Swimmer’s ear is an infection of the outer ear canal. Consider a study designed to investigate the following claim: A prescription ear drop is effective in relieving swimmer’s ear. Two designs are proposed for the study.
Design A: Obtain 125 volunteers from the population of people with swimmer’s ear. Randomly assign 75 of the volunteers to use the prescription ear drop each day. Assign the remaining 50 volunteers to use a placebo each day. Observe the number of people who experience relief from swimmer’s ear in each group after two weeks.
Design B: Randomly select 125 people from the population of people who have swimmer’s ear to use the prescription ear drop each day and observe the number of people who experience relief from swimmer’s ear after two weeks.

(a) Give an example of what people assigned to use a placebo in Design A might be asked to use instead of the prescription ear drop. Explain the benefit of the placebo in the context of the study.
(b) For which design can the results of the study be generalized to all people who have swimmer’s ear? Explain, in the context of the study, the characteristic of the design that allows for this generalization.

A researcher conducted the study described in Design A and estimated the difference in the proportions of people similar to those in the study who would experience relief for the two treatments. Assume all conditions for inference were met. The resulting 96 percent confidence interval (Prescription Ear Drop minus Placebo) is 0.26±0.17.

(c) Does the 96 percent confidence interval provide evidence to support the claim? Justify your answer.
(d) Suppose that the researcher instead decided to compute a 90 percent confidence interval for the same sample data. Would this change impact your answer in part (c)? Explain your reasoning.

The researcher plans to randomly select people from the study, one at a time and without replacement, to be interviewed. The interviews will continue until 18 people who had received the prescription ear drop are interviewed. Let the random variable D represent the total number of people interviewed.

(e) Explain, in the context of the study, why the random variable D does not follow a binomial distribution.