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 correct value of the test statistic to analyze the claim? A) t₆₆ = 1.848 B) t₆₇ = 1.848 C) t₆₆ = 1.874 D) t₆₇ = 1.874

Question

Quizplus · Accepted Answer

Since the population standard deviations are not equal, we should use the two-sample t-test with unequal variances. The formula for the test statistic is:
t = (x̄1 - x̄2) / sqrt((s1^2/n1) + (s2^2/n2))
Plugging in the given values, we get:
t = (360,000 - 340,000) / sqrt((50,000^2/36) + (40,000^2/36))
t = 20,000 / sqrt(694,444.4)
t ≈ 1.874
Therefore, the correct answer is C.

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