11. The relationship between confidence intervals and hypothesis testing 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 n₁ = 35 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 M₁ = 7.32 and the sample variance s2 = 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 halibut fillets sold at the northside location and computes the sample mean M₂ = 3.00 and the sample variance s2 = 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 halibut fillets sold per night at the southside restaurant and the mean number of halibut fillets sold per night at the northside restaurant. This 90% confidence interval is 4.32 ± 2.3499 halibut fillets. If she were to formulate null and alternative hypotheses as Ho: μ₁ - μ2 = 0, H₁: μ₁ - μ20 and conduct a hypothesis test with a = 0.10, the null hypothesis rejected based on the result that a difference of computed interval. Hence, she would conclude there a significant difference between the mean nightly sales of halibut fillets between the two restaurants.
11. The relationship between confidence intervals and hypothesis testing 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 n₁ = 35 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 M₁ = 7.32 and the sample variance s2 = 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 halibut fillets sold at the northside location and computes the sample mean M₂ = 3.00 and the sample variance s2 = 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 halibut fillets sold per night at the southside restaurant and the mean number of halibut fillets sold per night at the northside restaurant. This 90% confidence interval is 4.32 ± 2.3499 halibut fillets. If she were to formulate null and alternative hypotheses as Ho: μ₁ - μ2 = 0, H₁: μ₁ - μ20 and conduct a hypothesis test with a = 0.10, the null hypothesis rejected based on the result that a difference of computed interval. Hence, she would conclude there a significant difference between the mean nightly sales of halibut fillets between the two restaurants.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.4: Discrete Random Variables; Applications To Decision Making
Problem 10E
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