Question

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 study \(^{24}\) 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 4.9. 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. (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? If we use 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?

Short answer

The p-values indicate that sleep likely resulted in better recall ability compared to both the caffeine and placebo, with varying degrees of statistical significance. However, there is insufficient evidence to suggest a significant difference between caffeine and placebo. Therefore, based on this study alone, it would be recommended to get adequate sleep before an exam for better recall ability

Step-by-step solution

Interpreting p-value (Sleep vs Caffeine)

The p-value is \(0.003\) which is less than \(0.05\), which is a typical level of significance. Therefore, we reject the null hypothesis that there is no difference between the sleep and caffeine groups. Based on the test results, there is a significant difference between sleep and caffeine in terms of recall ability. The group with better recall ability is not specified in the question, but since we are rejecting the null hypothesis, one group had significantly better results than the other.

Interpreting p-value (Sleep vs Placebo)

The p-value is \(0.06\) which is greater than \(0.05\) but less than \(0.10\). If we use a \(5\%\) significance level, we fail to reject the null hypothesis, meaning there is not enough evidence to say the sleep group and the placebo group have different recall abilities. However, if we use a \(10\%\) significance level, we reject the null hypothesis and conclude there is a significant difference. The evidence of a difference in mean recall ability is stronger when a \(10\%\) significance level is used.

Interpreting p-value (Caffeine vs Placebo)

The p-value is \(0.22\) which is greater than both \(0.05\) and \(0.10\). This implies that there is insufficient evidence to reject the null hypothesis. There is not enough statistical evidence to suggest a difference in recall ability between the caffeine and placebo groups. Therefore, it would not be justified to conclude that caffeine impairs recall ability based solely on these test results.

Final recommendation based on the study

Considering the results, it cannot be conclusively said that one method is the best before an exam. However, since the sleep group did show a significant difference when compared to both caffeine and placebo groups (at different levels of significance), it could be suggested that getting some sleep might be more beneficial in recalling information. However, individual results can vary and ultimately, it depends on the person who is studying