The body mass index BMI for a sample of men and a women are

The body mass index (BMI) for a sample of men and a women are given. Assume the samples are simple random samples from populations with normal distributions. From the chart MEN mean BMI = 25.98 standard deviation = 3.71 From the chart WOMEN mean BMI = 23.19 standard deviation = 6.92 Construct a 95% confidence interval estimate of the standard deviation of BMI for men.

Solution

Confidence Interval
CI = (n-1) S^2 / ^2 right < ^2 < (n-1) S^2 / ^2 left
Where,
S = Standard Deviation
^2 right = (1 - Confidence Level)/2
^2 left = 1 - ^2 right
n = Sample Size

Since aplha =0.05
^2 right = (1 - Confidence Level)/2 = (1 - 0.95)/2 = 0.05/2 = 0.025
^2 left = 1 - ^2 right = 1 - 0.025 = 0.975
the two critical values ^2 left, ^2 right at 9 df are 19.0228 , 2.7
S.D( S^2 )=3.71
Sample Size(n)=10
Confidence Interval = [ 9 * 13.7641/19.0228 < ^2 < 9 * 13.7641/2.7 ]
= [ 123.8769/19.0228 < ^2 < 123.8769/2.7004 ]
= [ 6.512 , 45.8735 ]       
Confidence Interval s.d = [ Sqrt(6.512) < < Sqrt(45.8735) ] = [2.55 < < 6.76 ]