Question

29. Use technology to construct the confidence intervals for the population variance sigma squared and the population standard deviation sigma. Assume the sample is taken from a normally distributed population. cequals0.99​, ssquaredequals10.24​, nequals28 The confidence interval for the population variance is ​( nothing​, nothing​). ​(Round to two decimal places as​ needed.)

Answer 1

Solution :

Given that,

Point estimate = s² = 10.24

n = 28

Degrees of freedom = df = n - 1 = 27

²_L = ²_/2,df = 49.645

²_R = ²_{1 - /2,df} = 11.808

The 99% confidence interval for ² is,

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

27 * 10.24 / 49.645 < ² < 27 * 10.24 / 11.808

5.57 < ² < 23.42

(5.57 ,23.42 )