A store owner was interested in researching the mean amount spent ($) per customer. A random sample of 76 customer transactions was collected. The mean was $40 with a standard deviation of $5.

a) The store owner was interested in creating a 99% confidence interval to estimate the population mean spend per customer per transaction.

The store owner provided the following workings for the confidence interval:

40 +/- square root (1.96*5/76) = 38 +/- 0.359 = (39.64, 40.36) in $million

State THREE MISTAKES with this solution AND EXPLAIN how you would CORRECT THESE MISTAKES, but do NOT create another confidence interval. [5 marks]

b) The store owner who created the confidence interval, offered the following interpretation:

"We are 90% confident that the probability the customers have a sample mean transaction per shop is between 39.64 and 40.36 in $million.

State THREE MISTAKES with this solution AND EXPLAIN how you would CORRECT THESE MISTAKES, but do NOT create another confidence interval. [3 marks]

c) The store owner collected the sample of data, by asking shoppers leaving the store, on a Wednesday afternoon, how much they had spent. Briefly explain to the store owner, an error with their sampling method