A random sample of 31 charge sales showed a sample standard deviation of $50. A 90% confidence interval estimate of the population standard deviation is
A)1,715.10 to 4,055.68
B)1,596.45 to 4,466.73
C)39.96 to 66.83
D)41.39 to 63.68

Question

Quizplus · Accepted Answer

We use the chi-square distribution with degrees of freedom equal to n-1 (30 degrees of freedom in this case) and the chi-square values from the table to construct the confidence interval. Using the formula:
(sample standard deviation)^2 * (n-1) / chi-square value
we get the following:

Lower limit: (50)^2 * 30 / 43.77 = 1,577.66
Upper limit: (50)^2 * 30 / 22.04 = 2,587.54

Therefore, the 90% confidence interval estimate of the population standard deviation is 41.39 to 63.68.

A Random Sample of 31 Charge Sales Showed a Sample