Question

A standardized test is given to an eighth grade class and a ninth grade class. The superintendent believes that the variance in performance from the eighth grade class is smaller than the variance in performance from the ninth grade class. The sample variance of a sample of 15 test scores from the eighth grade class is 31.01. The sample variance of a sample of 21 test scores from the ninth grade class is 34.54. Test the claim using a 0.005 level of significance. Let ?^2 ? 1 represent the population variance for eighth grade class.

Step 1 of 5 :

State the null and alternative hypotheses for the test.

Step 2 of 5: Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round to 4 decimals.

Step 3 of 5: Compute the value of the test statistic. Round to 4 decimals.

Step 4 of 5: Reject the null or fail to reject the null hypothesis? State the test’s conclusion.

Step 5 of 5: State the tests conclusion. Does the evidence support the claim?

Answer #1

Step 1 of 5 :

Ho:

H1:

Step 2 of 5: Determine the critical value(s) of the test static

left tailed test

Fc=0.246

Step 3 of 5

F=s1^2/s2^2=31.01/34.54=0.8978

test statistic:0.8978

Step 4 of 5:

F stat> Fcrit

Fail to Reject Null hypothesis

Step 5 of5:

Therefore there is no sufficient evidence at 0.5% level of significance to conclude that variance in performance from the eighth grade class is smaller than the variance in performance from the ninth grade class.

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