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Chapter 13: Q. 13.15 (page 532)

Regarding one-way ANOVA, fill in the blanks in each of Exercises 13.15-13.17
13.15 A measure of variation among the sample means is called the ------ The mathematical abbreviation for it is--------

Short Answer

Expert verified

A measure of variation among the sample means is called the Treatment mean square. The mathematical abbreviation isMSTR.

Step by step solution

01

Given information

To find that a measure of variation among the sample means stands.

and the mathematical abbreviation.

02

Explanation

Treatment mean square: The treatment mean square is the difference between the sample means.
That is, the sum squares of the treatment is divided by (k-1).
MSTR=SSTRk-1is the formula for MSTR.

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Most popular questions from this chapter

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

b. Perform a residual analysis

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

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).

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.

d. decide, at the5%significance level, whether the data provide sufficient evidence to conclude that the means of the populations from which the samples were drawn are not all the same.

13.19 What does the term one-way signify in the phrase one-wayANOVA?

On page 539, we discussed how to use summary statistics (sample sizes, sample means, and sample standard deviations) to conduct a one-way ANOVA.

a. Verify the formula presented there for obtaining the mean of all the observations, namely,

x¯=n1x¯1+n2x¯2+⋯+nkx¯kn1+n2+⋯+nk.

b. Show that, if all the sample sizes are equal, then the mean of all the observations is just the mean of the sample means.

c. Explain in detail how to obtain the value of the F-statistic from the summary statistics.
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