These are my questions.
1. Suppose that a company wishes to examine the relationship of gender to job satisfaction, grouping job satisfaction into four categories: very satisfied, somewhat satisfied, somewhat dissatisfied and very dissatisfied. The company plans to ask the opinion of 100 employees. Should you, the company statistician, carry out a Chi-squared test of independence or a test of homogeneity?2. The data in the following table are taken from an article in the New York Times {April 20, 2001), "Victim's race affects killer's sentence". The data are from a study of all homicide cases in North lCarolina for the period 1993-1997 in which it was possible that a murder conviction would result in the death penalty. Qualitatively, what do you conclude from looking at the table? Discuss whether it is appropriate to use a Chi-squa red test to test that the combination of the victim's race and the defendant's race was independent of whether the defendant received the death penalty for convicted murderers in North lCarolina during the years 1993-1997. If it is appropriate, perform the test: state the null and alternative hypothesis, calculate the test statistic, and state your decision and conclusion. Defendant's race Victim's race Death -enal No death - enal Not white White \"m 3. Insulin pumps are used by diabetic patients to control blood glucose level, but a side effect, diabetic ketoacidosis [DKA], may occur. Mecklenburg et al. (1984) gathered data on incidence of DKA before and after pump therapy, shown in the following table. Test whether the rate of DKA is the same before and after therapy. State the null and alternative hypothesis, calculate the test statistic, and state your decision and conclusion. Before therapy After then-aw m_s_ 4. Examining medical data relative to students in the elementary school she directs, Miss Carter, the principal, noted that 200 students missed at least 5 days of school when they were 10 and 12; 165 students missed at least 5 days of school at 10 years of age but not at 12 years of age; 235 students missed at least 5 days of school at 12 years of age but not at 10, and 600 did not miss days of school neither at 10 nor at 12 years of age. Conduct a statistical analysis to test whether there was a signicant change in how often students got sick at 10 and 12 years of age. State the null and alternative hypothesis, calculate the test statistic, and state your decision and conclusion. 5. Let X1, X2, ."., Xn be independent random variables following a normal distribution, each with a different mean /; but with common variance o?; that is: Xi~ N(uj, 02) for i = 1,2, ..., n. Let X denote X = _ Show that for i = 1,2, ..., n: Cov(X;, X) = n
