Question

A random sample of 25 workers showed that the average workweek in the United States is down to only 35 hours, largely because of a rise in part-time workers. The variance of the sample was 18.49 hours. Assuming that the population is normally distributed, calculate a 98% confidence interval for the population standard deviation.

Answer 1

Solution :

Given that,

s² = 18.49

²_L = ²_/2,df = 42.980

²_R = ²_{1 - /2,df} = 10.856

The 98% confidence interval for is,

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

  24 * 18.49 / 42.980 < < 24 * 18.49 / 10.856

3.21 < < 6.39

(3.21 , 6.39)