Problem: Promising Results From a Specialty Catalog Survey
The preliminary survey results just came back on the specialty catalog project, and they look great! The average planned order size was $42.33, well above the $15 that was hoped for. The group leader will probably be delighted-after all, $42.33 for each of the 1,300,000 target addresses comes out to over $55 million in average sales! As part of the preparation for the meeting, one of your responsibilities is to look through the fine print of how the survey was done. The initial memo included few details beyond the $42.33 figure. After some calls, you locate the employee who did most of the work. Here is what you learn. A random sample was drawn from a proprietary database of 600,000 addresses of well-off people who purchase luxury items by mail, and 600 catalogs were mailed together with the questionnaire. You also learn that 55 of the 600 surveys were returned. Of these, 13 indicated that "Yes, I will place an order for items totaling $_________________ before the end of the year." These amounts were $9.97, $12.05, $29.27, $228.26, $6.10, $87.35, $27.48, $8.86, $19.95, $13.29, $44.06, $11.27, and $52.39. Well, you now know that there is substantial variability in order size. The 95% confidence interval about the mean extends from $5.82 to $78.84. Multiplying each of these by the size of the target mailing (1,300,000), you compute bounds from $7.6 million to $102.5 million. So even after taking randomness into account, it seems to look as though there is real money to be made here. Or is there?
Discussion Questions
1. Is it proper to multiply the average order size, $42.33, by the number of addresses (1,300,000) in the target mailing?
2. Is it better, as suggested, to multiply the endpoints of the confidence interval by the target mailing size?
3. Would it be better to multiply by the size of the frame used to select the random sample?
4. Should anything else trouble you about this situation?
5. What is your best estimate, with confidence limits, for potential catalog sales?