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3. Inference about the difference between two means ( equal variances) Aa Aa 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 prime rib steaks per night than the restaurant located on the west side of the city. The statistician selects a random sample of size nj = 42 nights that the eastside restaurant is open. For each night in the sample, he collects data on the number of prime rib steaks sold at the eastside location and computes the sample mean X1 = 14.32 and the sample variance s1 = 16. Likewise, he selects a random sample of size na = 31 nights that the westside restaurant is open. For each night in the sample, he collects data on the number of prime rib steaks sold at the westside location and computes the sample mean x2 = 12.47 and the sample variance s; = 15. 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 satisfied. Use the Distributions tool to help you answer the questions that follow. t Distribution Degrees of Freedom = 75 -5 -4 -3 - 2 2 The point estimate of #1 - 12 is The 99% confidence interval estimate of the difference between the mean number of prime rib steaks sold per night at the eastside restaurant and the mean number of prime rib steaks sold per night at the westside restaurant is LCL = to UCL = The statistician formulates the null and alternative hypotheses as Ho: 1 - 12 = 0, Hi: p1 - pz # 0 and conducts the hypothesis test at the .01 significance level. Since the p-value is , the statistician concludes that there enough evidence to infer that the mean nightly sales of prime rib steaks differs between the two restaurants