Chapter 15.2, Problem 14PB

More on blood pressure Refer to the previous exercise. The analysis there did not take into account the size of the change in blood pressure. Show how to do this with the Wilcoxon signed-ranks test.

1. a. State the hypotheses for that test, for the relevant one-sided alternative hypothesis.
2. b. Construct the sampling distribution for the rank sum of the positive differences when you consider the possible samples that have absolute differences in blood pressure of 20, 25, and 15.
3. c. Using the sampling distribution from part b, find and interpret the P-value. (When every difference is positive, or when every difference is negative, this test and the sign test give the same P-value for a given alternative hypothesis.)

Does exercise help blood pressure? Exercise 10.50 in Chapter 10 discussed a pilot study of people who suffer from abnormally high blood pressure. A medical researcher decides to test her belief that walking briskly for at least half an hour a day has the effect of lowering blood pressure. She randomly samples three of her patients who have high blood pressure. She measures their systolic blood pressure initially and then again a month later after they participate in her exercise program. The table shows the results. Show how to analyze the data with the sign test. State the hypotheses, find the P-value, and interpret.