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.

\(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}\text{Treatment}&\text{Number of Observations}&\text{Sample Mean}&\text{Sum of Squares (SS)}\backslash{h}{l}\in{e}\text{Private prep class}&{60}&{680}&{265},{500.00}\backslash{h}{l}\in{e}\text{High school prep class}&{60}&{650}&{276},{120.00}\backslash{h}{l}\in{e}\text{No prep class}&{60}&{635}&{302},{670.00}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)

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.)

\(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}\text{Source}&\text{Sum of Squares (SS)}&{d}{f}&\text{Mean Square (MS)}\backslash{h}{l}\in{e}\text{Between treatments}&&&\backslash{h}{l}\in{e}\text{Within treatments}&&&\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)

ANOVA summary tables typically have a "Total" row not induded in the partial table you just completed. Which of the following is a possible reason for induding this row?

a) The \(\displaystyle{M}{S}_{{\to{t}{a}{l}}}\) is used in the calculation of the F test statistic.

b) The \(\displaystyle{S}{S}_{{\to{t}{a}{l}}}\) is used in the calculation of the F test statistic.

c) The total sums of squares is the sometimes called the "error term"

d) The \(\displaystyle{S}{S}_{{\to{t}{a}{l}}}{i}{s}{s}{o}{m}{e}\times{e}{a}{s}{i}{e}{r}\to{c}{a}{l}{c}\underline{{a}}{t}{e}{t}{h}{a}{n}{P}{S}{K}{S}{S}_{{{b}{e}{t}{w}{e}{e}{n}}}\). Since \(\displaystyle{S}{S}_{{{w}{i}{t}{h}\in}}+{S}{S}_{{{b}{e}{t}{w}{e}{e}{n}}}={S}{S}_{{\to{t}{a}{l}}}\), you can use \(\displaystyle{S}{S}_{{\to{t}{a}{l}}}\) to calculate \(\displaystyle{S}{S}_{{{b}{e}{t}{w}{e}{e}{n}}}\).

In ANOVA, the F test statistic is the ? of the between-treatments variance and the within-treatments variance. the value of the F test statistic is ?

When the null hypothesis is true, the F test statistic is ? When the null hypotesis is false, the F test statistic is most likely ? In general, you should reject the null hypotesis for.