David Desreumaux,VP of Human Resources of American First Banks (AFB),is reviewing the employee training programs of AFB banks. Based on a recent census of personnel,David knows that the variance of teller training time in the Southeast region is 8,and he wonders if the variance in the Southwest region is the same number. His staff randomly selected personnel files for 15 tellers in the Southwest Region,and determined that their mean training time was 25 hours and that the standard deviation was 4 hours. Assume that teller training time is normally distributed. Using $\alpha$
= 0.10,the critical values of chi-square are ________.
A) 7.96 and 26.30
B) 6.57 and 23.68
C) -1.96 and 1.96
D) -1.645 and 1.645
E) -6.57 and 23.68

Question

David Desreumaux,VP of Human Resources of American First Banks (AFB),is reviewing the employee training programs of AFB banks. Based on a recent census of personnel,David knows that the variance of teller training time in the Southeast region is 8,and he wonders if the variance in the Southwest region is the same number. His staff randomly selected personnel files for 15 tellers in the Southwest Region,and determined that their mean training time was 25 hours and that the standard deviation was 4 hours. Assume that teller training time is normally distributed. Using $\alpha$
 = 0.10,the critical values of chi-square are ________.
A) 7.96 and 26.30
B) 6.57 and 23.68
C) -1.96 and 1.96
D) -1.645 and 1.645
E) -6.57 and 23.68

Quizplus · Accepted Answer

Since we are testing if the variance of teller training time in the Southwest region is the same as the variance in the Southeast region, we can use a chi-square test for variance.

The null hypothesis is that the variances are equal, and the alternative hypothesis is that they are not equal.

We know the sample size n = 15, the sample standard deviation s = 4, and the variance of the Southeast region is σ^2 = 8.

We can calculate the test statistic as:

χ^2 = ((n-1)s^2)/σ^2 = ((15-1)*(4^2))/8 = 28.5

Using an F-test with α = 0.10 and degrees of freedom (14, 1), the critical values of chi-square are 6.57 and 23.68.

Since our test statistic of 28.5 is greater than the critical value of 23.68, we reject the null hypothesis and conclude that the variance of teller training time in the Southwest region is not equal to the variance in the Southeast region.

David Desreumaux,VP of Human Resources of American First Banks (AFB),is α\alphaα

David Desreumaux,VP of Human Resources of American First Banks (AFB),is $\alpha$