Stat 461 Spring 2016 Homework #4 Due Friday, February 12 You must show all of your work in order to receive full and/or partial credit. No work = No Credit. 1. 10 points The bioactivity of four dierent drugs A, B, C, D for treating a particular illness was compared in a study. Complete the following ANOVA table for the data. Source Between treatments Within treatments Total Sums of squares 64.42 Degrees of freedom Mean square F 8.98 2.39 20 An experiment was conducted to test the eects of dierent diets on turkeys. Thirty turkeys were randomly assigned to ve diet groups, six per group. The measured response is weight gain (in pounds). Group Diet 1 Diet 2 Diet 3 Diet 4 Diet 5 4.1 5.2 6.3 6.5 9.2 Weight gains 3.3 3.1 4.2 3.6 4.8 4.5 6.2 5.5 6.1 7.2 7.1 7.4 6.8 7.3 7.5 6.9 9.6 9.2 9.1 9.3 4.4 6.2 6.7 7.0 8.9 2. Inference about a cell mean: 15 points (a) Find a 95% condence interval for 3 . (b) Without actually computing a test statistic, test the following null hypothesis against the two sided alternative: H0 : 3 = 3.50. Use = 0.05. P (c) Compute the appropriate test statistic and use it to test the following null hypothesis against the two sided alternative: H0 : 3 = 3.50. Use = 0.05. (d) Do the results in (b) and (c) agree? Comment on this. 3. Inference about a dierence in two cell means: 15 points (a) Construct a 95% condence interval for 1 2 . (b) Test the hypothesis H0 : 1 2 = 0 versus H0 : 1 2 = 0. Choose an appropriate for your hypothesis test so that it's conclusion will be the same as in (a). 4. Inference about a contrast: 20 points (a) Dene a contrast to make the following comparison: Diet 5 versus the average of all others. (b) Is this contrast signicant at the 0.05 level? Perform a hypothesis test. (c) Construct a 95% condence interval for the contrast dened above. 5. Simultaneous inference about a dierence in means: 20 points (a) For the dierence (1 2 ) in problem 3, a sceptic may claim that the test procedure (and condence interval) used are inappropriate. Explain the sceptic's point of view. (b) Construct appropriate condence intervals for the dierence using Tukey's, Bonferroni's and Scee's methods. Comment on the widths of these intervals. Under what condition is each of these the appropriate one to use. 6. Simultaneous inference for contrasts: 20 points (a) For the contrast dened in problem 4, a sceptic may claim that the test procedure (and condence interval) used are inappropriate. Explain the sceptic's point of view. (b) Construct appropriate condence intervals for the dierence using Bonferroni's and Scee's methods. Comment on the widths of these intervals. Under what condition is each of these the appropriate one to use. Why is Tukey's method not applicable here