Question

A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 95% confidence interval for the standard deviation, σ, of the scores of all subjects.

A) 17.2 < σ < 27.2

B) 16.9 < σ < 29.3

C) 17.5 < σ < 27.8

D) 16.6 < σ < 28.6

Answer 1

Solution :

Given that,

c = 0.95

s = 21.4

n = 27

At 95% confidence level the is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

/2,df = 0.025,26 = 41.92

and

1- /2,df = 0.975,26 = 13.84

2L = 2/2,df = 41.92

2R = 21 - /2,df = 13.84

The 95% confidence interval for is,

s (n-1) / /2,df < < s (n-1) / 1- /2,df

21.4 ( 27 - 1 ) / 41.92 < < 21.4 ( 27 - 1 ) / 13.84

16.9 < < 29.3

( 16.9 , 29.3)

OPtion B is correct.