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)TotalMean18.719.619.319.917.5 SD21.125.522.52222 n1221566171723412290238350739 (d) What is the p-value associated with the ANOVA test?p = What is the conclusion of the test?( )Since p < α we reject the idea that all of the means are different and accept that all of the means are the same( )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( )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( )Since p < α we reject the idea that all of the means are the same and accept that all of the means are different

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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

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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

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

( )Since p < α we reject the idea that all of the means are different and accept that all of the means are the same
( )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
( )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
( )Since p < α we reject the idea that all of the means are the same and accept that all of the means are different

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 + ...

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