.f.N = 2, d.f.D = 11

In Exercises 58, find the critical F@value for a right-tailed test using the level of significance a and degrees of freedom d.f.N and d.f.D.a = 0.10, d.f.N = 10, d.f.D = 15

In Exercises 58, find the critical F@value for a right-tailed test using the level of significance a and degrees of freedom d.f.N and d.f.D.a = 0.025, d.f.N = 7, d.f.D = 3

In Exercises 9 12, find the critical F@value for a two-tailed test using the level of significance a and degrees of freedom d.f.N and d.f.D a = 0.01, d.f.N = 6, d.f.D = 7

In Exercises 9 12, find the critical F@value for a two-tailed test using the level of significance a and degrees of freedom d.f.N and d.f.D a = 0.10, d.f.N = 24, d.f.D = 28

In Exercises 9 12, find the critical F@value for a two-tailed test using the level of significance a and degrees of freedom d.f.N and d.f.D a = 0.05, d.f.N = 60, d.f.D = 40

In Exercises 9 12, find the critical F@value for a two-tailed test using the level of significance a and degrees of freedom d.f.N and d.f.D a = 0.05, d.f.N = 27, d.f.D = 19

In Exercises 13 18, test the claim about the difference between two population variances s2 1 and s2 2 at the level of significance a. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology Claim: s2 1 7 s2 2; a = 0.10. Sample statistics: s2 1 = 773, n1 = 5 and s2 2 = 765, n2 = 6

In Exercises 13 18, test the claim about the difference between two population variances s2 1 and s2 2 at the level of significance a. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology Claim: s2 1 = s2 2; a = 0.05 Sample statistics: s2 1 = 310, n1 = 7 and s2 2 = 297, n2 = 8

In Exercises 13 18, test the claim about the difference between two population variances s2 1 and s2 2 at the level of significance a. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology Claim: s2 1 s2 2; a = 0.01. Sample statistics: s2 1 = 842, n1 = 11 and s2 2 = 836, n2 = 10

In Exercises 13 18, test the claim about the difference between two population variances s2 1 and s2 2 at the level of significance a. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology Claim: s2 1 s2 2; a = 0.05. Sample statistics: s2 1 = 245, n1 = 31 and s2 2 = 112, n2 = 28

In Exercises 13 18, test the claim about the difference between two population variances s2 1 and s2 2 at the level of significance a. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology Claim: s2 1 = s2 2; a = 0.01. Sample statistics: s2 1 = 9.8, n1 = 13 and s2 2 = 2.5, n2 = 20

In Exercises 13 18, test the claim about the difference between two population variances s2 1 and s2 2 at the level of significance a. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology Claim: s2 1 7 s2 2; a = 0.05. Sample statistics: s2 1 = 44.6, n1 = 16 and s2 2 = 39.3, n2 = 12

Comparing Two Variances In Exercises 1926, (a) identify the claim and state H0 and Ha, (b) find the critical value and identify the rejection region, (c) find the test statistic F, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology. Life of Appliances Company A claims that the variance of the lives of its appliances is less than the variance of the lives of Company Bs appliances. A sample of the lives of 20 of Company As appliances has a variance of 1.8. A sample of the lives of 25 of Company Bs appliances has a variance of 3.9. At a = 0.05, can you support Company As claim?

Comparing Two Variances In Exercises 1926, (a) identify the claim and state H0 and Ha, (b) find the critical value and identify the rejection region, (c) find the test statistic F, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.Fuel Consumption An automobile manufacturer claims that the variance of the fuel consumptions for its hybrid vehicles is less than the variance of the fuel consumptions for the hybrid vehicles of a top competitor. A sample of the fuel consumptions of 19 of the manufacturers hybrids has a variance of 0.21. A sample of the fuel consumptions of 21 of its competitors hybrids has a variance of 0.45. At a = 0.01, can you support the manufacturers claim? (Adapted from GreenHybrid)

Comparing Two Variances In Exercises 1926, (a) identify the claim and state H0 and Ha, (b) find the critical value and identify the rejection region, (c) find the test statistic F, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.. Heart Transplant Waiting Times The table at the left shows a sample of the waiting times (in days) for a heart transplant for two age groups. At a = 0.05, can you conclude that the variances of the waiting times differ between the two age groups? (Adapted from Organ Procurement and Transplantation Network)

Comparing Two Variances In Exercises 1926, (a) identify the claim and state H0 and Ha, (b) find the critical value and identify the rejection region, (c) find the test statistic F, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.Golf The table at the left shows a sample of the driving distances (in yards) for two golfers. At a = 0.10, can you conclude that the variances of the driving distances differ between the two golfers?

