Chapter 10, Problem 113CP

Mean of permutation distribution Refer to Example 11, which compared two doses of a medication in terms of the number of symptom-free days, using a permutation approach. Table 10.13 and Figure 10.9 showed the sampling distribution of the difference in sample means between the two doses. If truly the population distribution of the number of symptom-free days is identical for both doses (the null hypothesis), what value would you expect for the center of the sampling distribution of ${\bar{x}}_1-{\bar{x}}_2$? Find the mean of the sampling distribution given in Table 10.13. (Hint: Recall the formula for the mean of a discrete probability distribution from Chapter 6.)

Table 10.13 Sampling Distribution of ${\bar{x}}_1-{\bar{x}}_2$ Derived By Considering All Possible Permutations (Assignments).

The table shows each possible difference, how often it occurs among the 10 permutations, and the probability of observing this difference under the null hypothesis.