The US Centers for Disease Control and Prevention said about 72 million Americans—nearly one out of every four of the country’s 304 million residents—are considered obese. Millions more are designated as overweight.” The American trend toward obesity has prompted many physicians to offer weight-loss programs to their patients. [Source: Price, W. T. “Physicians Get into the Weight-Loss Business.” Florida Today, July 7, 2008.] A physician conducted an experimental study to compare the effectiveness of four different weight-loss programs. In the study, 64 obese adults were randomly assigned to the four programs so that each program had 16 adults. The programs lasted for six months. The weights of the subjects were measured before and after the programs, and each subject’s weight loss was computed in pounds. The following table summarizes the results of the study, giving the number of observations and the sample mean and variance of the subjects’ weight loss in each program. Treatment Number of Observations, n Sample Mean, M (Pounds) Sample Variance, s² (Pounds squared) Program A 16 10.2 105.4 Program B 16 22.1 100.6 Program C 16 17.9 99.7 Program D 16 19.5 95.7 The physician selects a significance level of α = 0.01. Why should she perform an analysis of variance (ANOVA) with α = 0.01 instead of simply using multiple t tests with α = 0.01 to compare the six pairs of group means? Multiple t tests at α = 0.01 result in an experimentwise alpha level smaller than α = 0.01. The probability of a Type I error when performing multiple t tests at α = 0.01 will be less than 0.01. An ANOVA avoids the problem of an inflated experimentwise alpha level. An ANOVA avoids the problem of an inflated testwise alpha level.

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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

Problem 1P

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“The US Centers for Disease Control and Prevention said about 72 million Americans—nearly one out of every four of the country’s 304 million residents—are considered obese. Millions more are designated as overweight.” The American trend toward obesity has prompted many physicians to offer weight-loss programs to their patients. [Source: Price, W. T. “Physicians Get into the Weight-Loss Business.” Florida Today, July 7, 2008.]

A physician conducted an experimental study to compare the effectiveness of four different weight-loss programs. In the study, 64 obese adults were randomly assigned to the four programs so that each program had 16 adults. The programs lasted for six months. The weights of the subjects were measured before and after the programs, and each subject’s weight loss was computed in pounds.

The following table summarizes the results of the study, giving the number of observations and the sample mean and variance of the subjects’ weight loss in each program.

Treatment	Number of Observations, n	Sample Mean, M (Pounds)	Sample Variance, s² (Pounds squared)
Program A	16	10.2	105.4
Program B	16	22.1	100.6
Program C	16	17.9	99.7
Program D	16	19.5	95.7

The physician selects a significance level of α = 0.01. Why should she perform an analysis of variance (ANOVA) with α = 0.01 instead of simply using multiple t tests with α = 0.01 to compare the six pairs of group means?

Multiple t tests at α = 0.01 result in an experimentwise alpha level smaller than α = 0.01.

The probability of a Type I error when performing multiple t tests at α = 0.01 will be less than 0.01.

An ANOVA avoids the problem of an inflated experimentwise alpha level.

An ANOVA avoids the problem of an inflated testwise alpha level.

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