As a sales analyst for the shoe retailer Foot Locker, one of your responsibilities is measuring store productivity and then reporting your conclusion back to management. Foot Locker uses sales per square foot as a measure of store productivity. While preparing your report for the second quarter results (Q2), you are able to determine that annual sales for last year ran at a rate of $406 per square foot. Therefore, $406 per square foot will be your sales estimate for the population of all Foot Locker stores during Q2. For your Q2 Sales Report, you decide to take a random sample of 64 stores. Using annual data from last year, you are able to determine that the standard deviation for sales per square foot for all 3,400 stores was $80. Therefore $80 per square foot will be your population standard deviation when compiling your Q2 report. For your random sample of 64 stores and using the population standard deviation of $80, you are able to calculate the standard error for your sample: You begin to wonder how a different sample size may affect your conclusion. Maybe a smaller sample size would save you time and money? On the other hand, maybe a larger sample size would offer a smaller standard error and thus a better estimate for management? To explore the effect of sample size on standard error, you substitute different sample sizes into your formula above and then generate a graph showing the results. (Your sample size of 64 is shown in yellow for reference). After looking at the effect of sample size on standard error of the mean, assuming the same population standard deviation, what is the best conclusion? a. Increasing sample size leads to a dramatic increase in the standard error at first, and increasing standard error leads to sample means that are closer to the population mean. b. Increasing sample size leads to a dramatic reduction in the standard error at first, but the benefits of increasing sample size on standard error are reduced as sample size is increased. c. Increasing sample size increases the standard error of the mean; therefore, it is best to use as small a sample as possible in order to minimize data collection and analysis costs. d. Increasing sample size has no effect on the magnitude of the standard error; therefore, using a very small sample size is preferable in order to minimize data collection and analysis costs.
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ase Problem: Foot Locker As a sales analyst for the shoe retailer Foot Locker, one of your responsibilities is measuring store productivity and then reporting your conclusion back to management. Foot Locker uses sales per square foot as a measure of store productivity. While preparing your report for the second quarter results (Q2), you are able to determine that annual sales for last year ran at a rate of $406 per square foot. Therefore, $406 per square foot will be your sales estimate for the population of all Foot Locker stores during Q2. For your Q2 Sales Report, you decide to take a random sample of 64 stores. Using annual data from last year, you are able to determine that the standard deviation for sales per square foot for all 3,400 stores was $80. Therefore $80 per square foot will be your population standard deviation when compiling your Q2 report. |
For your random sample of 64 stores and using the population standard deviation of $80, you are able to calculate the standard error for your sample:
You begin to wonder how a different
After looking at the effect of sample size on standard error of the mean, assuming the same population standard deviation, what is the best conclusion?
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