In Data 4.6 on page 240 we look at finger-tapping rates to see if ingesting caffeine increases average tap rate. Letting μ_cand μ_nrepresent the average tap rate of people who have had coffee with caffeine and without caffeine, respectively, the null and alternative hypotheses are
H₀: μ_c= μ_n
H_a: μ_c> μ_n

Data 4.6 on page 240

Many people feel they need a cup of coffee or other source of caffeine to €˜€˜get going€ in the morning. The effects of caffeine on the body have been extensively studied. In one experiment,14 researchers trained a sample of male college students to tap their fingers at a rapid rate. The sample was then divided at random into two groups of 10 students each. Each student drank the equivalent of about two cups of coffee, which included about 200 mg of caffeine for the students in one group but was decaffeinated coffee for the second group. After a 2-hour period, each student was tested to measure finger tapping rate (taps per minute). The students did not know whether or not their drinks included caffeine and the person measuring the tap rates was also unaware of the groups. This was a double-blind experiment with only the statistician analyzing the data having information linking the group membership to the observed tap rates. (Think back to Chapter 1: Why is this important?) The goal of the experiment was to determine whether caffeine produces an increase in the average tap rate. The finger-tapping rates measured in this experiment are summarized in Table 4.4 and stored in CaffeineTaps.

Table 2.4

(a) Sketch a smooth curve that roughly approximates the distribution in Figure 4.17 and shade in the proportion of area corresponding to the p-value for a difference in average sample tap rates of D = xÌ…_c ˆ’ xÌ…_n = 1.6. Which of the following values is closest to the p-value: 0.60, 0.45, 0.11, or 0.03?

Figure 4.17

(b) On another sketch of the distribution in Figure 4.17, shade in the proportion of area corresponding to the p-value for a difference in average sample tap rates of D = xÌ…_c ˆ’ xÌ…_n = 2.4. Which of the following values is closest to the p value: 0.60, 0.45, 0.11, or 0.03?
(c) Which of the results given in parts (a) and (b) provides the strongest evidence that caffeine increases average finger-tapping rate? Why?

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Caffeine Mean = 248.3 248 246 252 248 250 247 248 245 250 250 246 248 245 44 248 242 244 242 Mean = 244.8 No caffeine 242 246 120 100 - 80- 60 40- 20- -3.2 -2.4 -1.6 -0.8 0.0 0.8 1.6 2.4 3.2 DIfference Frequency