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 _

Name: 5.45 Coffee, depression, and physical activity: Caffeine is the world
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Description: 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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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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.

	Df	Sum Sq	Mean Sq	F value	Pr(>F)
coffee	________	_________	_______	________	0.0003
residuals	________	25564819	_______	_______	______
total	________	25575327	________	________	_______

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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

	$\leq$ 1 cup/week	2-6 cups/week	7cups/week	14-21cups/week	$\geq$ 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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