Question

Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. Assume that the population has a nomn to the same number of decimal places as the sample standard deviation. al distribution. Round the confidence interval limits 7) The mean replacement time for a random sample of 20 washing machines is 10.9 years and the standard deviation is 2.7 years. Construct a 99% confidence interval for the standard deviation, o, of the replacement times of all washing machines of this type. 7

Answer 1

Degrees of freedom df = n-1 = 20 - 1 = 19

99% confidence interval for $\sigma$ is

Sqrt [ (n-1) S² / $\chi ^{2}$$\alpha$/2 ] < $\sigma$ < Sqrt [ (n-1) S² / $\chi ^{2}$1-$\alpha$/2 ]

Sqrt [ 19 * 2.7² / 38.582 ] < $\sigma$ < sqrt [ 19 * 2.7² / 6.844 ]

1.9 < $\sigma$ < 4.5

99% CI for $\sigma$ is ( 1.9 , 4.5 )