To determine the relative effectiveness of different study strategies for the SAT, suppose three groups of students are randomly selected: one group took the SAT without any prior studying; the second group took the SAT after studying on their own from a common study booklet available in the bookstore; and the third group took the SAT after completing a paid summer study session from a private test-prep company. The means and standard deviations of the resulting SAT scores from this hypothetical study are summarized below:Since we are comparing more than 2 groups, we will use ANOVA to test whether the data provide evidence that SAT score is related to study strategy.
The following hypotheses were tested:
H0: μ1 = μ2 = μ3
Ha: μ1, μ2, and μ3 are not all equal
The analysis was run on the data and the following output was obtained:
Which of the following is a valid conclusion based on the output? Check all that apply.
A. The data provide strong evidence that SAT scores are related to learning strategy.
B. The data provide strong evidence that SAT scores are related to learning strategy in the following way: The mean SAT score for students who pay for coaching is higher than the mean SAT score for students who study themselves, which in turn is higher than that of students who do not study for the test.
C. The data provide strong evidence that the three mean SAT scores (representing the three learning strategies) are not all equal.
D. The data do not provide sufficient evidence that SAT scores are related to learning strategy.