James Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB.His staff randomly selected personnel files for 10 tellers in the southwest region, and determined that their mean training time was 25 hours and that the standard deviation was 5 hours.Assume that training times are normally distributed.The 90% confidence interval for the population variance of training times is ________.
A)11.83 to 83.33
B)2.37 to 16.67
C)2.66 to 13.51
D)13.30 to 67.67
E)15.00 to 68.00

Question

Quizplus · Accepted Answer

The confidence interval for the population variance is calculated using the chi-square distribution. With a sample size of 10, the degrees of freedom is 9. Using the chi-square distribution table, the 90% confidence interval for the variance is calculated as (n-1)s^2/χ²(α/2) to (n-1)s^2/χ²(1-α/2), which results in the interval 13.30 to 67.67.