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Chapter 13: Q.13.33 (page 542)

We stated earlier that a one-way ANOVA test is always right-tailed because the null hypothesis is rejected only when the test statistic, F, is too large. Why is the null hypothesis rejected only when F is too large?

Short Answer

Expert verified

Rejection of the null hypothesis.

Step by step solution

01

Given Information

Consider the fact that the ANOVA test is always right-tailed.

02

Explanation

The ratio of the mean squares F test is based on.

When F is excessively large, it suggests there is a lot of variation between the sample means compared to the variety within the samples.

This implies that at least one of the population means is different, implying that the alternative hypothesis is correct. The null hypothesis was then dismissed.

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Most popular questions from this chapter

Sample 1Sample 2Sample 31104941681062

we provide data from independent simple random samples from several populations. In each case,

a. compute SST, SSTR, and SSE by using the computing formulas given in Formula 13.l on page 535

b. compare your results in part (a) for SSTR and SSE with those you obtained in Exercises 13.24-13.29, where you employed the defining formulas.

c. construct a one-way ANOVA table.

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Staph Infections. In the article "Using EDE, ANOVA and Regression to Optimize Some Microbiology Data" (Journal of Statistics Education, Vol. 12, No. 2, online), N. Binnie analyzed bacteria culture data collected by G. Cooper at the Auckland University of Technology. Five strains of cultured Staphylococcus aureus bacteria that cause staph infections were observed for 24hours at 27oC. The following table reports bacteria counts, in millions, for different cases from each of the five strains.

At the 5%significance level, do the data provide sufficient evidence to conclude that a difference exists in mean bacteria counts among the five strains of Staphylococcus aureus? (Note: T1=104,T2=129, T3=185,T4=98,T5=194,ฮฃx2i=25,424.)

AnF-curve has df=(8,19). What is the number of degrees of freedom for the

a. denominator?

b. numerator?

13.20 Figure 13.6shows side-by-side boxplots of independent samples from three normally distributed populations having equal standard deviations. Based on these boxplots, would you be inclined to reject the null hypothesis of equal population means? Why?

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

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