Comprehensive Exam

Many graduate programs require students to pass a comprehensive exam (or qualifying exam, or something equivalent) before being admitted into candidacy to receive the degree. Suppose the population consists of all comprehensive exams (or equivalent) that are given to students in graduate programs, and of interest is the mean number of questions asked on the comprehensive exams. It is conjectured that the mean number of questions asked on all comprehensive exams is 8, and of interest is to test this conjecture versus the alternative that the mean number of questions asked on all comprehensive exams is different from 8.

State the appropriate null and alternative hypotheses that should be tested.

H0: = 8 versus Ha: < 8

H0: = 8 versus Ha: 8

H0: = 8 versus Ha: > 8

H0: = 8 versus Ha: 8

Consider the information provided and the hypotheses specified in question 1.A simple random sample of 81 comprehensive exams was selected and the number of questions asked on each comprehensive exam in the sample was recorded. The mean number of questions asked for this sample of 81 comprehensive exams was 7.3 with a standard deviation of 3.7. The distribution of the data was bimodal and slightly skewed to the left. If appropriate, use this information to test the hypotheses stated in question 1 at the = .10 level of significance.

What are the assumptions and are they met in this situation?

We had a simple random sample, and the distribution is skewed.Therefore, the assumptions are not satisfied.

The distribution is skewed so the Central Limit Theorem does not apply.

We do not have a simple random sample.

We had a simple random sample, and the sample size is large enough for the Central Limit Theorem to apply (n = 81 > 15). Therefore, the assumptions are satisfied.

Since the population standard deviation is unknown, the test statistic is......

T = -1.703

Z = -1.703

T = 1.703

Z = 1.703

The p-value is .0925. What is the correct decision at = .10 level of significance.

Since p-value < .10 we reject the null hypothesis

Since p-value >.10 we reject the null hypothesis

Since p-value > .10 we fail to reject the null hypothesis

Since p-value < .10 we fail to reject the null hypothesis

Choose the appropriate conclusion.

There is insufficient evidence that mean number of questions asked on all comprehensive exams is not different from 8.

There is sufficient evidence that the mean number of questions asked on all comprehensive exams is different from 8.

There is insufficient evidence that the mean number of questions asked on all comprehensive exams is different from 8.

There is sufficient evidence that the mean number of questions asked on all comprehensive exams is equal to 8.