David Desreumaux, VP of Human Resources of Maritime Boat Manufacturing (MBM), is reviewing the employee training programs of MBM factories.Based on a recent census of personnel, David knows that the variance of worker training time in New Brunswick is 8, and he wonders if the variance in Nova Scotia is the same number.His staff randomly selected personnel files for 15 workers in Nova Scotia, and determined that their mean training time was 25 hours and that the standard deviation was 4 hours.Assume that worker training time is normally distributed in the population.Using $\alpha$= 0.10, the appropriate decision is ___.
A)increase the sample size
B)reduce the sample size
C)do not reject the null hypothesis
D)maintain status quo
E)reject the null hypothesis

Question

Quizplus · Accepted Answer

Since we are trying to determine if the variance in Nova Scotia is the same as in New Brunswick, our null hypothesis is that the variance in Nova Scotia is also 8. Our alternative hypothesis is that the variance in Nova Scotia is not equal to 8.

We will use an F-test to compare the variances of the two populations. Since F1F1F1S1F1F1F10 = 0.10, we need to find the critical value of F with degrees of freedom of (n1-1) and (n2-1) = 14. Using an F-distribution table or calculator, we find that the critical value of F at alpha level 0.10 and degrees of freedom (14,14) is 2.50.

Next, we calculate the test statistic F as follows:

F = s1^2 / s2^2
F = 8 / 4^2
F = 0.50

Since the test statistic F is less than the critical value of 2.50, we do not reject the null hypothesis. Therefore, we can conclude that there is not enough evidence to suggest that the variance in Nova Scotia is different from 8.

David Desreumaux, VP of Human Resources of Maritime Boat Manufacturing α\alphaα

David Desreumaux, VP of Human Resources of Maritime Boat Manufacturing $\alpha$