The relationship between confidence intervals and hypothesis testing PLEASE answ
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The relationship between confidence intervals and hypothesis testing
PLEASE answer all 3 of the blanks, other times I have submitted I was left without complete answers. Thank you!
9. The relationship between confidence intervals and hypothesis testing Aa Aa In 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 38 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 M1 82.14 and the sample variance s 33. Likewise, he selects a random sample of size n2 42 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 M 81.36 and the sample variance s 28 The statistician checks and concludes that the data satisfy the required assumptions for the independent measures t test. Then he computes the 95% 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 95% confidence interval is 0.78 t 2.4566 salmon fillets. If he were to formulate null and alternative hypotheses as H o: H1 H2 0, H1: 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, he would conclude that there a significant difference between the mean nightly sales of salmon fillets between the two restaurants.Explanation / Answer
From the given data, we find that the 95% confidence interval is 0.78±2.4566 which is (-1.677, 3.237) If he were to formulate null and alternative hypothesis as Ho: 1 - 2 = 0 H1 : 1 - 2 0 and conduct a hypothesis test with = 0.05, the null hypothesis will not be rejected based on the result that a difference of zero lies within the computed interval. Hence, he would conclude that there does not exist a significant difference between the mean nightly sales of salmon fillets between the two restaurants.
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