ANOVA calculations and rejection of the null hypothesis The following table summ
ID: 3231072 • Letter: A
Question
ANOVA calculations and rejection of the null hypothesis The following table summarizes the results of a study on SAT prep courses, comparing SAT scores of students in a private preparation class, a high school preparation class, and no preparation class. Use the information from the table to answer the remaining questions. Using the data provided, complete the partial ANOVA summary table that follows. In some ANOVA summary tables you will see, the labels in the first (source) column are Treatment, Error, and Total. Which of the following reasons best explains why the within-treatments sum of squares is sometimes referred to as the "error sum of squares"? The within-treatments sum of squares measures treatment effects as well as random, unsystematic differences within each of the samples assigned to each of the treatments. These differences represent all of the variations that could occur in a study; therefore, they are sometimes referred to as "error" The within-treatments sum of squares measures random, unsystematic differences within each of the samples assigned to each of the treatments. These differences are not due to treatment effects because everyone within each sample received the same treatment; therefore, the differences are sometimes referred to as "error" Differences among members of the sample who received the same treatment occur when the researcher makes an error, and thus these differences are sometimes referred to as "error" Differences among members of the sample who received the same treatment occur because some treatments are more effective than others, so it would be an error to receive the less superior treatments.Explanation / Answer
From following calculations we have
Grand total G
117900
Grand Mean GM
655
Sum of Sqaures SS
844290
Total Sample size N
180
Number of Treatments k
3
Degree of freedom of between treatments =k-1
2
Within DF=N-k
177
Total Sum of sqaures TSS=SS-G^2/N
843635
Treatment Sum of Sqaures SStr=Sum(xbar-G)^2
1050
Within Treatments Sum of SqauresS=SSS=TSS-SSTR
842585
Source
Df
SS
MS
Between Treatment
2
1050
1050/2=525
Within Treatment
177
842585
842585/177=4760.37
Last- Question –Option-2
Grand total G
117900
Grand Mean GM
655
Sum of Sqaures SS
844290
Total Sample size N
180
Number of Treatments k
3
Degree of freedom of between treatments =k-1
2
Within DF=N-k
177
Total Sum of sqaures TSS=SS-G^2/N
843635
Treatment Sum of Sqaures SStr=Sum(xbar-G)^2
1050
Within Treatments Sum of SqauresS=SSS=TSS-SSTR
842585
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