Stat 461 Spring 2016 Homework #4 | Complete Solution

Stat 461 Spring 2016 Homework #4

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 di erent drugs A, B, C, D for treat- ing a particular illness was compared in a study. Complete the fol- lowing ANOVA table for the data. Source Sums of squares Degrees of freedom Mean square F P Between treatments 64:42 8:98 Within treatments 2:39
Total 20
An experiment was conducted to test the e ects of di erent diets on turkeys. Thirty turkeys were randomly assigned to ve diet groups, six per group. The measured response is weight gain (in pounds).
Group Weight gains
Diet 1 4.1 3.3 3.1 4.2 3.6 4.4
Diet 2 5.2 4.8 4.5 6.2 5.5 6.2
Diet 3 6.3 6.1 7.2 7.1 7.4 6.7
Diet 4 6.5 6.8 7.3 7.5 6.9 7.0
Diet 5 9.2 9.6 9.2 9.1 9.3 8.9
2. Inference about a cell mean: 15 points
(a) Find a 95% con dence 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.
(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 di erence in two cell means: 15 points
(a) Construct a 95% con dence interval for 1 􀀀 2.
(b) Test the hypothesis H0 : 1􀀀2 = 0 versus H0 : 1􀀀2 6= 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) De ne a contrast to make the following comparison: Diet 5 versus
the average of all others.
(b) Is this contrast signi cant at the 0.05 level? Perform a hypothesis test.
(c) Construct a 95% con dence interval for the contrast de ned above.
5. Simultaneous inference about a di erence in means: 20 points
(a) For the di erence (1􀀀2) in problem 3, a sceptic may claim that the test procedure (and con dence interval) used are inappropri- ate. Explain the sceptic's point of view.
(b) Construct appropriate con dence intervals for the di erence us- ing Tukey's, Bonferroni's and Sce e'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 de ned in problem 4, a sceptic may claim that the test procedure (and con dence interval) used are inappropri- ate. Explain the sceptic's point of view.
(b) Construct appropriate con dence intervals for the di erence us- ing Bonferroni's and Sce e'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?