The consumption of caffeine to benefit alertness is a common activity practiced by 90% of adults in North America. Often caffeine is used in order to replace the need for sleep. One recent study compares students€™ ability to recall memorized information after either the consumption of caffeine or a brief sleep. A random sample of 35 adults (between the ages of 18 and 39) were randomly divided into three groups and verbally given a list of 24 words to memorize. During a break, one of the groups takes a nap for an hour and a half, another group is kept awake and then given a caffeine pill an hour prior to testing, and the third group is given a placebo. The response variable of interest is the number of words participants are able to recall following the break.

The summary statistics for the three groups are in Table 4.8. We are interested in testing whether there is evidence of a difference in average recall ability between any two of the treatments. Thus we have three possible tests between different pairs of groups: Sleep vs Caffeine, Sleep vs Placebo, and Caffeine vs Placebo.

Table 4.8

(a) In the test comparing the sleep group to the caffeine group, the p-value is 0.003. What is the conclusion of the test? In the sample, which group had better recall ability? According to the test results, do you think sleep is really better than caffeine for recall ability?
(b) In the test comparing the sleep group to the placebo group, the p-value is 0.06. What is the conclusion of the test using a 5% significance level? Using a 10% significance level? How strong is the evidence of a difference in mean recall ability between these two treatments?
(c) In the test comparing the caffeine group to the placebo group, the p-value is 0.22. What is the conclusion of the test? In the sample, which group had better recall ability? According to the test results, would we be justified in concluding that caffeine impairs recall ability?
(d) According to this study, what should you do before an exam that asks you to recall information?

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Standard Group Sample Size Mean Deviation 15.25 12.25 Sleep Caffeine Placebo 3.3 12 12 3.5 11 13.70 3.0