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 = 31 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 X₁ = 14.93 and the sample variance s² = 24. Likewise, she selects a random sample of size П₂ = 37 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 X2 = 13.48 and the sample variance s² = 21. The statistician conducts an F-test of the ratio of two variances, and there is not enough evidence to infer that the population variances differ (you can assume that 01 = 02). Furthermore, histograms of the sample data suggest that the normality conditions are satisfied. Use the Distributions tool to help you answer the questions that follow. t Distribution Degrees of Freedom = 75 о -4 -3 -2 0 1 2 3 4 5 x ДАЛ The point estimate of 1 - 2 is The 99% confidence interval estimate of 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 is LCL = to UCL = The statistician formulates the null and alternative hypotheses as Ho: 1-2 = 0, H₁: 41 - 42 + 0 and conducts the hypothesis test at the 0.01 significance level. Since the p-value is , the statistician concludes that there enough evidence to infer that the mean nightly sales of halibut fillets differs between the two restaurants.
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 = 31 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 X₁ = 14.93 and the sample variance s² = 24. Likewise, she selects a random sample of size П₂ = 37 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 X2 = 13.48 and the sample variance s² = 21. The statistician conducts an F-test of the ratio of two variances, and there is not enough evidence to infer that the population variances differ (you can assume that 01 = 02). Furthermore, histograms of the sample data suggest that the normality conditions are satisfied. Use the Distributions tool to help you answer the questions that follow. t Distribution Degrees of Freedom = 75 о -4 -3 -2 0 1 2 3 4 5 x ДАЛ The point estimate of 1 - 2 is The 99% confidence interval estimate of 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 is LCL = to UCL = The statistician formulates the null and alternative hypotheses as Ho: 1-2 = 0, H₁: 41 - 42 + 0 and conducts the hypothesis test at the 0.01 significance level. Since the p-value is , the statistician concludes that there enough evidence to infer that the mean nightly sales of halibut fillets differs between the two restaurants.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section: Chapter Questions
Problem 8SGR
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Transcribed Image Text: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 = 31 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 X₁ = 14.93 and the sample variance s² = 24. Likewise,
she selects a random sample of size П₂ = 37 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 X2 = 13.48 and the sample variance s² = 21.
The statistician conducts an F-test of the ratio of two variances, and there is not enough evidence to infer that the population variances differ (you can
assume that 01 = 02). Furthermore, histograms of the sample data suggest that the normality conditions are satisfied.
Use the Distributions tool to help you answer the questions that follow.
t Distribution
Degrees of Freedom = 75
о
-4
-3
-2
0
1
2
3
4
5
x
ДАЛ
The point estimate of 1 - 2 is
The 99% confidence interval estimate of 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 is LCL =
to UCL =
The statistician formulates the null and alternative hypotheses as Ho: 1-2 = 0, H₁: 41 - 42 + 0 and conducts the hypothesis test at the 0.01
significance level. Since the p-value is
, the statistician concludes that there enough evidence to infer that the mean nightly sales of
halibut fillets differs between the two restaurants.
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