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satisfaction. The restaurant employs three chefs: Richard, Thomas, and Linda. Sarah decides to compare the following two candidate models: (A) y = Bo + B₁x₁1 +8, and (B) y = ßo + B₂x₂ + B₂x2 + 3x3 +8, where y denotes the tip (in euros), x, denotes the total price on the bill (in euros), X₂ is a dummy variable whose value is 1 if Thomas prepared the meal(s) and 0 otherwise, and x3 is another dummy whose value is 1 if Linda prepared the meals(s) and 0 otherwise.

satisfaction. The restaurant employs three chefs: Richard, Thomas, and Linda. Sarah decides to compare the following two candidate models: (A) y = Bo + B₁x₁1 +8, and (B) y = ßo + B₂x₂ + B₂x2 + 3x3 +8, where y denotes the tip (in euros), x, denotes the total price on the bill (in euros), X₂ is a dummy variable whose value is 1 if Thomas prepared the meal(s) and 0 otherwise, and x3 is another dummy whose value is 1 if Linda prepared the meals(s) and 0 otherwise.

Elementary Algebra
Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter5: Systems Of Linear Equations
Section5.2: Solve Systems Of Equations By Substitution
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Sarah studies Business and Management and she also has a part-time job as a waitress at a restaurant. The restaurant does not include service charges in their bills, and therefore Sarah often receives tips from the customers. Some customers give her very generous tips, while others leave hardly anything or nothing at all. Sarah began to wonder what the size of the tip may depend on. Just out of curiosity, she started to keep a record of the total prices on the bills and the tips she received. At first, she fit a simple linear regression model to the data and found that the size of the tip was significantly related to the total price. But at this point, she speculated that the tips may be affected by other factors as well, and an even better model could possibly be constructed by including further independent variables. For instance, the chef who prepares the dish(es) might affect the customers' satisfaction. The restaurant employs three chefs: Richard, Thomas, and Linda. Sarah decides to compare the following two candidate models: (A) y = Bo + B₁x₁ +8, and (B) y = B + ₁x₁ + B₂x2 + 3x3 +8, where y denotes the tip (in euros), x₁ denotes the total price on the bill (in euros), X₂ is a dummy variable whose value is 1 if Thomas prepared the meal(s) and 0 otherwise, and x; is another dummy whose value is 1 if Linda prepared the meals(s) and 0 otherwise. Sarah's data set consists of 64 orders. She would like to conduct a statistical test at a = .01 to determine if there is evidence that including information about the chef in the model significantly reduces the errors of the predictions. Name the statistical procedure she will use, specify the null and alternative hypotheses, and provide the critical value of the test statistic.
Transcribed Image Text:Sarah studies Business and Management and she also has a part-time job as a waitress at a restaurant. The restaurant does not include service charges in their bills, and therefore Sarah often receives tips from the customers. Some customers give her very generous tips, while others leave hardly anything or nothing at all. Sarah began to wonder what the size of the tip may depend on. Just out of curiosity, she started to keep a record of the total prices on the bills and the tips she received. At first, she fit a simple linear regression model to the data and found that the size of the tip was significantly related to the total price. But at this point, she speculated that the tips may be affected by other factors as well, and an even better model could possibly be constructed by including further independent variables. For instance, the chef who prepares the dish(es) might affect the customers' satisfaction. The restaurant employs three chefs: Richard, Thomas, and Linda. Sarah decides to compare the following two candidate models: (A) y = Bo + B₁x₁ +8, and (B) y = B + ₁x₁ + B₂x2 + 3x3 +8, where y denotes the tip (in euros), x₁ denotes the total price on the bill (in euros), X₂ is a dummy variable whose value is 1 if Thomas prepared the meal(s) and 0 otherwise, and x; is another dummy whose value is 1 if Linda prepared the meals(s) and 0 otherwise. Sarah's data set consists of 64 orders. She would like to conduct a statistical test at a = .01 to determine if there is evidence that including information about the chef in the model significantly reduces the errors of the predictions. Name the statistical procedure she will use, specify the null and alternative hypotheses, and provide the critical value of the test statistic.
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