In an effort to better manage his inventory levels, the owner of two steak and s

Question

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 halibut fillets per night than the restaurant located on the north side of the city. The statistician selects a random sample of size n_1 = 49 nights that the southside restaurant is open. For each night in the sample, she collects data on the number of halibut fillets sold at the southside location and computes the sample mean M_1 = 10.34 and the sample variance s^2_1 = 36. Likewise, she selects a random sample of size n_2 = 36 nights that the northside restaurant is open. For each night in the sample, she collects data on the number of halibut fillets sold at the northside location and computes the sample mean M_2 = 5.00 and the sample variance S^2_2 = 32. The statistician checks and concludes that the data satisfy the required assumptions for the independent-measures t test. Then she computes the 99% confidence interval for estimating the difference between the mean number of halibut fillets sold per night at the southside restaurant and the mean number of halibut fillets sold per night at the northside restaurant. This 99% confidence interval is 5.34 plusminus 3.3895 halibut fillets. If she were to formulate null and alternative hypotheses as H_0: mu_1 - mu_2 = 0, H_1: mu_1 - mu_2 notequalto 0 and conduct a hypothesis test with alpha = .01, she would conclude that there _____ a significant difference between the mean nightly sales of halibut fillets between the two restaurants.

Explanation / Answer

as our confidence interval does not contain 0 as probable values from above confidence interval; there is a signifcant differnece

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