10. Hypothesis Testing for Two Samples

"Finding a Critical F-Value for a Two-Tailed Test In Exercises 9–12, find the critical F-value for a two-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.10, d.f.N=24, d.f.D=28"

"Finding a Critical F-Value for a Two-Tailed Test In Exercises 9–12, find the critical F-value for a two-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.05, d.f.N=60, d.f.D=40"

"Finding a Critical F-Value for a Two-Tailed Test In Exercises 9–12, find the critical F-value for a two-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.05, d.f.N=27, d.f.D=19"

"In Exercises 9–12, find the critical F-value for a right-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.05,d.f.N=6,d.f.D=50"

"In Exercises 9–12, find the critical F-value for a right-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.01,d.f.N=12,d.f.D=10"

"In Exercises 9–12, find the critical F-value for a right-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.10,d.f.N=5,d.f.D=12"

"In Exercises 13–16, find the critical F-value for a two-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.10,d.f.N=15,d.f.D=27"

"In Exercises 13–16, find the critical F-value for a two-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.05,d.f.N=9,d.f.D=8"

"In Exercises 13–18, test the claim about the difference between two population variances σ₁² and σ₂² at the level of significance α. Assume the samples are random and independent, and the populations are normally distributed.

Claim: σ₁² > σ₂²; α = 0.10.

Sample statistics: s₁² = 773, n₁ = 5 and s₂² = 765, n₂ = 6"

"In Exercises 13–18, test the claim about the difference between two population variances σ₁² and σ₂² at the level of significance α. Assume the samples are random and independent, and the populations are normally distributed.

Claim: σ₁² = σ₂²; α = 0.05.

Sample statistics: s₁² = 310, n₁ = 7 and s₂² = 297, n₂ = 8"

"Performing a Two-Sample F-Test In Exercises 19–26, (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.

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 B’s appliances. A sample of the lives of 20 of Company A’s appliances has a variance of 1.8. A sample of the lives of 25 of Company B’s appliances has a variance of 3.9. At α=0.025, can you support Company A’s claim?"

"Performing a Two-Sample F-Test In Exercises 19–26, (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.

Carbon Monoxide Emissions An automobile manufacturer claims that the variance of the carbon monoxide emissions for a make and model of one of its vehicles is less than the variance of the carbon monoxide emissions for a top competitor’s equivalent vehicle. A sample of the carbon monoxide emissions of 19 of the manufacturer’s specified vehicles has a variance of 0.008. A sample of the carbon monoxide emissions of 21 of its competitor’s equivalent vehicles has a variance of 0.045. At α=0.10, can you support the manufacturer’s claim? (Adapted from U.S. Environmental Protection Agency)"

"Finding Left-Tailed Critical F-Values In this section, you only needed to calculate the right-tailed critical F-value for a two-tailed test. For other applications of the F-distribution, you will need to calculate the left-tailed critical F-value. To calculate the left-tailed critical F-value, perform the steps below.

1. Interchange the values for d.f.N and d.f.D.

2. Find the corresponding F-value in Table 7.

3. Calculate the reciprocal of the F-value to obtain the left-tailed critical F-value.

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

α=0.10, d.f.N=20, d.f.D=15"

"In Exercises 17–20, (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.

A travel consultant claims that the standard deviations of hotel room rates for Sacramento, CA, and San Francisco, CA, are the same. A sample of 36 hotel room rates in Sacramento has a standard deviation of \$51 and a sample of 31 hotel room rates in San Francisco has a standard deviation of \$37. At α=0.10, can you reject the travel consultant’s claim? (Adapted from Expedia)"