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 filet mignons per night than the restaurant located on the north side of the city. The statistician selects a random sample of size n 1 = 35 nights that the southside restaurant is open. For each night in the sample, she collects data on the number of filet mignons sold at the southside location and computes the sample mean M 3.68 and the sample variance s,: 36. Likewise, she selects a random sample of size n2 32 nights that the northside restaurant is open. For each night in the sample, she collects data on the number of filet mignons sold at the northside location and computes the sample mean M2 2.34 and the sample variance s' = 30. The statistician checks and concludes that the data satisfy the required assumptions for the independent-measures t test. Then she computes the 90% confidence interval for estimating the difference between the mean number of filet mignons sold per night at the southside restaurant and the mean number of filet mignons sold per night at the northside restaurant. This 90% confidence interval is 1.34 ± 2.3499 filet mignons. 0 and conduct a hypothesis test If she were to formulate null and alternative hypotheses as Ho: 1-2 = 0, H1 : 1-2 with -.10, the null hypothesis interval. Hence, she would conclude that there between the two restaurants. rejected based on the result that a difference of zero in the computed a significant difference between the mean nightly sales of filet mignons

Explanation / Answer

The interval is

1.34 +/- 2.3499

= -1.0099, 3.6899

As the interval doesn't contain the hypothized value 0, so the null hypothesis is rejected.

The null hypothesis is rejected on a result that a difference of zeo doesn't lie in the comuted interval. Hence sshe would conclude that there is a significant difference between the mean nightly sales of filet mignons between the two resurants.

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