The owner of a sporting goods store surveys a group of customers on (i) the average amount spent, and (ii) whether they purchased at least one item of clothing.
The results of a sample of 80 customers are:
Average amount spent: X ̅=49.50
Standard deviation: S=9.50.
Number who bought an item of supporter’s apparel: 20.
Construct a 95% confidence interval for the mean amount spent per shopper.
Construct a 95% confidence interval for the proportion of shoppers who bought at least one item of supporter’s apparel.
The owner of a competing store decides to conduct his own survey.
What sample size does he need if he wants to estimate a 90% confidence interval for the mean amount spent to within ±$3.00, assuming a standard deviation of $8.50?
What sample size does he need to estimate a 90% confidence interval for the proportion who purchase at least one item of supporter’s apparel to within ±0.05?
Based on your answers to c) and d), how large a sample should the store owner use?