In a randomized, double-blind study reported in the Journal of American Medical Association, research ers Waber et al. (2008) administered a pil 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 pi, men tioning no reason for the discount. In the recruitment advertisement the pill was described as an FDA-approved opioid analgesic," but in reality both groups were admin istered placebo pills. To simulate pain, the participants were admin istered electric shocks to the wrist. These shocks were calibrated to each participant's pain tolerance, prior to ad ministering the pills. In the article, the researchers present the summary statistics on the calibrated maximum toler- ance for the participants for the two group 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. s. Researchers Mean SD Regular-price pill 41 51.80 volts 18.70 volts Discount-price pill 4 54.90 volts 23.30 volts a. Explain why the researchers want to compare the pain b. State the appropriate null and the alternative hypotheses c. Name the appropriate theory-based method you would d. State the validity conditions that have to be met to be able tolerance of the treatment groups. in the context of the study use to test the hypotheses stated in part (b) to perform the test named in part (c). Are these condi tions 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.