(a) The following ANOVA table gives a summary of such an ANOVA test. Fill in the missing cell in the table (rounded to two decimal places). Source of Degrees of Sum of Mean square F statistic variation freedom squares Treatments 5 7419.81 1483.96 (between groups) Error (within 276 108,799.2 394.2 groups) Total 281 116,219.01 (b) How many locations were looked at by the manager? ? (c) For the ANOVA test, it is assumed that the variance is the same for each population of daily sales (that is, for the populations of daily sales for each location). What is an unbiased estimate of this common population variance based on the sample variances? ? (d) What is the p-value corresponding to the F statistic for the ANOVA test? Round your answer to at least three decimal places.
(a) The following ANOVA table gives a summary of such an ANOVA test. Fill in the missing cell in the table (rounded to two decimal places). Source of Degrees of Sum of Mean square F statistic variation freedom squares Treatments 5 7419.81 1483.96 (between groups) Error (within 276 108,799.2 394.2 groups) Total 281 116,219.01 (b) How many locations were looked at by the manager? ? (c) For the ANOVA test, it is assumed that the variance is the same for each population of daily sales (that is, for the populations of daily sales for each location). What is an unbiased estimate of this common population variance based on the sample variances? ? (d) What is the p-value corresponding to the F statistic for the ANOVA test? Round your answer to at least three decimal places.
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
![### ANOVA Test for Magazine Sales at Emma's On-the-Go
Emma’s On-the-Go, a large convenience store, is deciding on the optimal location within the store for its magazine rack. The manager tests different store locations by recording daily magazine sales in dollars over several days at each location. The aim is to determine if there is a significant difference in sales between the locations using a one-way, independent-samples ANOVA test.
#### ANOVA Table
The table below summarizes the ANOVA test results. You are required to fill in the missing values.
| Source of Variation | Degrees of Freedom | Sum of Squares | Mean Square | F Statistic |
|------------------------------|--------------------|----------------|---------------|-------------|
| Treatments (between groups) | 5 | 7419.81 | 1483.96 | ? |
| Error (within groups) | 276 | 108,799.2 | 394.2 | |
| Total | 281 | 116,219.01 | | |
#### Questions
**(a)** Fill in the missing F statistic in the table (rounded to two decimal places).
**(b)** How many locations were looked at by the manager?
- Answer here: [ ]
**(c)** For the ANOVA test, it is assumed that the variance is the same for each population of daily sales. What is an unbiased estimate of this common population variance based on the sample variances?
- Answer here: [ ]
**(d)** What is the p-value corresponding to the F statistic for the ANOVA test? Round your answer to at least three decimal places.
- Answer here: [ ]
**(e)** Can we conclude, using the 0.05 level of significance, that there is a difference in the mean daily sales among the different locations?
- Circle one: Yes / No
#### Steps for Solving
- **F Statistic Calculation:** The F statistic is found by dividing the mean square between groups by the mean square within groups.
- **Degrees of Freedom Explanation:** The degrees of freedom for treatments is the number of groups minus one. The degrees of freedom for error is the total number of observations minus the number of groups.
- **Common Variance Estimate:** This is often the mean of the variances within the groups.
- **p-Value Interpretation:** The p-value indicates the probability that the observed data would](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F438f9e3e-5163-4042-928f-6af00166f2ed%2F7c19c32d-cf20-4a5d-a290-33f9dd619bd9%2Fxyx5vn_processed.png&w=3840&q=75)
Transcribed Image Text:### ANOVA Test for Magazine Sales at Emma's On-the-Go
Emma’s On-the-Go, a large convenience store, is deciding on the optimal location within the store for its magazine rack. The manager tests different store locations by recording daily magazine sales in dollars over several days at each location. The aim is to determine if there is a significant difference in sales between the locations using a one-way, independent-samples ANOVA test.
#### ANOVA Table
The table below summarizes the ANOVA test results. You are required to fill in the missing values.
| Source of Variation | Degrees of Freedom | Sum of Squares | Mean Square | F Statistic |
|------------------------------|--------------------|----------------|---------------|-------------|
| Treatments (between groups) | 5 | 7419.81 | 1483.96 | ? |
| Error (within groups) | 276 | 108,799.2 | 394.2 | |
| Total | 281 | 116,219.01 | | |
#### Questions
**(a)** Fill in the missing F statistic in the table (rounded to two decimal places).
**(b)** How many locations were looked at by the manager?
- Answer here: [ ]
**(c)** For the ANOVA test, it is assumed that the variance is the same for each population of daily sales. What is an unbiased estimate of this common population variance based on the sample variances?
- Answer here: [ ]
**(d)** What is the p-value corresponding to the F statistic for the ANOVA test? Round your answer to at least three decimal places.
- Answer here: [ ]
**(e)** Can we conclude, using the 0.05 level of significance, that there is a difference in the mean daily sales among the different locations?
- Circle one: Yes / No
#### Steps for Solving
- **F Statistic Calculation:** The F statistic is found by dividing the mean square between groups by the mean square within groups.
- **Degrees of Freedom Explanation:** The degrees of freedom for treatments is the number of groups minus one. The degrees of freedom for error is the total number of observations minus the number of groups.
- **Common Variance Estimate:** This is often the mean of the variances within the groups.
- **p-Value Interpretation:** The p-value indicates the probability that the observed data would
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
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