Question

The waiting times​ (in minutes) of a random sample of 20 people at a bank have a sample standard deviation of 3.4 minutes. Construct a confidence interval for the population variance sigma squared and the population standard deviation sigma. Use a 90 % level of confidence. Assume the sample is from a normally distributed population.

Answer 1

Chi square critical value with 0.10 level with 19 df = 10.117 , 30.144

90% confidence interval for is

(n-1) S² / R < < (n-1) S² / L

(20 - 1) * 3.4² / 30.144 < < (20-1) * 3.4² / 10.117

7.29 <\ < 21.71

90% CI for is ( 7.29 , 21.71 )

90% confidence interval for is

Sqrt [ (n-1) S² / R] < < sqrt [(n-1) S² / L]

sqrt [(20 - 1) * 3.4² / 30.144 ] < < sqrt [(20-1) * 3.4² / 10.117 ]

2.7 < < 4.66

90% CI for is ( 2.7 , 4.66 )