Chapter 27, Problem 27.18CYS

To determine

To identify: The purpose of analysis of variance is to compare

Answer to Problem 27.18CYS

Correct answer: Option (c); the means of several populations.

Explanation of Solution

Reason for the correct option:

One-way ANOVA is used to compare more than two groups of means or comparing the several population mean.

Therefore, the correct option is (c).

Reason for the incorrect options:

Option (a) is incorrect because the ANOVA F statistic does not compare the variances of several populations.

Option (b) is incorrect because the ANOVA F statistic does not compare the proportions of successes in several populations.

Thus, the purpose of analysis of variance is to compare the means of several populations.

Statistics Concept Introduction

Introduction:

One-way analysis of variance:

It is analyzed by only one factor. This is used for testing the equality of three or more samples from populations with equal means or not. That is, one-way ANOVA is used to compare more than two groups of means using only one factor.

The general hypotheses for one-way ANOVA is:

Null hypothesis:

$H_0:{\mu }_1={\mu }_2={\mu }_3=\mathrm{...}$

Alternative hypothesis:

$H_a:$ At least one of the means is different from the other means