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 variance is different.
B)Fail to reject the null hypothesis and conclude no significant difference in the variance.
C)Reject the null hypothesis and conclude the variance is the same.
D)Fail to reject the null hypothesis and conclude the variance is 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 variance is different. 
B)Fail to reject the null hypothesis and conclude no significant difference in the variance. 
C)Reject the null hypothesis and conclude the variance is the same. 
D)Fail to reject the null hypothesis and conclude the variance is the same.

Quizplus · Accepted Answer

To compare the variance, we need to perform a two-sample F-test. Using the data provided, we can calculate the variance of each professor's grading procedure. Professor A's variance is 24.25 and Professor B's variance is 13.19. The F-statistic is calculated as the ratio of the larger variance to the smaller variance, which gives us 24.25/13.19 = 1.839. Using an F-distribution table with degrees of freedom (9,9) and a significance level of 0.05, we find the critical value to be 2.70. Since our calculated F-statistic is less than the critical value, we fail to reject the null hypothesis that the variances are equal. Therefore, we conclude that there is no significant difference in the variance. The correct answer is B.

Two Accounting Professors Decided to Compare the Variance of Their