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. Treatment Private prep class High school prep class No prep class Number of Observations 60 60 Source Between treatments Within treatments 60 Sample Mean 650 645 625 Using the data provided, complete the partial ANOVA summary table that follows. (Hint: T, the treatment total, can be calculated as the sample mean times the number of observations. G, the grand total, can be calculated from the values of T once you have calculated them.) Sum of Squares (SS) 132,750.00 147,500.00 Sum of Squares (SS) df Mean Square (MS) 162,250.00 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 variance is sometimes referred to as the "error variance"? The within-treatments variance 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." The within-treatments variance 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." 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." In ANOVA, the F test statistic is the within-treatments variance. The value of the F test statistic is When the null hypothesis is true, the F test statistic is false, the F test statistic is most likely hypothesis for 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. of the between-treatments variance and the . When the null hypothesis is . In general, you should reject the null