Subdivision: Trouble in Suburbia
Located on the outskirts of a large city, the suburb of Peaceful Valley comprises approximately 6,000 upscale homes. The subdivision came about 10 years ago when a developer built an earthen dam on Peaceful River and created Peaceful Lake, a meandering 20-acre body of water. The lake became the centerpiece of the development, and the first 1,000 half-acre lots were sold as lakefront property. Now Peaceful Valley is fully developed with 50 streets, all approximately the same length with about 120 houses on each street.
Peaceful Valley's residents are primarily young, professional, dual-income families with one or two school-age children. Peaceful Valley has not been living up to its name in recent months. The Suburb Steering Committee has recommended that the community build a swimming pool, tennis court, and meeting room facility on four adjoining vacant lots in the back of the subdivision. Construction cost estimates range from $1.5 million to $2 million, depending on the size of the facility. Currently, every Peaceful Valley homeowner is billed $100 annually for maintenance, security, and upkeep of the development. About 75% of residents pay this fee. To finance the proposed recreational facility, every Peaceful Valley household would be expected to pay a one-time fee of $500, and annual fees would increase to $250 based on facility maintenance cost estimates. Objections to the recreational facility come from various quarters.
For some, the one-time fee is unacceptable; for others, the notion of a recreational facility is not appealing. Some residents have their own swimming pools, belong to local tennis clubs, or otherwise have little use for a meeting room facility. Other Peaceful Valley homeowners see the recreational facility as a wonderful addition where their children could learn to swim, play tennis, or just hang out under supervision. The president of the Peaceful Valley Suburb Association has decided to conduct a survey to poll the opinions and preferences of Peaceful Valley homeowners regarding the swimming pool, tennis court, and meeting room facility concept. Review the following possible sample methods. Indicate your reactions and answers to the questions associated with each possible method.
1. There is only one street into/out of the subdivision. The president is thinking of paying his teenage daughter to stand at the stop light at the entrance to Peaceful Valley next week between the hours of 7 and 8:30 a.m. to hand out questionnaires to exiting drivers while they wait for the red light to change. The handouts would include addressed, postage-paid envelopes for returns. Identify what sample method the president would be using, list its pros and cons, and indicate how representative a sample would result.
2. The chairperson of the Suburb Steering Committee thinks the 1,000 homeowners whose houses are on the waterfront properties of Peaceful Lake are the best ones to survey because they paid more for their lots, their houses are bigger, and they tend to have lived in Peaceful Valley longer than other residents. If these 1,000 homeowners are used for the sample, what sample method would be involved, what are its pros and cons, and how representative a sample would result?
3. Assume that the Steering Committee chairperson's point that the 1,000 waterfront owners are not the same as the other 5,000 Peaceful Valley Subdivision homeowners is true. How should this fact be used to draw a representative sample of the entire subdivision? Identify the probability sampling method that is most appropriate, and indicate, step-by-step, how it should be applied here.
4. How would you select a simple random sample of those Peaceful Valley homeowners who paid their subdivision association dues last year? What, if any, sample bias, might result from this approach?
5. How could a two-step cluster sample be used here? Identify this sample method and describe how it could be used to select a representative sample of Peaceful Valley households?