Exercise 4.82 on page 261 describes a study in which a sample of 24 adults are randomly divided equally into two groups and given a list of 24 words to memorize. During a break, one group takes a 90-minute nap while another group is given a caffeine pill. The response variable of interest is the number of words participants are able to recall following the break. We are testing to see if there is a difference in the average number of words a person can recall depending on whether the person slept or ingested caffeine. The data are shown in Table 4.12 and are available in SleepCaffeine.  

Table 4.12

(a) Define any relevant parameter(s) and state the null and alternative hypotheses.

(b) What assumption do we make in creating the randomization distribution?

(c) What statistic will we record for each of the simulated samples to create the randomization distribution? What is the value of that statistic for the observed sample?

(d) Where will the randomization distribution be centered?

(e) Find one point on the randomization distribution by randomly dividing the 24 data values into two groups. Describe how you divide the data into two groups and show the values in each group for the simulated sample. Compute the sample mean in each group and compute the difference in the sample means for this simulated result.

(f) Use StatKey or other technology to create a randomization distribution. Estimate the p-value for the observed difference in means given in part (c). 

(g) At a significance level of α = 0.01, what is the conclusion of the test? Interpret the results in context.

Exercise 4.82

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

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Mean = 15.25 Mean = 12.25 18 13 Sleep Caffeine 14 11 18 17 21 16 17 14 15 12 13 6. 18 12 14 14 16 10 15 10 으으 Standard Group Sample Size Mean Deviation Sleep Caffeine Placebo 15.25 12.25 12 3.3 12 3.5 11 13.70 3.0