Question

Construct the confidence interval for the ratio of the population variances given the following sample statistics. Round your answers to four decimal places.

n1=20 , n2=22, s12=28.072, s22=16.71, 95%level of confidence

Answer 1

Solution:

Given that,

s1² =28.072

s2² =  16.71

So , s1² / s2² = 28.072/16.71 = 1.67995212448

n₁ = 20

n₂ = 22

d.f._{1 =}  n₁ - 1 = 19

d.f._{2 =}  n₂ - 1 = 21

At 95% confidence level

= 0.05

/ 2 = 0.025 and 1 - ( / 2) = 0.975

= F _0.025,19,21 = 2.442

and

  = F _0.975,19,21 = 0.401

The 95% confidence interval for / is,

(1.67995212448/ 2.442) <   / < (1.67995212448/ 0.401 )

0.6879   < / < 4.1894

The 95% confidence interval for / is   ( 0.6879 , 4.1894)