Question

Given in the table are the course evaluation scores for random samples of male professors and female professors. Assume that the two samples are selected from normal distributed populations and do not assume that the population standard deviations are equal. Use 0.05 significance level to test the claim that the male professors and female professors course evaluation scores are from the population with the same mean. Let the male professor as the first population.

	Mean	Standard deviation	Simple size
Male Professor	4.01	0.53	53
Female professor	3.79	0.51	40

1. What is the test statistics?

A. ?=2.025
B. ?=−2.025
C. ?=2.025
D. ?=−2.025
E. ?=71.288

2. State the conclusion for the test.

A. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the male professors and female professors course evaluation scores are from the population with the same mean.
B. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that the male professors and female professors course evaluation scores are from the population with the same mean.
C. Reject the null hypothesis. There is not sufficient evidence to support the claim that the male professors and female professors course evaluation scores are from the population with the same mean.
D. Reject the null hypothesis. There is sufficient evidence to support the claim that the male professors and female professors course evaluation scores are from the population with the same mean.
E. None of the above.

3. What is the confidence level to use if we want to construct the confidence interval that is suitable for testing the claim that the male professors and female professors course evaluation scores are from the population with the same mean?

4. Does the confidence interval support the conclusion found with the hypothesis test?

A. 5%
B. 10%
C. 90%
D. 95%
E. 99%

48. Does the confidence interval support the conclusion?

A. No, because the confidence interval contains zero.
B. No, because the confidence interval contains only positive values.
C. Yes, because the confidence interval contains zero.
D. Yes, because the confidence interval contains only positive values.
E. Yes, because the confidence interval contains only negative values.

Answer 1

Since the population standard deviations are unknown, we shall use t-test for the difference between means. It is also given that the population variances (or standard deviations) are assumed to be unequal.

Null Hypothesis (H0): The male professors and female professors course evaluation scores are from the population with the same mean (claim). ​​​​​​.

Alternative Hypothesis (H1): The male professors and female professors course evaluation scores are not from the population with the same mean. ​​​​​​.

(where, =the population mean of course evaluation scores of male professors; =the population mean of course evaluation scores of female professors).

1.

Option A. "?=2.025" is correct.

2.

Option C. "Reject the null hypothesis. There is not sufficient evidence to support the claim that the male professors and female professors course evaluation scores are from the population with the same mean" is correct.

3.

Option D. "95%" is correct.

Confidence level =1 - significance level =1 - 0.05 =0.95 =95%.

4.

Option D. "Yes, because the confidence interval contains only positive values" is correct.

95% confidence interval for the difference between population means =(0.004, 0.436).

Here is the hypothesis test:

The degrees of freedom, df is calculated by using the following formula: