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Chapter 13: Q.13.39 (page 542)

Fill in the missing entries in the partially completed one-way ANOVA tables.

Short Answer

Expert verified

The completed ANOVA table is

sourcedfSSMS=SSIdfF=statisticTreatment32.1240.7080.75error2018.8800.944total2321.004

Step by step solution

01

Given Information

Given data:

02

Explanation

Determine the degree of treatment freedom.

MSTR=SSTRk-1

0.708=2.124k-1

鈬�k-1=2.1240.708

k-1=3

Determine the total number of degrees of freedom.

totaldf=errordf-treatmentdf

=20+3

=23
03

Explanation

Calculate the MSE error:

F-statistic=MSTRMSE

0.75=0.708MSE

MSE=0.944

MSE (mean square error):

MSE=SSEn-k

SSE=MSE(n-k)

=0.944(20)

=18.88

Calculate the total sum of squares (SST):

SST=SSTR+SSE

=2.124+18.88

=21.004

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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.

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