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?

Name: Problem 102, Chapter 4: Statistics Unlocking the Power of Data
Uploaded: 2022-02-16T19:37:10-08:00
Duration: 3 min 9 s
Channel: Lucas Finney

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?

Statistics Unlocking the Power of Data

Robin H. Lock, Patti… 2nd Edition

Chapter 4, Problem 102

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Solved by Expert Lucas Finney

02/16/2022

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003. This p-value is less than the common significance level of 0.05, so we reject the null hypothesis. This means there is a statistically significant difference in recall ability between the sleep group and the caffeine group. Show more…

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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?

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Key Concepts

Experimental Design

Experimental design refers to the structured approach used to conduct an experiment in order to control for external variables and establish causal relationships. In studies comparing different treatments, this usually involves randomly assigning participants to different treatment groups to ensure that any observed differences can be attributed to the treatments rather than other factors.

Hypothesis Testing

Hypothesis testing is a statistical method used to determine whether there is enough evidence in a sample of data to infer that a certain condition holds for the entire population. In the context of comparing experimental treatments, it involves setting up a null hypothesis (usually stating no difference between groups) and an alternative hypothesis (suggesting a difference exists), and then using a test statistic to calculate a p-value that informs the decision to reject or fail to reject the null hypothesis.

p-value Interpretation

A p-value is the probability of observing data as extreme as, or more extreme than, what was actually observed, assuming that the null hypothesis is true. It is used as a decision tool in hypothesis testing. A small p-value indicates that such extreme results are unlikely under the null hypothesis, leading researchers to reject it in favor of the alternative hypothesis, while a larger p-value suggests insufficient evidence to conclude a difference exists.

Significance Level

The significance level, often denoted by alpha, is a threshold set by the researcher before conducting the test to determine when a p-value is considered sufficiently small to reject the null hypothesis. Common levels are 0.05 or 0.10, which equate to a 5% or 10% risk of concluding that a difference exists when there is none. The choice of significance level affects the sensitivity of the test and the balance between Type I and Type II errors.

Statistical vs Practical Significance

It is important to distinguish between statistical significance and practical significance. Statistical significance means that the observed results are unlikely to have occurred by chance, given the null hypothesis. However, even statistically significant differences may not be practically meaningful if the effect size is small or if the real-world implications are negligible. Researchers must consider both aspects when making conclusions and recommendations based on study results.

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