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:
n x s
Group1 12 1014.1 4.9
Group2 12 1015.8 5.1
Group3 9 1023.7 5.7
Use the following output
Analysis for variance of SAT
DF SS MS F P
Group 2 625.2 312.6 11.43 0.000
Error 30 820.7 27.4
total 32 1445.9
we can conclude that:
(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.
(e) Both (a) and (c) are correct.

The p-value of the test is very small for all the commonly used significance level. The null hypothesis will be rejected at any commonly used significance level.

Conclusion:

There is enough evidence to support the claim that at least on of the strategy have an effect on the SAT scores of students.

This implies that the three mean SAT scores are not all equal and the SAT scores are related to learning strategy.

Thus, the correct option is (e).