Question

A simple random sample from a population with a normal distribution of 100 body temperatures has x overbar equals 99.10 degrees and s equals 0.65 degrees Construct an 80​% confidence interval estimate of the standard deviation of body temperature of all healthy humans.

Answer 1

Solution :

Given that,

c = 0.80

s = 0.65

n = 100

At 80% confidence level the is ,

= 1 - 80% = 1 - 0.80 = 0.20

/ 2 = 0.20 / 2 = 0.10

_/2,df = _0.10,99 = 117.41

and

_{1- /2,df} = _0.90,99 = 81.45

²_L = ²_/2,df = 117.41

²_R = ²_{1 - /2,df} = 81.45

The 80% confidence interval for is,

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

0.65( 100 - 1 ) / 117.41< < 0.65( 100 - 1 ) / 81.45

0.60 < < 0.72

( 0.60 , 0.72)