Question

Attempts: Average: /12 ANOVA calculations and rejection of the null hypothesis Aa Aa 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. Number of Sum of Observations Sample Mean Squares (SS) 650 645 625 Treatment Private prep class High school prep class No prep class 60 60 60 132,750.00 147,500.00 162,250.00 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.) Source Between treatments Within treatments Sum of Squares (SS) df Mean Square (MS) 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" O 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." O Differences among members of the sample who received the same treatment occur when the researcher O Differences among members of the sample who received the same treatment occur because some treatments O The within-treatments variance measures random, unsystematic differences within each of the samples makes an error, and thus these differences are sometimes referred to as "error are more effective than others, so it would be an error to receive the less superior treatments 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 In ANOVA, the F test statistic is the variance. The value of the F test statistic is of the between-treatments variance and the within-treatments When the null hypothesis is true, the F test statistic is statistic is most likely When the null hypothesis is false, the F test . In general, you should reject the null hypothesis for

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Answer 1

Source	SS	df	MS
between	21000.00	2.000	10500.0000
within	442500.00	177.000	2500.0000

the within treatments variance measures random, unsystematic,,,,,,,,,,,,,,,,

in ANOVA ; the F test statistic is the ratio of the between treatments variance and the witih in ....

when the null hypothesis is true , the F test statitic is closer to 1 , when the nul;;;;is most likely large. IN general you should reject the null hypothesis for large values of F