Does a zinc supplement taken at the onset of cold symptoms reduce the time one has a cold? Five volunteers (Dan, Hal, Joe, Kay, and Zoe) agree to take part in an experiment. Three are assigned completely at random to receive the zinc supplement and the other two receive the placebo. The experiment is double-blind. The results are (times are duration of cold in hours):

zinc: 38(Dan) 31(Joe) 35(Kay)

placebo: 44(Hal) 47(Zoe)

a) there are ten possible ways to assign the subjects

(b)For each, determine the difference in mean length of cold (mean for the placebo group minus mean for the zinc group). Combine any duplicates ( I possibly can not understand what is duplicates) and make a table of the possible mean differences and the corresponding probability of each under the null hypothesis of no treatment effect. (Each of the 10 possible assignments of subjects to treatments has probability 1/10 under the null hypothesis.) This is the permutation distribution.