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 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

Quizplus · Accepted Answer

The null hypothesis in this case is that the variance of worker training time in Nova Scotia is also 8, while the alternative hypothesis is that it's different from 8. Since we're comparing variances of two populations, we should use the F-test to find out if the difference is significant or not.

The formula for F is:
F = s1^2 / s2^2
where s1^2 is the sample variance of the first population, and s2^2 is the sample variance of the second population.

In this case, s1^2 = 8 (given) and s2^2 = 4^2 = 16 (calculated from the sample). Thus,
F = 8/16 = 0.5

To determine the critical values of F at the 10% level of significance (alpha = 0.10), we need to look up the F-distribution table with degrees of freedom (df1 = n1 - 1 and df2 = n2 - 1) of 14 and 8, respectively. The critical values are 0.417 and 2.700.

Since our calculated F-value of 0.5 falls between these two critical values, we fail to reject the null hypothesis. Therefore, we can conclude that there's not enough evidence to suggest that the variance of worker training time in Nova Scotia is different from 8.

To find the critical values of chi-square, we can rearrange the formula for F to get:
F = s1^2 / s2^2 = 1 / (s2^2 / s1^2) = 1 / (8/16) = 2
Then, we can look up the chi-square distribution table with df = 14 and find the values that correspond to a probability of 0.05 in each tail (because this is a two-tailed test). The critical values are approximately 6.57 and 23.68. Therefore, the answer is B.

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

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