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.
1. In this chapter, you studied the chi-square distribution and three principal applications of the distribution.
(a) Outline the basic ideas behind the chi-square test of independence. What is a contingency table? What are the null and alternate hypotheses? How is the test statistic constructed? What basic assumptions underlie this application of the chi-square distribution?
(b) Outline the basic ideas behind the chi-square test of goodness of fit. What are the null and alternate hypotheses? How is the test statistic constructed? There are a number of direct similarities between tests of independence and tests of goodness of fit. Discuss and summarize these similarities.
(c) Outline the basic ideas behind the chi-square method of testing and estimating a standard deviation. What basic assumptions underlie this process?
(d) Outline the basic ideas behind the chi-square test of homogeneity. What are the null and alternate hypotheses? How is the test statistic contructed? What basic assumptions underlie the application of the chi-square distribution?
2. The F distribution is used to construct a one-way ANOVA test for comparing several sample means.
(a) Outline the basic purpose of ANOVA. How does ANOVA avoid high risk due to multiple type I errors?
(b) Outline the basic assumption for ANOVA.
(c) What are the null and alternate hypotheses in an ANOVA test? If the test conclusion is to reject the null hypothesis, do we know which of the population means are different from each other?
(d) What is the F distribution? How are the degrees of freedom for numerator and denominator determined?
(e) What do we mean by a summary table of ANOVA results? What are the main components of such a table? How is the final decision made?