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:

Question

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.

Question 4
Select one answer.
10 pointsIf we let ì1, ì2, and ì3 be the mean SAT scores for students who use learning strategies 1, 2, and 3, respectively, the appropriate hypotheses in this case are:
(a)

(b)

(c)

(d)

(e) Both (a) and (c) are correct.
(f) Both (b) and (d) are correct.
Question 5
Select one answer.
10 pointsOne of the conditions that allows us to use ANOVA safely is that of equal (population) standard deviations. Can we assume that this condition is met in this case?
(a) No, since the three sample standard deviations are not all equal.
(b) No, since the population standard deviations are not given, so we cannot check this condition.
(c) Yes, since 5.7 - 4.9 < 2.
(d) Yes, since 5.7 / 4.9 < 2.
Question 6
Select one answer.
10 pointsUsing the following output:

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.
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Answer 1

Question 4: The appropriate hypotheses in this case are:

(c) μ1 = μ2 = μ3 (null hypothesis) and μ1 ≠ μ2 ≠ μ3 (alternative hypothesis)

Question 5: We cannot assume that the condition of equal population standard deviations is met in this case because (b) the population standard deviations are not given, so we cannot check this condition.

Question 6: Based on the given output, we can conclude that (c) the data provide strong evidence that the three mean SAT scores (representing the three learning strategies) are not all equal.

Answer 2

Question 4 asks about the appropriate hypotheses in this case. To determine the hypotheses, we need to consider the mean SAT scores for the three different study strategies. Let's assign these means as μ1, μ2, and μ3 for study strategies 1, 2, and 3, respectively.

The null hypothesis (H0) assumes that there is no difference in the mean SAT scores across the study strategies, so H0: μ1 = μ2 = μ3.

The alternative hypothesis (Ha) assumes that there is a difference in the mean SAT scores across the study strategies, so Ha: at least one mean is different.

Therefore, the appropriate hypotheses in this case are (c): H0: μ1 = μ2 = μ3 and Ha: at least one mean is different.

Moving on to Question 5, it asks whether we can assume the assumption of equal population standard deviations is met. Unfortunately, the question does not provide the information about the population standard deviations. Therefore, we cannot check this condition. Hence, the correct answer is (b): No, since the population standard deviations are not given, so we cannot check this condition.

Lastly, Question 6 is about the conclusion we can draw from the given output. The output shows the p-value for the ANOVA test. In this case, the p-value is less than the significance level (typically 0.05), indicating that there is strong evidence to reject the null hypothesis.

Since we reject the null hypothesis, we can conclude that there is strong evidence that the three mean SAT scores (representing the three learning strategies) are not all equal. Hence, the correct answer is (c): the data provide strong evidence that the three mean SAT scores (representing the three learning strategies) are not all equal.

Answer 3

Data is missing.

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