Question

Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. Assume that the population has a normal distribution. Weights of men: 90% confidence; n = 14, = 155.7 lb, s = 13.6 lb

A. 11.0 lb < σ < 2.7 lb

B. 10.1 lb < σ < 19.1 lb

C. 10.4 lb < σ < 20.2 lb

D. 10.7 lb < σ < 17.6 lb

Answer 1

Solution :

Given that,

c = 0.90

s = 13.6

n = 14

At 98% confidence level the is ,

= 1 - 90% = 1 - 0.90= 0.10

/ 2 = 0.10/ 2 = 0.05

_/2,df = _0.05,13 = 22.36

and

_{1- /2,df} = _0.95,13 = 5.89

²_L = ²_/2,df = 22.36

²_R = ²_{1 - /2,df} = 5.89

The 98% confidence interval for is,

s (n-1) / _/2,df < < s (n-1) / _{1- /2,df}

13.6( 14 - 1 ) / 22.36< < 13.6( 14 - 1 ) / 5.89

10.4< < 20.2

( 10.4, 20.2)

Option c is correct.