For each of the situations presented below, propose a specific sampling plan and justify your proposal. Then calculate the appropriate sample size for the study using the information provided. Inflate the sample size to accommodate the incidence rate, reachable rate, and response rate anticipated.

a.An airline is interested in offering a meal service on its flights and wants to determine whether the service will be profitable and useful in enhancing customer satisfaction among members of its frequent flyer program. The frequent flyer program is very popular among the airline's customers, making a census impossible due to the large number of members. Still, the airline wants reliable results that can be generalized to the population of members of its frequent flyer program. Further, it wants to ensure that all levels of the program are represented: elite status, preferred status, and standard.

Currently, the airline estimates that approximately 70% of the members of its frequent flyer program desire access to on-board meals. The airline's executives require a precision level accurate within plus or minus 2% and want to have 95% confidence in the estimate. Because the population is pre-qualified, the incidence rate is 100%. The researcher expects to reach 90% of those selected with a response rate of 30%.

b.A group of business people is considering the purchase of a Curves fitness center franchise for a location in the business district of a moderate-sized town. They are concerned that the monthly fee might be too high and demand would suffer. To address this problem, they decide to survey women who live within a 10-mile radius of the proposed site to assess the monthly amount women would pay for access to a fitness facility.

The business people require an estimate within $10 of the average amount that women would pay and desire 99% confidence in the estimate. Based on past studies, the standard deviation of monthly family expenditures on fitness fees is $20. The incidence rate, defined as the rate of women in the households in the area, is 80%. The researcher expects to reach 50% of households selected, and achieve a 30% response rate.