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Chapter 13: Q.13.14 (page 532)

For a one-way ANOVA test, suppose that, in reality, the null hypothesis is false. Does that mean that no two of the populations have the same mean? If not, what does it mean?

Short Answer

Expert verified

No, The fact that the null hypothesis is false does not rule out the possibility of the two populations having the same mean.

Step by step solution

01

Concept Introduction 

ANOVA splits noted accumulated variability within a set of data into two components: systematic factors and random factors.

02

Explanation

The hypothesis for one-way ANOVA is as follows:

Null hypothesis :H0:渭1=渭2=渭3鈥�鈥�鈥�鈥�鈥�..=渭k

Alternative hypothesis: Ha

One of the means is different. ANOVA is being used to compare multiple groups of means in a single comparison. The null hypothesis is false because 'at least one of them is different,' but no two populations have the same mean.

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Most popular questions from this chapter

Consider the following hypothetical samples

a. Obtain the sample mean and sample variance of each of the three samples.

b. Obtain SST, SSTR and SSE by using the defining formulas and verify that the one-way ANOVA identity holds.

c. Obtain SST, SSTR and SSE by using the computing formulas.

d. Construct the one-way ANOVA table.

Fill in the missing entries in the partially completed one-way ANOVA table

Consider a F-curve with df=(2,14)

Find the F-value with an area0.01 to its right.

In one-way ANOVA, identify a statistic that measures

a. the variation among the sample means.

b. the variation within the samples.

We have provided data from independent simple random samples from several populations. In each case, determine the following items.

a. SSTR

b. MSTR

c. SSE

d. MSE

e. F
See all solutions

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