Refer to the previous exercise comparing improvement scores under two therapies for depression patients.
a. State the null hypothesis of equal population distributions in the context of this experiment.
b. Argue that if the null hypothesis is true, the sampling distribution for the difference in sample means is P( -20) = 2/6, P( -10) = 1/6, P(10) = 1/6, P(20) = 2/6.
c. Find the permutation P-value for testing the null hypothesis in part a (which implies the population mean scores are the same) against the alternative that the population mean improvement score is larger under therapy 1, using the difference in the sample means as a test statistic. Interpret it.