Question

Construct the 95% interval estimate for the ratio of the population variances using the following results from two independently drawn samples from normally distributed populations. (Round "F" value and final answers to 2 decimal places. You may find it useful to reference the appropriate table: chi-square table or F table)

Sample 1: x⎯⎯ 1 = 197, s21 = 21.2, and n1 = 7

Sample 2: x⎯⎯ 2 = 192.9, s22 = 16.7, and n2 = 6

Confidence interval _____ to ______

Answer 1

Solution :

Given that,

s1² = 21.2

s2² = 16.7

s1² / s2² = 21.2/16.7 = 1.26946107784

n1 = 7

n2 = 6

At 95% confidence level ,

= 0.05

/ 2 = 0.05 / 2 = 0.025

1 - (/2) = 0.975

_{F /2,n1 - 1 , n2 - 1} = F_{0.025,6, 5} = 6.98

and

_{F1- /2,n1-1,n2-1} = F_0.975,6,5 = 0.17

The 95% confidence interval for / is,

(s1² / s2²) / _{F /2,n1 - 1 , n2 - 1} < / < (s1² / s2²) / _{F1- /2,n1-1,n2-1}

(1.26946107784 / 6.98) < / < (1.26946107784/ 0.17)

   0.19 < / < 7.47

Confidence interval : 0.19 to 7.47