Question

A simple random sample from a population with a normal distribution of 108 body temperatures has x = 98.30 degrees F° and s = 0.68 degrees F°

Construct a 95% confidence interval estimate of the standard deviation of body temperature of all healthy humans.

(Round to two decimal places as needed.)

Answer 1

Solution :

Given that,

s = 0.68

s² = 0.4624

n = 108

Degrees of freedom = df = n - 1 = 108 - 1 = 107

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 = 137.517

²_R = ²_{1 - /2,df} = 80.267

The 95% confidence interval for is,

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

107 * 0.4624 / 137.517 < < 107 * 0.4624 / 80.267

0.60 < < 0.79

(0.60 , 0.79)