State the null and alternative hypotheses for the test. Determine the critical v

Question

State the null and alternative hypotheses for the test.

Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer(s) to four decimal places.

Compute the value of the test statistic. Round your answer to four decimal places.

Make a decision.

State the test's conclusion. Does the evidence support the claim?

A standardized test is given to a tenth grade class and a seventh grade class. The superintendent believes that the variance in performance from the tenth grade class is greater than the variance in performance from the seventh grade class. The sample variance of a sample of 19 test scores from the tenth grade class is 23.79. The sample variance of a sample of 17 test scores from the seventh grade class is 4.88. Test the claim using a 0.025 level of significance. Let ? represent the population variance for tenth grade class

Explanation / Answer

Solution:

Here, we have to use F test for population variances. The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: Population variances of test scores of tenth grade students and seventh grade students are same.

Alternative hypothesis: Ha: Population variance of test scores of tenth grade students is more than population variance of test scores of seventh grade students.

H0: 12 = 22 versus Ha: 12 > 22

This is an upper tailed or right tailed test. This is one tailed test.

We are given

n1 = 19, S1^2 = 23.79

n2 = 17, S2^2 = 4.88

= 0.025

df1 = n1 – 1 = 19 – 1 = 18

df2 = n2 – 1 = 17 – 1 = 16

Test statistic formula is given as below:

F = S1^2/S2^2 = 23.79/4.88 = 4.8750

Critical value = 2.7170

(By usign F-table)

P-value = 0.0013

(By using F-table)

P-value < = 0.025

So, we reject the null hypothesis that Population variances of test scores of tenth grade students and seventh grade students are same.

There is sufficient evidence to conclude that Population variance of test scores of tenth grade students is more than population variance of test scores of seventh grade students.

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