A study (J. Amer. Med. Assoc., vol. 284, p. 831, 2000) considered whether daily consumption of 1200 mg of garlic could reduce tick bites. The study used a crossover design with a sample of Swedish military conscripts, half of whom used placebo first and garlic second and half the reverse. The authors did not present the data, but the effect they described is consistent with garlic being more effective with 37 subjects and placebo being more effective with 29 subjects. Does this suggest a real difference between garlic and placebo, or are the results consistent with random variation? Answer by:

a. Identifying the relevant variable and parameter. (Hint: The variable is categorical with two categories. The parameter is a population proportion for one of the categories.)
b. Stating hypotheses for a large-sample two sided test and checking that sample size guidelines are satisfied for that test.
c. Finding the test statistic value.
d. Finding and interpreting a P-value and stating the conclusion in context.