Question

16. In a hypothesis test, the claim is μ≤28 while the sample of 29 has a mean of 41 and a standard deviation of 5.9. In this hypothesis test, would a z test statistic be used or a t test statistic and why?

z test statistic would be used as the mean is less than than 30

t test statistic would be used as the sample size is less than 30

t test statistic would be used as the standard deviation is less than 10

z test statistic would be used as the sample size is greater than 30

17. A university claims that the mean time professors are in their offices for students is at least 6.5 hours each week. A random sample of twelve professors finds that the mean time in their offices is 6.2 hours each week. With a population standard deviation of 0.49 hours, can the university’s claim be supported at α=0.05?

Yes, since the test statistic is in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported

No, since the test statistic is not in the rejection region defined by the critical value, the null is rejected. The claim is the null, so is not supported

No, since the test statistic is in the rejection region defined by the critical value, the null is rejected. The claim is the null, so is not supported

Yes, since the test statistic is not in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported

18. A credit reporting agency claims that the mean credit card debt in a town is greater than $3500. A random sample of the credit card debt of 20 residents in that town has a mean credit card debt of $3547 and a standard deviation of $391. At α=0.10, can the credit agency’s claim be supported?

Yes, since p-value of 0.30 is greater than 0.10, fail to reject the null. Claim is null, so is supported

No, since p-value of 0.30 is greater than 0.10, fail to reject the null. Claim is alternative, so is not supported

No, since p-value of 0.30 is greater than 0.10, reject the null. Claim is null, so is not supported

Yes, since p-value of 0.30 is less than 0.54, reject the null. Claim is alternative, so is supported

19. A car company claims that its cars achieve an average gas mileage of at least 26 miles per gallon. A random sample of eight cars form this company have an average gas mileage of 25.2 miles per gallon and a standard deviation of 1 mile per gallon. At α=0.06, can the company’s claim be supported?

Yes, since the test statistic of -2.26 is not in the rejection region defined by the critical value of -1.77, the null is not rejected. The claim is the null, so is supported

No, since the test statistic of -2.26 is in the rejection region defined by the critical value of -1.77, the null is rejected. The claim is the null, so is not supported

Yes, since the test statistic of -2.26 is in the rejection region defined by the critical value of -1.55, the null is rejected. The claim is the null, so is supported

No, since the test statistic of -2.26 is not in the rejection region defined by the critical value of -1.24, the null is not rejected. The claim is the null, so is supported

20. A researcher wants to determine if daily walks together strengthen a marriage. One group of wives and one group of husbands are selected and take walks each day. After 2 weeks, all are asked if they felt their marriage was stronger based on the walks and the results of the two groups are compared. To be a valid matched pair test, what should the researcher consider in creating the two groups?

That the husbands and wives selected were married to each other

That the both groups were positive on marriage before the walks

That all husbands and wives in the test had been married about the same amount of time

That the wives group was positive on marriage before the walks

Answer 1

16. Correct answer: Option (A) t test statistic would be used as the sample size is less than 30

17. Correct answer: (D) Yes, since the test statistic is not in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported.

z Test
Test Statistic, z: -2.1209
Critical z: 1.6449
P-Value: 0.9830

18.
Correct answer: (A) Yes, since p-value of 0.30 is greater than 0.10, fail to reject the null. Claim is null, so is supported.

t Test
Test Statistic, t: 0.5376
Critical t: 1.7291
P-Value: 0.2986

19.
Correct answer: (B) No, since the test statistic of -2.26 is in the rejection region defined by the critical value of -1.77, the null is rejected. The claim is the null, so is not supported