Question

9. Factors affecting power Aa Aa 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-tail hypotheses. H1: 0 Since you want to maximize the power of your study, you are considering which factors might decrease power so that you can 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. (Hint: Remember that for this alternative hypothesis, you will reject the null hypothesis for large values of the test statistic.) 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 X 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 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 test statistic, making it less likely you will reject the null hypothesis. This denominator increases when either the sample size (n) the overall 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 Sample size (n) a/Vn

There are choices for each blank

1. An increase in a (such as using a =0.1 instead of a= 0.05 / A decrease in a (such as using a = 0.01 instead of a 0.05)

2. An increase / A decrese

3. numerator / denominator

4. increase / decrease

5. more / less

6. standard deviation / (standard deviation/root n) / X bar / n

7. A decrease / An increase

8. decrease / increase

9. increase / decrease

Answer 1

1. A decrease in a (such as using a=0.01 instead of a=0.05)

A decrease in a makes the rejection region smaller, hence making it harder to reject the true null hypothesis.

2. A decrease 3. Numerator 4. decrease 5. less

6. Standard deviation 7. Increase 8. decreases 9.increases

The value of a can be adjusted, it depends on the confidence level, suppose if I want to be 95% confident, the value of a will be 1-(0.95)=0.05