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------------------------------------------------ Consider the hypotheses [tex]H_0: \mu = 103[/tex] versus [tex]H_1: \mu > 103[/tex]. Explain what the director is testing and perform the test at the [tex]\alpha = 0.01[/tex] level of significance. Write a conclusion for the test.

Choose the correct answer below.

A. The director is testing if the sample provides sufficient evidence that the population mean IQ score is actually equal to 103.

B. The director is testing if the sample provides sufficient evidence that the population mean IQ score is actually not greater than 103.

C. The director is testing if the sample provides sufficient evidence that the population mean IQ score is actually not equal to 103.

D. The director is testing if the sample provides sufficient evidence that the population mean IQ score is actually greater than 103.

The director is testing the hypothesis that the population mean IQ score is greater than 103. Without the sample data, the test at the α=0.01 level of significance can't be performed. The conclusion, based on the hypotheses, is that the sample might provide evidence to support the alternative hypothesis.

Explanation:

This question relates to hypothesis testing in statistics, specifically relating to the population mean, μ. The null hypothesis (H0: μ=103) proposes that the population mean IQ is 103, while the alternative hypothesis (H1: μ>103) disputes this, suggesting the average IQ level is greater than 103.

To perform the test at the α=0.01 level of significance, the test statistic and corresponding p-value of the sample data need to be computed. However, without that data, I can't perform the test for you.

So, given the context of the hypotheses, the correct answer is D: The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually greater than 103.

This conclusion is based on the specifics of the hypotheses being tested. It's important to remember that rejecting the null doesn't prove the alternative. It simply means the sample provides enough evidence to support the alternative at the specified level of significance.

Learn more about Hypothesis Testing here:

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