The preliminary survey results just came back on the specialty catalog project, and they look great! The average planned order size was $53.94, well above the $15 that was hoped for. The group leader will probably be delighted-- after all, $53.94 for each of the 1,300,000 target addresses comes out to over $70 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 $53.94 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 togehter with the questionnaire. You also learn that 74 of the 600 surveys were returned. Of these, 9 indicated that 'Yes, I will place an order for items totaling $_____ before the end of the year.' These amounts were $7.97, $12.05, $29.27, $228.26, $2.28, $7.25, $114.39, $31.64, and $52.39.
Well, you now know that there is substantial variability in order size. The 95% confidence interval about the mean extends from $3.10 to $104.79. Multiplying each of these by the size of the target mailing (1,300,000), you compute bounds from $4,030,000 to $136,227,000. So even after taking randomness into account, it seems to look as though there is real money to be made here. OR IS THERE?
QUESTION--- Is it proper to multiply the average order size, $53.94, by the number of addresses (1,300,000)in the target mailing?
I will first point out a few major problems that stroke me right from the get go.
#1) We have a 12% response rate. That means that only 12% of people answered the survey. Though we got enough people to assume the central limit theorem and that our sample will act as the population, this figure is low. There are many reasons why the response rate is low - but perhaps one of them could be that these individuals have no interest in your catalogue.
2) Only 9 individuals said that they would place an order. That is only 1.5% of people. This is the key. What is going ...
The solution examines the survey results for an average order size.