In: Statistics and Probability
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.
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 )