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:

Standard deviation:

Number who bought an item of supporter's apparel: 20.

a)Construct a 95% and 99% confidence interval for the mean amount spent per shopper, and interpret your results, commenting on any differences you might observe.

b)Construct a 90% and 95% confidence interval for the proportion of shoppers who bought at least one item of supporter's apparel. Interpret your results, commenting on any differences you might observe.

The owner of a competing store decides to conduct his own survey.

c)What sample size does he need if he wants to estimate a 90% confidence interval for the mean amount spent to within , assuming a standard deviation of $8.50? How would the sample size change if he were to estimate it a 99% confidence interval instead ? Explain answer.