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Math · Statistics And Probability
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Score: 15 Attempts: 10. The relationship between confidence intervals and hypothesis testing Aaa Aa 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 n1 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 M1 9.09 and the sample variance s 28. 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 M 7.49 and the sample variance s 27 The statistician checks and concludes that the data satisfy the required assumptions for the independent-measures t test. Then she computes the 95% 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 95% confidence interval is 60 t 2.5624 filet mignons. If she were to formulate nu and alternative hypotheses as H 0: H1 H2 0, H 1: H1 H2 0 and conduct a hypothesis test with a 05, the null hypothesis rejected based on the result that a difference of zero in the computed interval. Hence, she would conclude that there a significant difference between the mean nightly sales of filet mignons between the two restaurants

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