Stat 514       Test 1      Take Home problems

 1. A sample of team batting averages for 5 American League baseball teams yields: Boston .282, Toronto .264, Cleveland .273, Minnesota .259, and Seattle .256.  A sample of team batting averages for 5 National League baseball teams yields: Atlanta .264, Florida .272, Houston .256, Milwaukee .258, and Los Angeles .257.  Based on these data, find a nonparametric estimate of the shift (location difference) parameter, and calculate a 95% confidence interval for the parameter.  Note: Bring all of your calculations for this problem to the in-class test – if using a SAS macro program, use the print=’y’ option.

  2. The book reading experimental data that we used in class has been repeated on a larger data set.  The results were:

                                           group     y
                                            old      7
                                            old      5
                                            old      3
                                            old      3
                                            old      4
                                            old      4
                                            old      3
                                            old      4
                                            old      5
                                            old      3
                                            old      7
                                            old      6
                                            old      4
                                            old      3
                                            old      3
                                            old      3
                                            old      6
                                            old      3
                                            old      3
                                            old      3
                                            new     10
                                            new      5
                                            new      5
                                            new      4
                                            new      4
                                            new      4
                                            new      5
                                            new      3
                                            new      7
                                            new      5
                                            new      3
                                            new      6
                                            new      4
                                            new      6
                                            new      5
                                            new      4
                                            new      3
                                            new      5
                                            new      6
                                            new      8

a. Perform a test of a location difference, to see if subjects with the new treatment read more books than those in the old treatment group.

b. Perform an omnibus test of a difference in distributions between the two groups.

c. What would be an appropriate test to use to test for a scale difference between the two groups?  Briefly explain.

3. On pages 56-7 in our text, the authors discuss the Type I error performance of the RMDhat test.  Briefly summarize (no more than 5 sentences) their results.

4. A small randomized experiment yields the following values for group A: 3.1, 5.6, 4.4, and for group B: 3.7, 6.1, 7.2.   Enumerate the permutation distribution for the Wilcoxon test for these data (by hand), and calculate the permutation p value for the research  hypothesis that the location of group B is larger than for group A.