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 appropriate decision is ________.
A) increase the sample size
B) reduce the sample size
C) fail to reject the null hypothesis
D) maintain status quo
E) reject the null hypothesis

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 appropriate decision is ________.
A) increase the sample size
B) reduce the sample size
C) fail to reject the null hypothesis
D) maintain status quo
E) reject the null hypothesis

Quizplus · Accepted Answer

The null hypothesis is that the variance of teller training time in the Southwest region is also 8, which can be written as:

H0: σ2 = 8

The alternative hypothesis is that the variance is not equal to 8:

Ha: σ2 ≠ 8

To test this hypothesis, we can use an F-test with the following formula:

F = s2 / σ2

Where s2 is the sample variance and σ2 is the population variance under the null hypothesis. The test statistic follows an F-distribution with n-1 degrees of freedom for the numerator (where n is the sample size) and the degrees of freedom for the denominator equal to the degrees of freedom for the population variance (which we don't know, but assume to be equal in both regions) minus n.

Using the given information, we can calculate the test statistic:

F = 42.5 / 8 = 5.3125

The critical values for an F-distribution with 14 degrees of freedom in the numerator and 28 degrees of freedom in the denominator (assuming equal population variances) at a significance level of 0.10 are 0.4296 and 2.7581.

Since our calculated F-value of 5.3125 is greater than the upper critical value of 2.7581, we reject the null hypothesis. Therefore, we can conclude that the variance of teller training time in the Southwest region is significantly different from 8. The best choice is to reject the null hypothesis (E).

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 $\alpha$