Question

A sample of 40 songs from a student’s iTunes playlist showed a mean length of 3.542 minutes with a standard deviation of 0.311 minute. Construct a 95% confidence interval for the population standard deviation. (Round your answers to 4 decimal places.)

Answer 1

Solution :

Given that,

s = 0.311

s² = 0.096721

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 * 0.096721 / 58.120 < < 39 * 0.096721 / 23.654

0.2548 < < 0.3993

(0.2548 , 0.3993)