In a series of tests to study the efficacy of ginkgo biloba on memory, Solomon et al. first looked at differences in memory tests of people six weeks before and after joining the study [“Ginkgo for Memory Enhancement: A Randomized Controlled Trial,” Journal of the American Medical Association (2002, Vol. 288, pp. 835–840)]. For 99 patients receiving no medication, the average increase in category fluency (number of words generated in one minute) was 1.07 words with a standard deviation of 3.195 words. Researchers wanted to know whether the mean number of words recalled was positive.

(a) Is this a one- or two-sided test?

(b) Perform a hypothesis test to determine whether the mean increase is zero.

(c) Why can this be viewed as a paired t-test?

(d) What does the conclusion say about the importance of including placebos in such tests?