Chapter 14, Problem 36E

Exercises 33 through 36 refer to the following story: The manufacturer of a new vitamin (vitamin X) decides to sponsor a study to determine the vitamin's effectiveness in curing the common cold. Five hundred college students having a cold were recruited from colleges in the San Diego area and were paid to participate as subjects in this study. The subjects were each given two tablets of vitamin X a day. Based on information provided by the subjects themselves, $457$ of the $500$ subjects were cured of their colds within $3$ days. (The average number of days a cold lasts is $4.87$ days.) As a result of this study, the manufacturer launched an advertising campaign based on the claim that “vitamin X is more than $90\%$ effective in curing the common cold.”

Make some suggestions for improving the study.