Question

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.

• A: Ho: μ₁ = μ₂ = μ₃ = μ₄ = μ₅
  Ha: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄ ≠ μ₅
• B: Ho: μ₁ = μ₂ = μ₃ = μ₄ = μ₅
  Ha: At least one pair of means is the same
• C: 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

(d) What is the p-value associated with the ANOVA test?
p =

(e) What is the conclusion of the test?

• A: Since p < α we reject the idea that all of the means are the same and accept that all of the means are different
• B: Since p < α we reject the idea that all of the means are the same and accept that at least one of the means is different
• C: Since p < α we reject the idea that all of the means are different and accept that all of the means are the same
• D: Since p<α we reject the idea that at least one of the means is different and accept that all of the means are the same

Answer 1