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The principal of a middle school claims that test scores of the seventh-graders at his school vary less than the test scores of the seventh-graders at a neighboring school, which have variation described by σ = 14.7. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.A. There is not sufficient evidence to support the claim that the standard deviation is greater than 14.7.B. There is sufficient evidence to support the claim that the standard deviation is greater than 14.7.C. There is sufficient evidence to support the claim that the standard deviation is less than 14.7.D. There is not sufficient evidence to support the claim that the standard deviation is less than 14.7.

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Answer:

C. There is sufficient evidence to support the claim that the standard deviation is less than 14.7.

Step-by-step explanation:

Let σ be the true standard deviation of the test scores of the seventh-graders at principal's school.

Then null and alternative hypotheses are:

[tex]H_{0}[/tex]: σ = 14.7

[tex]H_{a}[/tex]: σ < 14.7

If the conclusion is to reject the null hypothesis, then there is significant evidence that σ<14.7

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