A drug store chain provides an app to its customers to track their shopping habits. One statistic the app tracks is the amount of money the customer saves by purchasing sale items. The company's sales team pulls data from the previous year for a random sample of 50 customers. They find that the mean amount of money saved by these customers in the previous year is $154 with a standard deviation of $26.

(a) Construct a 99% confidence interval for the true mean amount of money saved by all customers in the previous year by purchasing sale items.

(b) The sales team would like to repeat this study with the goal of obtaining a smaller margin of error. Propose two changes that would decrease the margin of error. What are potential drawbacks if those changes are implemented?