1. You work as a writer for a local lifestyle magazine that is deciding what the best restaurant in town is. This will be done by using restaurant reviews from Yelp and it has come down to the two fan favorites, restaurant A and restaurant B. On one hand restaurant A is somewhat new, and although it does not have too many reviews yet the ones it has already received have been quite high. On the other hand, restaurant B is an old school local restaurant that has been around for ages and has many solid reviews. Restaurant A has an average rating of u = 4.78 over 31 reviews with a sample standard deviation of o = 0. 41. Restaurant B has an average rating of H = 4. 66 over 152 reviews with a sample standard deviation of o = 0. 24. Assume that both samples of reviews are random samples for which we do not know the true population standard deviations. a. (1.5 points) Build the 95% and 99% confidence interval for the average rating of both restaurant A and restaurant B. You should have two distinct confidence intervals for both restaurants (4 total confidence intervals). b. (1 point) Interpret each of the 95% confidence intervals found in part a). Be as complete as possible. c. (0.5 point) Why is the 95% confidence interval for restaurant A significantly wider than the 95% confidence interval for restaurant B? d. (1.5 points) Build the 95% confidence interval for the difference in average rating between restaurant A and restaurant B (only one confidence interval). e. (1.5 points) Interpret the 95% confidence interval found in part d). Is there evidence of one of the two restaurants being preferred? Why or why not