Question

Consider the following measures based on independently drawn samples from normally distributed populations: (You may find it useful to reference the appropriate table: chi-square table or F table)

Sample 1: s21s12 = 221, and n₁ = 16
Sample 2: s22s22 = 208, and n₂ = 11

a. Construct the 95% interval estimate for the ratio of the population variances. (Round "F" value and final answers to 2 decimal places.)

Confidence interval _______ to _______

B. Using the confidence interval from Part (a), test if the ratio of the population variances differs from 1 at the 5% significance level.

	The 95% confidence interval the value 1. Thus, we conclude that the population variances differ at the 5% significance level.

Answer 1

a) The 95% confidence interval is given by

Here c = 0.95,

Hence the required confidence interval is

B. The hypothesis are

If 1 lies in the above interval we say that population variances does not differ from 1.

Here interval is ( 0.28, 3.25 ) . 1 does not lie in the interval. Hence we conclude that population variances differs from 1, at 5% level of significance.