Question

The following hypotheses are given:

H₀ : σ₁² − σ₂² ≤ 0

H₁ : σ₁² − σ₂² > 0

A random sample of eight observations from the first population resulted in a standard deviation of 40. A random sample of forty eight observations from the second population showed a standard deviation of 43. At the 0.10 significance level, is there more variation in the first population?

a. State the decision rule. (Round the final answer to 2 decimal places.)

Reject H₀ if F >                 .

b. Compute the value of the test statistic. (Round the final answer to 2 decimal places.)

Value of the test statistic                

c. What is your decision regarding H_o?

(Click to select)  Do not reject  Reject

Answer 1

As we are testing whether there is more variation in the first population, therefore this is a one tailed test. For 0.1 level of significance, we have for n₁ - 1, n₂ - 1 = 7, 47 degrees of freedom, we have from the F distribution tables here:

Therefore Reject H₀ when F > 1.85

b) The test statistic value here is computed as:

Therefore 0.87 is the value of test statistic value here.

c) As the test statistic value here is 0.87 < 1.85, therefore it lies in the non rejection region and we cannot reject the null hypothesis here. Do not Reject H0 here is the correct answer.