Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams, with the following results: At the 5% level of significance, what is the decision regarding the null hypothesis?
A) Reject the null hypothesis and conclude the variances are different.
B) Fail to reject the null hypothesis and conclude no significant difference in the variances.
C) Reject the null hypothesis and conclude the variances are the same.
D) Fail to reject the null hypothesis and conclude the variances are the same.

Question

Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams, with the following results:  At the 5% level of significance, what is the decision regarding the null hypothesis?
A) Reject the null hypothesis and conclude the variances are different. 
B) Fail to reject the null hypothesis and conclude no significant difference in the variances. 
C) Reject the null hypothesis and conclude the variances are the same. 
D) Fail to reject the null hypothesis and conclude the variances are the same.

Quizplus · Accepted Answer

To compare variances, we use the F-test. The null hypothesis is that the variances are equal, while the alternative hypothesis is that they are different. Using a two-tailed F-test with $\alpha=0.05$ and degrees of freedom $(9,9)$, the calculated F-statistic is 3.03, and the critical values are 0.328 and 3.03. Since the calculated F-value is greater than the critical value, we reject the null hypothesis and conclude that the variances are different. Therefore, the best choice is A.

Two Accounting Professors Decided to Compare the Variance of Their