Fourth Examination Study Guide

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1. Understand what might be reasonable null and alternative hypotheses for a given problem (note that for alternative hypotheses there may be more than one “right answer” since we have a choice between one-sided and two-sided hypotheses/tests).

2. Understand the roles of the null and alternative hypotheses in a statistical test.

3. Be able to correctly compute the appropriate test statistic (i.e., $z$ or $t$) for a statistical test.

4. Understand the definition of a p-value — it is a probability, but a probability of what?

5. Understand how to compute a p-value based on a $z$ or $t$ test statstic.

6. Understand the decision rule for whether or not to reject a null hypothesis.

7. Understand what is meant by statistically significant and how it relates to the decision made be a statistical test.

8. Understand how to conduct a statistical test concerning $\mu$ using a confidence interval.

9. Understand simple versus composite hypotheses.

10. How do we conduct a statistical test with a composite null hypothesis?

11. Understand how to conduct a sign test — mainly how do we compute the p-value for the test?

12. What are type I and type II errors?

13. What is the probability of making a type I error (assuming the null hypothesis is true)?

14. How does increasing/decreasing the significance level affect the probabilities of type I and type II errors (assuming such an error is possible)?

15. What is meant by the power of a statistical test?

16. What can be done to increase the power of a statistical test?

17. As usual, be comfortable with notation (e.g., $H_0$, $H_a$, $\mu$, $p$, $\bar{x}$, $s$, $n$, $\hat{p}$, $z$, $t$, $\alpha$).

Formulas/expressions you should understand when and how to use.

$$z = \frac{\hat{p}-p}{\sqrt{p(1-p)/n}}$$ $$t = \frac{\bar{x}-\mu}{s/\sqrt{n}}$$ $$np \ge 15, \ \ \ n(1-p) \ge 15$$