Suppose you are planning to use a test of the population mean when the populatio

Question

Suppose you are planning to use a test of the population mean when the population standard deviation is known (a z test) to test the following one-tailed hypotheses. H_0: mu lessthanorequalto 0 H_1: mu > 0 Since you want to maximize the power of your study, you are considering which factors might decrease power so that you adjust your plans to avoid them, if possible, before conducting your research. The following are your considerations for decreasing power. Fill in any missing words/values. _____ decreases the power of the z test, because this change in a makes it less likely you will reject the null hypothesis. This change makes it harder to correctly reject a false null hypothesis-meaning that power is decreased. _____ in M decreases the power of the z test, because this change in the _____ of the test statistic for the z test _____ the overall test statistic, making it _____ likely you will reject the null hypothesis. The denominator of the test statistic for the z test is _____, _____ in this denominator decreases the power of the z test, because this change _____ the overall test statistic, making it less likely you will reject the null hypothesis. This denominator increases when either the sample size (n) _____ or the population standard deviation. All of the factors discussed previously affect the power of the z test. As the person making the decisions about how the research will be conducted, which of the following factors can you possibly influence? Check all that apply: M Sample size (n) alpha alpha/Squareroot n

Explanation / Answer

Decrease in level of significance decreases the power of the z-test. Decrease in M decreases the power of the z-test, because this change in the observed value of the test statistic for the z test decreases the overall test statistic making it less likely you will reject the null hypothesis. The denominator of the test statistics is / n. Increase in the denominator decreases the power of the z-test because this change decreases the overall test statistic making it less likely you will reject the null hypothesis. This denominator increases when either the sample size decreases or the population standard deviation increases. M n / n

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