Question

A simple random sample from a population with a normal distribution of 100 body temperatures has x=98.90 degrees Upper F°F and s=0.63 degrees Upper F°F. Construct an 95​% confidence interval estimate of the standard deviation of body temperature of all healthy humans.

Answer 1

Solution :

Given that,

s = 0.63

s² = 0.3969

n = 100

Degrees of freedom = df = n - 1 = 100 - 1 = 99

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 = 128.422

²_R = ²_{1 - /2,df} = 73.361

The 95% confidence interval for is,

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

99 * 0.3969 / 128.422 < < 99 * 0.3969 / 73.361

0.55 < < 0.73

( 0.55 ,0.73 )