Question 2: (15 pts) Participants are measured on a 10-point depression scale after taking one or another of the following drugs for six months: a placebo, a natural herb (St. John's Wort), a tricyclic antidepressant (Elavil), and an SSRJ drug (Prozac). The mean, and variance depression rating for each group is shown in the following table. ___ St. John's Wort ___ -- -_ We are interested in testing whether, at the signicance level a = .01, the population variances of depression rating for the four drugs are the same. Assume the normality of amount of damage to the auto for three types of autos. (a) State the null and alternate hypotheses, (b) Report the value of the test statistic, (c) Find the critical value, and (d) Report your decision regarding the null hypothesis and your conclusion in the context of the problem. Question 4: (20 pts) A small independent stock broker has created four sector portfolios for her clients. Each portfolio always has five stocks that may change from year to year. The volatility (coefcient of variation) of each stock is recorded for each year. Table below shows the descriptive statistics for the study. Toe 2007 2007 Health 22.2 15.74 5.765 3.253 7.407 3.798 27.567 10.028 0.688 8.057 2007 18.36 2009 27.98 2009 mm 22.84 2009 25-46 2009 23-92 E 2007 18.52 a) Write down a contrast that compares I. Year 2007 and Year 2009 II. Energy type and Health type b) If we are interested in just the two comparisons in (a), use the Bonferroni method to test the comparison in a(II). Consider a2 = 0.05. Question 5: (20 pts) A student taking a cognitive psychology class decides to conduct a memory experiment examining recall for nonsense (e.g., sleemta) versus real (e. g., sleeve) words. In his study, she had 24 subjects. Half of the participants in his study learn nonsense words while the other half study real ones. The student decide to also see how the environment where the learning occurs affects recall, so that half the students learn their words in a very warm room (Le, 82 degrees F) while the remaining students are placed in an ambient room (70 degrees F) during the study. (a). What type of model would be most appropriate to analyze the data? Why? (b). Write an appropriate model according to your answer for part (a), clearly explaining each term in the model. (c). Write appropriate null and alternative hypotheses that can be used to answer the researcher's questions. (d). Complete the following ANOVA table based on your model in part b. Source Learning Environment Word T p e Interaction Error Total (e). Use the AN OVA table in (d) to perform a test of the hypotheses in part (c). (1:.05 Question 6: (20 pts) A psychologist compares the mean amount of time of Rapid Eye Movement (REM) sleep for subjects under four conditions. She uses four groups of subjects, with 10 subjects in each group. The SAS output for the analysis is shown in next pages. Use this output to answer the following questions. (a) Write an appropriate ANOVA model for this research question. (b) Specify the appropriate null and alternative hypotheses for this research question. Perform a test of hypothesis using significance level a= .05 and report the observed test statistic, p-value and your decision regarding the null hypothesis and your conclusion in the context of the problem. (c) If you see any differences in part (b), using the Tukey method find out where the differences are. Use a= .05. (d) Use the SNK method to find out where the differences are. Consider the individual comparison error rate a= .05. Do the results agree with those of the Tukey method in (c). (e) Use the Bonferroni method to test all the pairwise comparisons. Consider ay= .05.Do the results agree with those of the Tukey method in (c) and (d)? (f) Test the homogeneity of variances among the four groups at significance level a= .05 using the Bartlett test. Specify the appropriate null and alternative hypotheses. Report the observed test statistic, p-value and your decision regarding the null hypothesis