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 +s, and (B) y = Bo + B₂x1 + 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 x3 is another dummy whose value is 1 if Linda prepared the meals(s) and 0 otherwise. Sarah's data set consists of 124 orders. She would like to conduct a statistical test at a = .05 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.
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 +s, and (B) y = Bo + B₂x1 + 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 x3 is another dummy whose value is 1 if Linda prepared the meals(s) and 0 otherwise. Sarah's data set consists of 124 orders. She would like to conduct a statistical test at a = .05 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.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman