(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 constructed? What basic assumptions underlie the application of the chi-square distribution?