5.45 Coffee, depression, and physical activity: Caffeine is the world's most widely used stimulant, with approximately 80% consumed in the form of coffee. Participants in a study investigating the relationship between coffee consumption and exercise were asked to report the number of hours they spent per week on moderate (e.g., brisk walking) and vigorous (e.g., strenuous sports and jogging) exercise. Based on these data the researchers estimated the total hours of metabolic equivalent tasks (MET) per week, a value always greater than 0. The table below gives summary statistics of MET for women in this study based on the amount of coffee consumed. Caffeinated coffee consumption ≤ 1 cup/week (1) 2-6 cups/week (2) 1 cup/day (3) 2-3 cups/day (4) ≥ 4 cups/day (5) Total Mean 18.7 19.6 19.3 19.9 17.5 SD 21.1 25.5 22.5 22 22 n 12215 6617 17234 12290 2383 50739 (a) Write the hypotheses for evaluating if the average physical activity level varies among the different levels of coffee consumption. ( )Ho: μ1 = μ2 = μ3 = μ4 = μ5 Ha: At least one pair of means is the same ( )Ho: μ1 = μ2 = μ3 = μ4 = μ5 Ha: μ1 ≠ μ2 ≠ μ3 ≠ μ4 ≠ μ5 ( )Ho: μ1 = μ2 = μ3 = μ4 = μ5 Ha: At least one of the means is different (b) Assume that all of the conditions required for this inference are satisfied. (c) Below is part of the output associated with this test. Fill in the empty cells. Df Sum Sq Mean Sq F value Pr(>F) coffee ________ _________ _______ ________ 0.0003 residuals ________ 25564819 _______ _______ ______ total ________ 25575327 ________ ________ _______
5.45 Coffee, depression, and physical activity: Caffeine is the world's most widely used stimulant, with approximately 80% consumed in the form of coffee. Participants in a study investigating the relationship between coffee consumption and exercise were asked to report the number of hours they spent per week on moderate (e.g., brisk walking) and vigorous (e.g., strenuous sports and jogging) exercise. Based on these data the researchers estimated the total hours of metabolic equivalent tasks (MET) per week, a value always greater than 0. The table below gives summary statistics of MET for women in this study based on the amount of coffee consumed. Caffeinated coffee consumption ≤ 1 cup/week (1) 2-6 cups/week (2) 1 cup/day (3) 2-3 cups/day (4) ≥ 4 cups/day (5) Total Mean 18.7 19.6 19.3 19.9 17.5 SD 21.1 25.5 22.5 22 22 n 12215 6617 17234 12290 2383 50739 (a) Write the hypotheses for evaluating if the average physical activity level varies among the different levels of coffee consumption. ( )Ho: μ1 = μ2 = μ3 = μ4 = μ5 Ha: At least one pair of means is the same ( )Ho: μ1 = μ2 = μ3 = μ4 = μ5 Ha: μ1 ≠ μ2 ≠ μ3 ≠ μ4 ≠ μ5 ( )Ho: μ1 = μ2 = μ3 = μ4 = μ5 Ha: At least one of the means is different (b) Assume that all of the conditions required for this inference are satisfied. (c) Below is part of the output associated with this test. Fill in the empty cells. Df Sum Sq Mean Sq F value Pr(>F) coffee ________ _________ _______ ________ 0.0003 residuals ________ 25564819 _______ _______ ______ total ________ 25575327 ________ ________ _______
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 11PPS
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5.45 Coffee, depression, and physical activity: Caffeine is the world's most widely used stimulant, with approximately 80% consumed in the form of coffee. Participants in a study investigating the relationship between coffee consumption and exercise were asked to report the number of hours they spent per week on moderate (e.g., brisk walking) and vigorous (e.g., strenuous sports and jogging) exercise. Based on these data the researchers estimated the total hours of metabolic equivalent tasks (MET) per week, a value always greater than 0. The table below gives summary statistics of MET for women in this study based on the amount of coffee consumed.
Caffeinated coffee consumption
| ≤ 1 cup/week (1) | 2-6 cups/week (2) | 1 cup/day (3) | 2-3 cups/day (4) | ≥ 4 cups/day (5) | Total | |
|---|---|---|---|---|---|---|
| Mean | 18.7 | 19.6 | 19.3 | 19.9 | 17.5 | |
| SD | 21.1 | 25.5 | 22.5 | 22 | 22 | |
| n | 12215 | 6617 | 17234 | 12290 | 2383 | 50739 |
(a) Write the hypotheses for evaluating if the average physical activity level varies among the different levels of coffee consumption.
- ( )Ho: μ1 = μ2 = μ3 = μ4 = μ5
Ha: At least one pair of means is the same - ( )Ho: μ1 = μ2 = μ3 = μ4 = μ5
Ha: μ1 ≠ μ2 ≠ μ3 ≠ μ4 ≠ μ5 - ( )Ho: μ1 = μ2 = μ3 = μ4 = μ5
Ha: At least one of the means is different
(b) Assume that all of the conditions required for this inference are satisfied.
(c) Below is part of the output associated with this test. Fill in the empty cells.
| Df | Sum Sq | Mean Sq | F value | Pr(>F) | |
|---|---|---|---|---|---|
| coffee | ________ | _________ | _______ | ________ | 0.0003 |
| residuals | ________ | 25564819 | _______ | _______ | ______ |
| total | ________ | 25575327 | ________ | ________ | _______ |
Expert Solution
Step 1
1 cup/day is 7cups/week
2-3 cups/day is 14-21 cups/week
4 cups/day is 28 cups/week
| 1 cup/week | 2-6 cups/week | 7cups/week | 14-21cups/week | 28cups/week | Total | |
| Mean | 18.7 | 19.6 | 19.3 | 19.9 | 17.5 | |
| SD | 21.1 | 25.5 | 22.5 | 22 | 22 | |
| n | 12215 | 6617 | 17234 | 12290 | 2383 | 50739 |
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