Exhibit 10.7. A stats professor at a large university hypothesizes that students

Question

Exhibit 10.7.

A stats professor at a large university hypothesizes that students who take statistics in the morning typically do better than those who take it in the afternoon. He takes independently random samples, each of size 36, consisting of students who took a morning and an afternoon class, and compares the scores of each group on a common final test. He finds that the morning group scored an average of 74 with a standard deviation of 8, while the evening group scored an average of 68 with a standard deviation of 10. The population standard deviation of scores is unknown but assumed to be equal for morning and evening classes. Let 1 and 2 represent the population mean final test scores of statistics courses offered in the morning and the afternoon, respectively.

Refer to Exhibit 10.7. What is the appropriate critical value(s) to test the professor's claim at the 1% significance level?

A) 2.381 and 2.381

B) 2.326 and 2.326

C) 2.326

D) 2.381

Explanation / Answer

Assuming population variances as equal,

Degrees of freedom = n1 + n2 - 2 = 36 + 36 - 2 = 70

For 70 degrees of freedom and one tailed test, critical value at 0.01 significance level

= 2.381

Option D is correct.

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