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Statistics: Setting up null and alternative hypotheses, interpreting Type I and Type II errors

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We know from past research that very satisfied customers give the XYZ-Box video game system a satisfaction rating on our rating scale that is at least 42. Suppose that the manufacturer of the XYZ-Box wishes to use a random sample of 65 satisfaction ratings to provide evidence supporting the claim that the mean satisfaction rating for the XYZ-box exceeds 42.

a. Letting m represent the mean satisfaction rating for the XYZ-Box, set up the null and alternative hypotheses needed if we wish to attempt to provide evidence supporting the claim that m exceeds 42.

b. In the context of this situation, interpret making a Type I error; interpret making a Type II error.

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Solution Summary

This posting explains how to set up a null hypothesis and an alternative hypothesis for a sample question that would involve a z-test. It also explains the meaning of a Type I error and a Type II error and describes what each would mean in the context of this example.

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a. When we're setting up the null and alternative hypotheses, remember that you want to reject the null and accept the alternative. So you want your null hypothesis to be the 'uninteresting' finding: the one that would be against your research hypothesis, or what you expect to show in the study. In the above example, the manufacturer hopes to show that the satisfaction rating is greater than 42. This is your alternative ...

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