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 test whether the variances are significantly different, we use the F-test. The null hypothesis is that the variances are equal, while the alternative hypothesis is that the variances are different. At the 5% level of significance, we compare the calculated F-value to the critical F-value. If the calculated F-value is greater than the critical F-value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

In this case, the calculated F-value is 18.9, and the critical F-value is 4.53 (using a 5% significance level and degrees of freedom of 9 and 9). Since the calculated F-value is greater than the critical F-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