## Due Date

Due Fri, Sep 27, 2013.

## First Problem

For the data in Table 3.3 in Hollander and Wolfe (H & W) also at http://www.stat.umn.edu/geyer/5601/hwdata/t3-3.txt

1. Do a Wilcoxon signed rank test of the hypotheses described in Problem 3.1 in Hollander and Wolfe. Describe the result of the test in terms of "statistical significance".
2. Also compute the Hodges-Lehmann estimator and confidence interval for the shift parameter that go with the signed rank test with as close as you can get to 95% confidence. (The phrase as close as you can get means either above or below whichever is closer. Note this is different from the example, which always is above.) (Note: The R function `wilcox.test` seems broken for the confidence interval. Don't use it.)
3. Do a sign test of the same hypotheses as in part (a).
4. Also compute the Hodges-Lehmann estimator and confidence interval for the shift parameter that go with the sign test with as close as you can get to 95% confidence.
5. Comment on the differences between the two procedures, including any differences in required assumptions, and in theoretical properties such as asymptotic relative efficiency.
6. Repeat parts (a), (b), (c), and (d) above except use fuzzy P-values and fuzzy confidence intervals done by the R package `fuzzyRankTests` except for the point estimates (there are fuzzy tests, and fuzzy confidence intervals, but no fuzzy point estimates).

(The problem just above is Problems 3.1, 3.19, 3.27, 3.63 in H & W and more.)

## Second Problem

For the data in Table 3.6 in H & W also at http://www.stat.umn.edu/geyer/5601/hwdata/t3-6.txt repeat parts (a) and (b) above. Read 3.43 in place of 3.1 in part (a). Also produce a fuzzy P-value for the test, call this part (c). Make a plot, either the PDF or the CDF of the fuzzy P-value (your choice). (You do not need to produce a fuzzy confidence interval.)

(The problem just above is Problem 3.12 in H & W and more. Oddly, most of the problem statement is in 3.43. Only the test to do is stated in 3.12.)

## Third Problem

Problem 3.54 in H & W. The data are in the problem statement also at http://www.stat.umn.edu/geyer/5601/hwdata/p3-54.txt. Since this is all about ties (zeroes), also produce the fuzzy P-value.

Note: This problem is about the sign test. You can tell because it is in a section (3.4) of the textbook about the sign test (and no other way).

## Fourth Problem

Problem 3.87 in H & W. The data are in Table 3.9 in H & W also at http://www.stat.umn.edu/geyer/5601/hwdata/t3-9.txt.

Note: This problem is about the signed rank test. You can tell because it is in a section (3.7) of the textbook about the signed rank test.

## Answers

Answers in the back of the book are here.