Question

A simple random sample from a population with a normal distribution of 104 body temperatures has x=98.50 degrees Upper F and s=0.64 degrees Upper F. Construct a 99​% confidence interval estimate of the standard deviation of body temperature of all healthy human

Answer 1

Here s = 0.64 and n = 104
df = 104 - 1 = 103

α = 1 - 0.99 = 0.01
The critical values for α = 0.01 and df = 103 are Χ^2(1-α/2,n-1) = 69.785 and Χ^2(α/2,n-1) = 143.712

CI = (sqrt(103*0.64^2/143.712) , sqrt(103*0.64^2/69.785))
CI = (0.5418 , 0.7775)