Question

To find the standard deviation of the diameter of wooden​ dowels, the manufacturer measures 19 randomly selected dowels and finds the standard deviation of the sample to be s equals =0.16. Find the​ 95% confidence interval for the population standard deviation sigma σ. Round to two decimal places.

A. 0.13 less than < sigma σ less than <0.22

B. 0.15 less than < sigma σ less than <0.21

C. 0.11 less than < sigma σ less than <0.25

D. 0.12 less than < sigma σ less than <0.24

Answer 1

Solution :

Given that,

s = 0.16

s² = 0.0256

n = 19

Degrees of freedom = df = n - 1 = 19 - 1 = 18

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 = 31.526

²_R = ²_{1 - /2,df} = 8.231

The 95% confidence interval for is,

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

18 * 0.0256 / 31.256 < < 18 * 0..0256 / 8.231

0.12 < < 0.24

( 0.12 , 0.24)

D. 0.12 less than < sigma σ less than <0.24