Question

The age of managers in particular industry is normally distributed with mean μ=35. A group of 30 managers was sampled and resulted in a mean of 39 and standard deviation of 3.5. Construct a 95% confidence interval for the population standard deviation.

Answer 1

95% confidence interval for $\sigma$ is

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

Sqrt [ (30 - 1) 3.5² / 45.722 ] < $\sigma$ < Sqrt [ (30 - 1) 3.5² / 16.047 ]

2.7003 < $\sigma$ < 4.7051

95% CI is ( 2.7003 , 4.7051)