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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:μ1=μ2=μ3……………..=μk

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

Sample 1 Sample 2
 Sample 3 Sample 4
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Fill in the missing entries in the partially completed one-way ANOVA tables.

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

Following are the notations for the three sums of squares. State the name of each sum of squares and the source of variation each sum of squares represents.

a. SSE

b. SSTR

c. SST

a. Obtain individual normal probability plots and the standard deviations of the samples.

b. Perform a residual analysis.

c. Use your results from parts (a) and (b) to decide whether conducting a one-way ANOVA test and the data is reasonable. If so, also do parts d-f.

d. Use a one-way ANOVA test to decide, at the 5%significance level, whether the data provide sufficient evidence to conclude that a difference exists among the means of the populations from which the samples were taken.

e. Interpret your results from part (d).

Weight Loss and BMI. In the paper "Voluntary Weight Reduction in Older Men Increases Hip Bone Loss: The Osteoporotic Fractures in Men Study" (Journal of Clinical Endocrinology & Metabolism, Vol. 90, Issue 4. Pp. 1998-2004), K. Ensrud et al. reported on the effect of voluntary weight reduction on hip bone loss in older men. In the study, 1342 older men participated in two physical examinations an average of 1.8years apart. After the second exam, they were categorized into three groups according to their change in weight between exams: weight loss of more than 5%, weight gain of more than , and stable weight (between 5%loss and5% gain). For purposes of the hip bone density study, other characteristics were compared, one such being body mass index (BMI). On the Weissstats site, we provide the BMI data for the three groups, based on the results obtained by the researchers.
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