Comparing Two Variances In Exercises 1926, (a) identify the claim and state H0 and Ha, (b) find the critical value and identify the rejection region, (c) find the test statistic F, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.Science Assessment Tests A state school administrator claims that the standard deviations of science assessment test scores for eighth-grade students are the same in Districts 1 and 2. A sample of 12 test scores from District 1 has a standard deviation of 36.8 points, and a sample of 14 test scores from District 2 has a standard deviation of 32.5 points. At a = 0.10, can you reject the administrators claim? (Adapted from National Center for Education Statistics)

Comparing Two Variances In Exercises 1926, (a) identify the claim and state H0 and Ha, (b) find the critical value and identify the rejection region, (c) find the test statistic F, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.U.S. History Assessment Tests A state school administrator claims that the standard deviations of U.S. history assessment test scores for eighth-grade students are the same in Districts 1 and 2. A sample of 10 test scores from District 1 has a standard deviation of 30.9 points, and a sample of 13 test scores from District 2 has a standard deviation of 27.2 points. At a = 0.01, can you reject the administrators claim? (Adapted from National Center for Education Statistics)

Comparing Two Variances In Exercises 1926, (a) identify the claim and state H0 and Ha, (b) find the critical value and identify the rejection region, (c) find the test statistic F, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.Annual Salaries An employment information service claims that the standard deviation of the annual salaries for actuaries is greater in New York than in California. You select a sample of actuaries from each state. The results of each survey are shown in the figure. At a = 0.05, can you support the services claim? (Adapted from Americas Career InfoNet) s2 = $29,000 n2 = 61 Actuaries in California s1 = $39,700 n1 = 41 Actuaries in New York s1 = $33,000 n1 = 28 Public relations managers in Florida Public relations managers in Louisiana s2 = $18,200 n2 = 24 FIGURE FOR EXERCISE 25 FIGURE FOR EXERCISE 26

Comparing Two Variances In Exercises 1926, (a) identify the claim and state H0 and Ha, (b) find the critical value and identify the rejection region, (c) find the test statistic F, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.Annual Salaries An employment information service claims that the standard deviation of the annual salaries for public relations managers is greater in Florida than in Louisiana. You select a sample of public relations managers from each state. The results of each survey are shown in the figure. At a = 0.05, can you support the services claim? (Adapted from Americas Career InfoNet)

In Exercises 27 and 28, find the right- and left-tailed critical F-values for a two-tailed test using the level of significance a and degrees of freedom d.f.N and d.f.D.a = 0.05, d.f.N = 6, d.f.D = 3

In Exercises 27 and 28, find the right- and left-tailed critical F-values for a two-tailed test using the level of significance a and degrees of freedom d.f.N and d.f.D.a = 0.10, d.f.N = 20, d.f.D = 15

In Exercises 29 and 30, construct the confidence interval for s2 1 s2 2. Assume the samples are random and independent, and the populations are normally distributed. Cholesterol Contents In a recent study of the cholesterol contents of grilled chicken sandwiches served at fast food restaurants, a nutritionist found that random samples of sandwiches from Restaurant A and from Restaurant B had the sample statistics shown in the table. Construct a 95% confidence interval for s2 1 s2 2, where s2 1 and s2 2 are the variances of the cholesterol contents of grilled chicken sandwiches from Restaurant A and Restaurant B, respectively. (Adapted from Burger King Brands, Inc. and McDonalds Corporation.) Cholesterol contents of grilled chicken sandwiches Restaurant A Restaurant B s2 1 = 10.89 s2 2 = 9.61 n1 = 16 n2 = 12 Carbohydrate contents of grilled chicken sandwiches Restaurant A Restaurant B s2 1 = 5.29 s2 2 = 3.61 n1 = 16 n2 = 12 TABLE FOR EXERCISE 29 TABLE FOR EXERCISE 30

In Exercises 29 and 30, construct the confidence interval for s2 1 s2 2. Assume the samples are random and independent, and the populations are normally distributed.Carbohydrate Contents In a recent study of the carbohydrate contents of grilled chicken sandwiches served at fast food restaurants, a nutritionist found that random samples of sandwiches from Restaurant A and from Restaurant B had the sample statistics shown in the table. Construct a 95% confidence interval for s2 1 s2 2, where s2 1 and s2 2 are the variances of the carbohydrate contents of grilled chicken sandwiches from Restaurant A and Restaurant B, respectively. (Adapted from Burger King Brands, Inc. and McDonalds Corporation.)