Chapter 10, question 9: answer all please

9. The relationship between confidence intervals and hypothesis testing In an effort to better manage her inventory levels, the owner of two steak and seafood restaurants, both located in the same city, hires a statistician to conduct a statistical study. The owner is interested in whether the restaurant located on the east side sells more filet mignons per night than the restaurant located on the west side of the city. The statistician selects a random sample of size n, = 49 nights that the eastside restaurant is open. For each night in the sample, he collects data on the number of filet mignons sold at the eastside location and computes the sample mean M, = 6.65 and the sample variance s= 36. Likewise, he selects a random sample of size n, = 36 nights that the westside restaurant is open. For each night in the sample, he collects data on the number of filet mignons sold at the westside location and computes the sample mean M, = 4.31 and the sample variance s= 32. The statistician checks and concludes that the data satisfy the required assumptions for the independent-measures t test. Then he computes the 99% confidence interval for estimating the difference between the mean number of filet mignons sold per night at the eastside restaurant and the mean number of filet mignons sold per night at the westside restaurant. This 99% confidence interval is 2.34 + 3.3895 filet mignons. If he were to formulate null and alternative hypotheses as H.: , - , = 0, H,: J, - J, # 0 and conduct a hypothesis test with a = 0.01, the null hypothesis rejected based on the result that a difference of zero in the computed interval. Hence, he would conclude that there a significant difference between the mean nightly sales of filet mignons between the two restaurants