Question: To test the effectiveness of a new drug designed to relieve pain, 200 patients were randomly selected and divided into two equal groups. One group of 100 patients was given a pill containing the drug while the other group of 100 was given a placebo. What can we conclude about the effectiveness of the drug if 62 of those actually taking the drug felt a beneficial effect while 41 of the patients taking the placebo felt a beneficial effect? Use the following parts to determine a conclusion. Let p_l denote the proportion of those taking the drug who felt a beneficial effect and p₂ denote the proportion of those taking the placebo who felt a beneficial effect.

a. Find the point estimates for the population proportions p₁ and p₂.

b. Construct a 90% confidence interval for each of the population proportions stated above. Determine if there is a difference in the proportions stated above using the confidence intervals.

c. At a = 0.10 and using p-values, test the claim that there is no difference between the proportions stated above.

d. Interpret your results (What can we conclude?)