Question

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 prime rib steaks per night than the restaurant located on the west side of the city. The statistician selects a random sample of size n1 = 34 nights that the eastside restaurant is open. For each night in the sample, he collects data on the number of prime rib steaks sold at the eastside location and computes the sample mean M1 = 10.11 and the sample variance s²? = 49. Likewise, he selects a random sample of size n2 = 44 nights that the westside restaurant is open. For each night in the sample, he collects data on the number of prime rib steaks sold at the westside location and computes the sample mean M2 = 7.89 and the sample variance s²? = 41. The statistician checks and concludes that the data satisfy the required assumptions for the independent-measures t test. Then he computes the 99% confidence interval for estimating the difference between the mean number of prime rib steaks sold per night at the eastside restaurant and the mean number of prime rib steaks sold per night at the westside restaurant. This 99% confidence interval is 2.22 ± 4.0231 prime rib steaks. If he were to formulate null and alternative hypotheses as H0: ?1 – ?2 = 0, H1: ?1 – ?2 ? 0 and conduct a hypothesis test with ? = .01, 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 prime rib steaks between the two restaurants.

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 prime rib steaks per night than the restaurant located on the west side of the city.

The statistician selects a random sample of size n1 = 34 nights that the eastside restaurant is open. For each night in the sample, he collects data on the number of prime rib steaks sold at the eastside location and computes the sample mean M1 = 10.11 and the sample variance s²? = 49. Likewise, he selects a random sample of size n2 = 44 nights that the westside restaurant is open. For each night in the sample, he collects data on the number of prime rib steaks sold at the westside location and computes the sample mean M2 = 7.89 and the sample variance s²? = 41.

The statistician checks and concludes that the data satisfy the required assumptions for the independent-measures t test. Then he computes the 99% confidence interval for estimating the difference between the mean number of prime rib steaks sold per night at the eastside restaurant and the mean number of prime rib steaks sold per night at the westside restaurant. This 99% confidence interval is 2.22 ± 4.0231 prime rib steaks.

If he were to formulate null and alternative hypotheses as H0: ?1 – ?2 = 0, H1: ?1 – ?2 ? 0 and conduct a hypothesis test with ? = .01, 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 prime rib steaks between the two restaurants.

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 prime rib steaks per night than the restaurant located on the west side of the city.

The statistician selects a random sample of size n1 = 34 nights that the eastside restaurant is open. For each night in the sample, he collects data on the number of prime rib steaks sold at the eastside location and computes the sample mean M1 = 10.11 and the sample variance s²? = 49. Likewise, he selects a random sample of size n2 = 44 nights that the westside restaurant is open. For each night in the sample, he collects data on the number of prime rib steaks sold at the westside location and computes the sample mean M2 = 7.89 and the sample variance s²? = 41.

The statistician checks and concludes that the data satisfy the required assumptions for the independent-measures t test. Then he computes the 99% confidence interval for estimating the difference between the mean number of prime rib steaks sold per night at the eastside restaurant and the mean number of prime rib steaks sold per night at the westside restaurant. This 99% confidence interval is 2.22 ± 4.0231 prime rib steaks.

If he were to formulate null and alternative hypotheses as H0: ?1 – ?2 = 0, H1: ?1 – ?2 ? 0 and conduct a hypothesis test with ? = .01, 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 prime rib steaks between the two restaurants.

Added by Alicia M.

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