2. Inference about the difference between two means (equal variances) In an effort to better manage his 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 south side sells more filet mignons per night than the restaurant located on the north side of the city. The statistician selects a random sample of size n1 = 34 nights that the southside restaurant is open. For each night in the sample, she collects data on the number of filet mignons sold at the southside location and computes the sample mean in = 5.13 and the sample variance s? = 49. Likewise, she selects a random sample of size 112 = 44 nights that the northside restaurant is open. For each night in the sample, she collects data on the number oflet mignons sold at the northside location and computes the sample mean i2 = 2.68 and the sample variance 8% = 41. The statistician conducts an F-test of the ratio of two variances, and there is not enough evidence to infer that the population variances differ (you can assume that 01 = 02). Furthermore, histograms of the sample data suggest that the normality conditions are satised. Use the Distributions tool to help you answer the questions that follow. t Distribution Degrees of Freedom = 75 [ 0 0 AAA -5 -4 -3 -I2 -1 o 1 I2 3 4 5 The point estimate of [11 u; is V . The 99% confidence interval estimate of the difference between the mean number of filet mignons sold per night at the southside restaurant and the mean number of filet mignons sold per night at the northside restaurant is LCL = v to UCL = v . The statistician formulates the null and alternative hypotheses as H0: pl l12 = 0, H1: lll - p2 0 and conducts the hypothesis test at the 0.01 significance level. Since the p-value is V , the statistician concludes that there V enough evidence to infer that the mean nightly sales of let mignons differs between the two restaurants