Question

A simple random sample from a population with a normal distribution of 106 body temperatures has x overbarequals98.50degrees Upper F and sequals0.65degrees Upper F. Construct a 95​% confidence interval estimate of the standard deviation of body temperature of all healthy humans.

Answer 1

Solution :

Given that,

c = 0.95

s = 0.65

n = 106

At 95% confidence level the is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

/2,df = 0.025,105 = 135.25

and

1- /2,df = 0.975,105 = 78.54

2L = 2/2,df = 135.25

2R = 21 - /2,df = 78.54

The 95% confidence interval for is,

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

0.65( 106 - 1 ) / 135.25 < < 0.65 ( 106 - 1 ) / 78.54

0.57 < < 0.75

( 0.57 , 0.75)