Economic Growth

Case #9

1. Is it proper to multiply the average order size, $42? 33, by the number of addresses (1,300,000) in the target mailing?

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• a. No, there is far too much variability in responses, including a massive outlier, to have any confidence in this average. The response rate is very low, one would be concerned as to why the rate of response was only 9. 2%. The question would therefore be whether the remaining 90. 8% will follow the same pattern or will they buy anything at all.

2. There is also the question of whether the sampling frame is representative of the population in this case the target mailing list. Is it better, as suggested, to multiply the endpoints of the confidence interval by the target mailing size?

• a. No, it doesn’t show how the data is spread within the range, from the minimum to the maximum. Instead, it only provides the two extremes. Even if the endpoints were within said a 95% Confidence Interval from the mean, the mere fact that we are using the target mailing population makes it improper as the sample mean does not seem to be representative of the population mean.

3. Would it be better to multiply by the size of the frame used to select the random sample? It’s better but, there was not enough of a response to multiply against the entire 600,000 frames. Of that frame, less than a thousandth of a percent responded. 600 samples would have been a better number, unfortunately, the amount of response was less than 10% of the mailings, resulting in an even more minuscule amount of information to represent a large population. In the end, the response is simply not enough to ascertain any real information.

4. Should anything else trouble you about this situation?

• a. The survey forces far too many assumptions on the analysts. There was a very low response rate for the questionnaire, causing the sample to be far too low. As for those who replied with an affirmative answer, the numbers are far too varied to make any real conclusions. There are no insights as to whether the numbers placed to represent the buyer’s wealth, intent to buy, or if it’s simply a number placed in jest. If there was a higher response rate, the mean could be trusted. The targeted mailing market is not well defined. It is unclear whether the 1. 3 million targeted addresses are wealthy, poor, or a mixture of both. It is also unclear as to whether these are new targets or if the 600,000 addresses used to choose the random sample are included.

5. What is your best estimate, with confidence limits, for potential catalog sales?

• a. We are 95% confident after removing the outlier at $228. 26 that sales will fall between $11. 57 and $42. 10. This is because the removal of the outlier vastly affected x? The mean was reduced from $42. 33 to $26. 83, while the standard deviation went from $60. 41 to $24. 02, a difference of $36. 39.

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