## 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

- 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".
- 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.) - Do a sign test of the same hypotheses as in part (a).
- 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.
- Comment on the differences between the two procedures, including any differences in required assumptions, and in theoretical properties such as asymptotic relative efficiency.
- 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.