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7. 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 prime rib steaks per night than the restaurant located on the north side of the city. The statistician selects a random sample of size n, = 48 nights that the southside restaurant is open. For each night in the sample, she collects data on the number of prime rib steaks sold at the southside location and computes the sample mean M, = 18.43 and the sample variance s = 22. Likewise, she selects a random sample of size n, = 41 nights that the northside restaurant is open. For each night in the sample, she collects data on the number of prime rib steaks sold at the northside location and computes the sample mean M, = 14.11 and the sample variance s = 21. 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 prime rib steaks sold per night at the southside restaurant and the mean number of prime rib steaks sold per night at the northside restaurant. This 95% confidence interval is 4.32 ± 1.9621 prime rib steaks. If she were to formulate null and alternative hypotheses as H,: P, - P, = 0, H,: P, - P, + 0 and conduct a hypothesis test with a = 0.05, the null ▼ in the computed interval. Hence, she would conclude that there hypothesis rejected based on the result that a difference of zero a significant difference between the mean nightly sales of prime rib steaks between the two restaurants.

7. 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 prime rib steaks per night than the restaurant located on the north side of the city. The statistician selects a random sample of size n, = 48 nights that the southside restaurant is open. For each night in the sample, she collects data on the number of prime rib steaks sold at the southside location and computes the sample mean M, = 18.43 and the sample variance s = 22. Likewise, she selects a random sample of size n, = 41 nights that the northside restaurant is open. For each night in the sample, she collects data on the number of prime rib steaks sold at the northside location and computes the sample mean M, = 14.11 and the sample variance s = 21. 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 prime rib steaks sold per night at the southside restaurant and the mean number of prime rib steaks sold per night at the northside restaurant. This 95% confidence interval is 4.32 ± 1.9621 prime rib steaks. If she were to formulate null and alternative hypotheses as H,: P, - P, = 0, H,: P, - P, + 0 and conduct a hypothesis test with a = 0.05, the null ▼ in the computed interval. Hence, she would conclude that there hypothesis rejected based on the result that a difference of zero a significant difference between the mean nightly sales of prime rib steaks between the two restaurants.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 58E: What is meant by the sample space of an experiment?
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7. 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 prime rib steaks per night than the restaurant located on the north side of the city. The statistician selects a random sample of size n, 48 nights that the southside restaurant is open. For each night in the sample, she collects data on the number of prime rib steaks sold at the southside location and computes the sample mean M, = 18.43 and the sample variance s? = 22. Likewise, she selects a random sample of size n, = 41 nights that the northside restaurant is open. For each night in the sample, she collects data on the number of prime rib steaks sold at the northside location and computes the sample mean M, = 14.11 and the sample variance s, = 21. 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 prime rib steaks sold per night at the southside restaurant and the mean number of prime rib steaks sold per night at the northside restaurant. This 95% confidence interval is 4.32 ± 1.9621 prime rib steaks. If she were to formulate null and alternative hypotheses as H,: H, - P, = 0, H,: H, - H, + 0 and conduct a hypothesis test with a = :0.05, 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 prime rib steaks between the two restaurants.
Transcribed Image Text:7. 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 prime rib steaks per night than the restaurant located on the north side of the city. The statistician selects a random sample of size n, 48 nights that the southside restaurant is open. For each night in the sample, she collects data on the number of prime rib steaks sold at the southside location and computes the sample mean M, = 18.43 and the sample variance s? = 22. Likewise, she selects a random sample of size n, = 41 nights that the northside restaurant is open. For each night in the sample, she collects data on the number of prime rib steaks sold at the northside location and computes the sample mean M, = 14.11 and the sample variance s, = 21. 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 prime rib steaks sold per night at the southside restaurant and the mean number of prime rib steaks sold per night at the northside restaurant. This 95% confidence interval is 4.32 ± 1.9621 prime rib steaks. If she were to formulate null and alternative hypotheses as H,: H, - P, = 0, H,: H, - H, + 0 and conduct a hypothesis test with a = :0.05, 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 prime rib steaks between the two restaurants.
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