Given the following information about a hypothesis test of the difference between two variances based on independent random samples,what is the critical value of the test statistic at a significance level of .05? Assume that the samples are obtained from normally distributed populations. $H _ { A } : \sigma ^ { 2 } A \sigma ^ { 2 } B , \bar { X } _ { 1 } = 12 , \bar { X } _ { 2 } = 9 , s _ { 1 } = 5 , s _ { 2 } = 3 , n _ { 1 } = 13 , n _ { 2 } = 10$
A)3.87
B)3.44
C)3.07
D)2.8
E)2.38

Question

Given the following information about a hypothesis test of the difference between two variances based on independent random samples,what is the critical value of the test statistic at a significance level of .05? Assume that the samples are obtained from normally distributed populations. $H _ { A } : \sigma ^ { 2 } A > \sigma ^ { 2 } B , \bar { X } _ { 1 } = 12 , \bar { X } _ { 2 } = 9 , s _ { 1 } = 5 , s _ { 2 } = 3 , n _ { 1 } = 13 , n _ { 2 } = 10$
A)3.87
B)3.44
C)3.07
D)2.8
E)2.38

Quizplus · Accepted Answer

The test statistic for testing the difference between two variances based on independent random samples follows the F-distribution.

The formula for the test statistic is:

F = (s1^2 / s2^2)

Where s1^2 is the sample variance of sample 1, and s2^2 is the sample variance of sample 2.

The critical value of the test statistic at a significance level of .05 can be obtained from an F-table with degrees of freedom df1 = n1-1 (for sample 1) and df2 = n2-1 (for sample 2).

Using the values given in the problem, we get:

F = (5^2/3^2) = 8.33

df1 = 13-1 = 12

df2 = 10-1 = 9

Looking at the F-table, with df1 = 12 and df2 = 9, at a significance level of .05, the critical value is 3.07.

Therefore, the best choice is C) 3.07.

Given the Following Information About a Hypothesis Test of the Difference