Question

Problem A: A market research director at LED Electronics wants to study women’s spending on electronics. A survey of the store’s credit card holders is designed in order to estimate the proportion of women who purchase their electronics primarily from LED Electronics and the mean yearly amount of money that women spend on electronics. A previous survey found that the standard deviation for the amount women spend on electronics in a year is approximately $35. Cannot use PHstat or Excel for this part. Compute the values manually.

1. What sample size is needed to have a 90% confidence of estimating the population proportion to within ±0.052?

2. What sample size is needed to have 97.5% confidence of estimating the population mean within ± $5?

3. In order to keep the survey costs within budgets, the market research director decided to do a pilot survey of 25 women. The pilot survey results indicate the standard deviation for the amount women spend on apparels is $20. Based on this new information, what additional sample size is needed (i.e. in addition to the pilot survey sample) to have a 97.5% confidence of estimating the population mean within ±$5?

4. If the cost of surveying an additional women is $12, how much money did the market research director save by revising the estimate for sample size (as in part c of the question above) based on the results of the pilot survey compared to the sample size he would have used had he not conducted the pilot survey (as in part b of the question above)?

Problem B: Refer to the Problem A above. Suppose that the market research director cannot afford to survey as many women as required in part (a) of Q7 and has indicated that the maximum sample size can be 100 women. Assume that the sample size is reduced to 100:

1. Without changing the confidence level, indicate specifically what must be changed and by how much?

2. Without changing the margin of error, indicate specifically what must be changed and by how much?

Answer 1