should be clearly marked. Please put your name in 5. Continue with problem 3 the upper right corner. (a) A Box-Cox transformation of Yr was performed and 1. Recall problem 1 of homework 2 : A rehabilitation cen- the best value of A was found to be A = 0.60. Ding- ter researcher was interested in examining the relationship nostic plots are found on the last page. Would you say between physical fitness prior to surgery and the time (in errors closer to a normal distribution? Explain. days) for successful completion of physical therapy. The (b) The p-values for Shapiro-Wilks, and Brown Forsythe fitness levels were measured as "Below Average" (group D). are (respectively): 0.2984, 0.009843. Would you say "Average" (group II), or "Above Average" (group III). the overall fit has improved? Explain your answer. Diagnostic plots are found on the back page. (c) A transformation of Y* = In(Y ) was also attempted, (a) From the plots, does it appear that the errors are nor- and the diagnostic plots are found on the last page. mally distributed? Justify your answer. Does it appear as though the groups have constant (b) From the plots, does it appear as if there are outliers? variance? Explain your answer. Justify your answer. (d) The p-values for Shapiro-Wilks, and Brown Forsythe (c) From the plota, does it appear that the groups have (for the In transformation) are (respectively): 0.00396, equal variance? Justify your answer. 0.9609. Would you say the overall fit has improved? Explain your answer. (d) Considering the sample size of each group, would you 8liggest removing any observations? Why or why not. (e) Out of the three possible datasets (the original, A = 0.60, and the In transformation), which dataset would 2. Continue with Problem 1. you suggest we use, if any? (a) The Shapiro-Wilks p-value is: 0.8587. State your con- 6. Data was collected on youths (in grades 9-12) on if they clusion about the appropriate hypothesis in terms of smoke cigarettes regularly (Yea, No), if they smoked mari- the problem. juana regularly (YesM, NoM), and the number of hours of (b) The Brown-Forsythe p-value is: 0.7717. State your sleep they get (on average). Group means for all factors, conclusion about the appropriate hypothesis in terms and all treatment levels follow: of the