A restaurant chain has two locations in a medium-sized town and, believing that it has oversaturated the market for its food, is considering closing one of the restaurants. The manager of the restaurant with a downtown location claims that his restaurant generates more revenue than the sister restaurant by the freeway. The CEO of this company, wishing to test this claim, randomly selects 36 monthly revenue totals for each restaurant. The revenue data from the downtown restaurant have a mean of $360,000 and a standard deviation of $50,000, while the data from the restaurant by the freeway have a mean of $340,000 and a standard deviation of $40,000. Assume there is no reason to believe the population standard deviations are equal, and let μ₁ and μ₂ denote the mean monthly revenue of the downtown restaurant and the restaurant by the freeway, respectively. At the 5% significance level, does the evidence support the manager's claim? A) No, because the test statistic value is less than the critical value. B) Yes, because the test statistic value is less than the critical value. C) No, because the test statistic value is greater than the critical value. D) Yes, because the test statistic value is greater than the critical value.

Question

Quizplus · Accepted Answer

To determine if the evidence supports the manager's claim, we can conduct a two-sample t-test for the difference in means. The null hypothesis (H0) would state that there is no difference in mean monthly revenue between the two restaurants (μ1 - μ2 = 0), while the alternative hypothesis (Ha) would claim that the downtown restaurant has a higher mean monthly revenue (μ1 - μ2 > 0). Given the sample means, standard deviations, and sizes, we calculate the test statistic. If the test statistic is greater than the critical value from the t-distribution at the 5% significance level, we reject the null hypothesis in favor of the alternative, supporting the manager's claim. The details provided do not include the exact test statistic or critical value, but the correct interpretation is that if the test statistic is indeed greater than the critical value, it indicates the evidence supports the manager's claim that the downtown restaurant generates more revenue.

A Restaurant Chain Has Two Locations in a Medium-Sized Town