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 95% confidence interval for the population variance of training times is ________.
A)11.83 to 83.32
B)2.37 to 16.67
C)2.66 to 13.51
D)13.30 to 67.57
E)15.40 to 68.28

Question

Quizplus · Accepted Answer

To calculate the 95% confidence interval for the population variance when the sample is normally distributed, we use the chi-square distribution. The formula involves the sample variance (s^2), the sample size (n), and the chi-square values for the desired level of confidence. The sample variance here is 5^2 = 25. With n = 10, the degrees of freedom (df) are n-1 = 9. For a 95% confidence interval and 9 degrees of freedom, the chi-square values from tables are approximately 2.7 (lower) and 19.02 (upper). The confidence interval for the variance is calculated as [(n-1)s^2 / χ²_upper, (n-1)s^2 / χ²_lower] = [9*25/19.02, 9*25/2.7] = [11.83, 83.32].