Problem: In a test of the quality of two television commercials A and B, each commercial was shown in a separate test area six times over a one-week period. In the following week, a telephone survey was conducted to identify individuals who had seen the commercials. The individuals who had seen the commercials were asked to state the primary message in the commercial. Of 200 individuals who saw Commercial A, 60 recalled the primary message, while 63 of 150 individuals who saw Commercial B were able to recall the primary message. Let Populations1 and 2 represent the individuals who saw Commercials A and B, respectively.

Required:

(a) Compute an approximate 99% confidence interval for the difference in the proportions of individuals who saw Commercials A and B who are able to recall the primary message.

(b) Justify the use of the confidence interval formula used in (a).