Question

A standardized test is given to a seventh grade class and an eleventh grade class. The superintendent believes that the variance in performance for the two grades is different. The sample variance of a sample of 20 test scores from the seventh grade class is 29.56. The sample variance of a sample of 12 test scores from the eleventh grade class is 12.45. Construct the 90 % confidence interval for the ratio of the population variances. Round your answers to four decimal places.

Answer 1

Ans:

100(1- ) percent confidence interval for / is

        
1-(a2)

Given that

alpha=1-0.9=0.1

alpha/2=0.05

n₁=20,n₂=12

df1=20-1=19

df₂=12-1=11

s₁^2=29.56,s₂^2=12.45

critical F values:

FINV(0.05,19,11)=2.6581

1/FINV(0.05,11,19)=0.5348

90% confidence ingterval for ratio of population varainces:

(29.56/12.45)/2.6581< population variance ratio <(29.56/12.45)/0.5348

0.8932< population variance ratio <4.4399