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ning X ? a secure https://ng.cengage.com/static/nb/ui/evo/index.html?deploymentid-568707236005661 8796341460296&es; MINDTAP From Cengage Q Search this cour Complete: Chapter 10 Problem Set 8. The relationship between confidence intervals and hypothesis testing Aa Aa an effort to better manage her 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 east side sells more salmon fillets per night than the restaurant located on the west side of the city. The statistician selects a random sample of size n 36 nights that the eastside restaurant is open. For each night in the sample, he collects data on the number of salmon fillets sold at the eastside location and computes the sample mean M, - 45, 14 and the sample variance sl = 25. Likewise, he selects a random sample of size n-49 nights that the westside restaurant is open. For each night in the sample, he collects data on the number of salmon fillets sold at the westside location and computes the sample mean M2 48.89 and the sample variance s 20 The statistician checks and concludes that the data satisfy the required assumptions for the independent-measures t test. Then he computes the 90% confidence interval for estimating the difference between the mean number of salmon fillets sold per night at the eastside restaurant and the mean number of salmon fillets sold per night at the westside restaurant. This 90% confidence interval is-3.751.7164 salmon fillets. If he were to formulate null and alternative hypotheses as Ho: ?1--H2-0, H1???-?2 # 0 and conduct a hypothesis test with ?·.10, the null hypothesis interval. Hence, he 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 salmon filletsExplanation / Answer
The 90% confidence interval is
-3.75 +/- 1.7164
= -5.4664, -2.0336
the null hypothesis is rejected based on the result that a difference of zero does not lie in the computed interval. Hence, he would conclude that there is a significant difference between the mean nightly sales of salmon fillets between the two resturants.
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