In a randomized, double-blind study reported in the Journal of American Medical Association, researchers Waber et al. (2008) administered a pill to each of 82 healthy paid volunteers from Boston, Massachusetts, but told half of them that the drug had a regular price of $2.50 per pill, whereas the remaining participants were told that the drug had a discounted price of $0.10 per pill, mentioning no reason for the discount. In the recruitment advertisement the pill was described as an FDA-approved €œopioid analgesic,€ but in reality both groups were administered placebo pills. To simulate pain, the participants were administered electric shocks to the wrist. These shocks were calibrated to each participant€™s pain tolerance, prior to administering the pills. In the article, the researchers present the summary statistics on the calibrated maximum tolerance for the participants for the two groups. Researchers wondered if evidence exists for a difference in average pain tolerance between the two groups. The distribution of maximum tolerance scores are not strongly skewed in either group.

a. Explain why the researchers want to compare the pain tolerance of the treatment groups.
b. State the appropriate null and the alternative hypotheses in the context of the study.
c. Name the appropriate theory-based method you would use to test the hypotheses stated in part (b).
d. State the validity conditions that have to be met to be able to perform the test named in part (c). Are these conditions met? How are you deciding?
e. Regardless of your answer to part (d), perform the theory-based test proposed in part (c). Be sure to include a test statistic value and a p-value in your answer.
f. Interpret your p-value in the context of the study.
g. Determine a 95% confidence interval for comparing the tolerance levels between the two groups.

h. Summarize your conclusions about the research question of the study. Be sure to comment on statistical significance, confidence/estimation, causation, and generalization.

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Mean SD Regular-price pill 51.80 volts 18.70 volts 41 Discount-price pill 54.90 volts 23.30 volts 41