Question

A sample of 40 CDs from a student's collection showed a mean length of 52.74 minutes with a standard deviation of 13.21 minutes. Construct a 95% confidence interval for the population standard deviation. (Use Excel for all calculations and do not round any intermediate calculations. Round your answers to 4 decimal places.)

Answer 1

Solution :

Given that,

s = 13.21

s² = 174.5041

n = 40

Degrees of freedom = df = n - 1 = 39

At 95% confidence level the ² value is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

1 - / 2 = 1 - 0.025 = 0.975

²_L = ²_/2,df = 58.120

²_R = ²_{1 - /2,df} = 23.654

The 95% confidence interval for is,

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

  39 * 174.5041 / 58.120 < < 39 * 174.5041 / 23.654

10.8211 < < 16.9621

(10.8211 , 16.9621)