9. 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 n1 = 31 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 M₁ = 21.21 and the sample variance s² = 24. Likewise, she selects a random sample of size n2 = 37 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 M2 = 19.49 and the sample variance s² = 21. The statistician checks and concludes that the data satisfy the required assumptions for the independent-measures t test. Then she computes the 99% 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 99% confidence interval is 1.72 ±3.0536 prime rib steaks. If she were to formulate null and alternative hypotheses as Ho: p1 - U2 = 0, H₁: p1 - μ2 = 0 and conduct a hypothesis test with a = 0.01, 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.
9. 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 n1 = 31 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 M₁ = 21.21 and the sample variance s² = 24. Likewise, she selects a random sample of size n2 = 37 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 M2 = 19.49 and the sample variance s² = 21. The statistician checks and concludes that the data satisfy the required assumptions for the independent-measures t test. Then she computes the 99% 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 99% confidence interval is 1.72 ±3.0536 prime rib steaks. If she were to formulate null and alternative hypotheses as Ho: p1 - U2 = 0, H₁: p1 - μ2 = 0 and conduct a hypothesis test with a = 0.01, 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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Transcribed Image Text:9. 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 n₁ = 31 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 M₁ = 21.21 and the sample variance s= 24. Likewise, she
selects a random sample of size n2 = 37 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 M2 = 19.49 and the sample variance s² = 21.
The statistician checks and concludes that the data satisfy the required assumptions for the independent-measures t test. Then she computes the 99%
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 99% confidence interval is 1.72 ± 3.0536 prime rib steaks.
If she were to formulate null and alternative hypotheses as Ho: p1 - μ2 = 0, H₁: μ₁ − µ2 = 0 and conduct a hypothesis test with a = 0.01, 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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