Bounty, a Procter & Gamble (P&G) brand, competes with several other paper towel brands. Brawny has been the market leader for the past several years, while Bounty, Viva, and Scott have been market followers. In an attempt to make Bounty more competitive, its brand manager has decided to undertake an extensive market research investigation of the paper towel market in the United States, in an effort to discover unsatisfied latent needs in paper towel users and identify the strengths and weaknesses of competitors. The manager is hopeful that this endeavor will generate some significant improvements for Bounty that will ultimately result in appreciable market share. In particular, the decision has been made to purchase panel access, meaning that the online survey will be completed by individuals who have joined the ranks of a panel data company and agreed to periodically answer surveys online. Although these individuals are compensated by their panel companies, the companies claim that their panel members are highly representative of the general population. Also, because the panel members have provided extensive information about themselves such as demographics, lifestyles, and product ownership, which is all stored in the panel company database, a client can purchase these data without needing to ask these questions on its survey.

After doing some investigation, the Bounty marketing team has concluded that several panel companies can provide a representative sample of U.S. households. Among these are FocusVision, Innovate, and Lightspeed GMI, and their costs and services seem comparable. For a “blended” online survey of about 25 questions, the cost is roughly $10 per completed response. “Blended” means a combination of stored database information and answers to online survey questions. Thus, the costs of these panel company services are based on the number of respondents, and each company will bid on the work based on the nature and size of the sample.

The Bounty brand manager is operating under two constraints.

First, P&G top management has agreed to pay the total cost for all the research, and it is up to the Bounty brand manager to spend this budget prudently. If a large portion of the budget is expended on a single activity, such as the cost of an online panel sample, there is less available for other research activities. Second, the Bounty brand manager knows that P&G top management will expect this project to have a large sample size. Of course, from past experience, the brand manager realizes that large sample sizes are generally not required from a sample error standpoint, but he must be prepared to respond to questions, reservations, or objections from his P&G managers when the sample size is proposed.

As preparation for the possible need to convince top management that his recommendation is the right decision for the sample size for the Bounty survey, and with the help of his marketing research staff specialist, he decides to make a table that specifies sample error and cost of the sample.

For each of the possible sample sizes listed here, calculate the associated expected cost of the panel sample and the sample error.

1. 20,000 

2. 10,000 

3. 5,000 

4. 2,500 

5. 1,000 

6. 500