At two different branches of a department store, pollsters randomly sampled 100 customers at store 1 and 80 customers at store 2, all on the same day. At Store 1, the average amount purchased was $41.25 per customer with a sample standard deviation of $24.25. At Store 2, the average amount purchased was $45.75 with a sample standard deviation of $34.76. Required:
a. Construct a 95% confidence interval for the mean amount purchased per customer in Store 1 and Store 2.
b. Construct a 95% confidence interval for the difference between the means of purchases per customer of the two stores.