Question

The duration (in days) of 14 randomly selected space shuttle flights have a standard deviation of 3.54 days. Construct the 99% confidence interval for the population variance and the population standard deviation.

Answer 1

Solution :

Given that,

s = 3.54

Point estimate = s² = 12.5316

n = 14

Degrees of freedom = df = n - 1 = 13

²_L = ²_/2,df = 29.819

²_R = ²_{1 - /2,df} = 3.565

(a)

The 99% confidence interval for ² is,

(n - 1)s² / ²_/2 < ² < (n - 1)s² / ²_{1 - /2}

13 * 12.5316 / 29.819 < ² < 13 * 12.5316 / 3.565

5.46 < ² < 45.70

(b)

The 99% confidence interval for is,

2.34 < < 6.76