Discuss each of the following topics in class or review the topics on your own. Then write a brief but complete essay in which you summarize the main points. Please include formulas and graphs as appropriate.
The most important questions in life usually cannot be answered with absolute certainty. Many important questions are answered by giving an estimate and a measure of confidence in the estimate. This was the focus of Chapter 8. However, sometimes important questions must be answered in a more straightforward manner by a simple yes or no. Hypothesis testing is the statistical process of answering questions with a straightforward yes or no and providing an estimate of the risk in accepting the answer.
1. Review and discuss type I and type II errors associated with hypothesis testing.
2. Review and discuss the level of significance and power of a statistical test.
3. The following statements are very important. Give them some careful thought and discuss them.
(a) When we fail to reject the null hypothesis, we do not claim that it is absolutely true. We simply claim that at the given level of significance, the data were not sufficient to reject the null hypothesis.
(b) When we accept the alternate hypothesis, we do not claim that the null hypothesis is absolutely false. We do claim that at the given level of significance, the data presented enough evidence to reject the null hypothesis.
4. In the text, it is said that a statistical test is a package of five basic ingredients. List these ingredients, discuss them in class, and write a short description of how these ingredients relate to the above discussion questions.
5. As access to computers becomes more and more prevalent, we see the P-value reported in hypothesis testing more frequently. Review the use of the P-value in hypothesis testing. What is the difference between the level of significance of a test and the P-value? Considering both the P-value and level of significance, under what conditions do we reject or fail to reject the null hypothesis?