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. Which of the following is the appropriate critical value(s) to test the manager's claim at the 5% significance level? A) 1.645 B) 1.668 C) 1.960 D) 1.997

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Quizplus · Accepted Answer

Since the population standard deviations are unknown and unequal, we must use the t-distribution for the hypothesis test. The appropriate critical value(s) for a two-tailed test at the 5% significance level with 34 degrees of freedom (df= n1+n2-2=36+36-2=70) is t=1.668, obtained from a t-distribution table or a calculator. Therefore, if the calculated t-statistic is greater than 1.668 or less than -1.668, we would reject the null hypothesis and conclude that there is evidence that the downtown restaurant generates more revenue than the restaurant by the freeway.

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