Customers of a large grocery chain who are members of the chains incentives program spend an average of $45 per visit to the grocery. In an attempt to try and increase the amount spent by these regular customers at their stores, the chain institute a new feature of the incentive program where customers receive an extra 5% discount on groceries when they spend $50 or more. A sample of 100 customers in the program is randomly selected and it is discovered that the next time they go to the store they spend an average of $53 with a standard deviation of $28. a. Does this provide sufficient evidence that the true mean is now significantly more than $45? Conduct appropriate hypothesis test. Be sure to specify your null and alternative hypothesis, test statistic, P value, and conclusion. b. Construct a 99% confidence interval for the true average amount customer spend when this new feature is added to the incentive program .