Question

Exercise 3. Construct a 90% confidence interval for the population standard deviation σ of a random sample of 30 men who have a mean weight of 173.5 pounds with a standard deviation of 12.2 pounds. Assume the population is normally distributed.

Answer 1

Solution :

Given that,

s = 12.2

s² = 148.84

²_L = ²_/2,df = 42.557

²_R = ²_{1 - /2,df} = 17.708

The 90% confidence interval for is,

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

  29 * 148.84 / 42.557 < < 29 * 148.84 / 17.708

10.07 < < 15.61

(10.07 , 15.61)