Using four methods to teach ANOVA, do these four samples differ enough from each other to reject the null hypothesis that type of instruction has no effect on mean test performance?Method to teach ANOVA Mean SD Nmethod 1 (single teacher) 4.85 0.360 34method 2 (co-teachers) 4.61 0.715 31method 3 (computer) 4.61 0.688 36method 4 (lab) 4.38 0.793 32Since we are comparing more than 2 groups, we will use ANOVA to test whether the data provide evidence that test score is related to teaching method.One 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? Yes, since 0.793 − 0.360 < 2. No, since 0.793/0.360 > 2 No, since the four sample standard deviations are not all equal. No, since the population standard deviations are not given, so we cannot check this condition.

o 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 = μ3Ha: μ1, μ2, and μ3 are not all equalThe 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. The data provide strong evidence that SAT scores are related to learning strategy. 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. The data provide strong evidence that the three mean SAT scores (representing the three learning strategies) are not all equal. The data do not provide sufficient evidence that SAT scores are related to learning strategy.

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.Let μ1, μ2, and μ3 be the mean SAT scores for students who use learning strategies 1, 2, and 3, respectively, the appropriate hypotheses in this case are:H0: µ1 = µ2 = µ3Ha: µ1 ≠ µ2 ≠ µ3H0: µ1 ≠ µ2 ≠ µ3Ha: µ1 = µ2 = µ3H0: µ1 = µ2 = µ3Ha: µ1, µ2, µ3 are not all equalH0: µ1, µ2, µ3 are not all equalHa: µ1 = µ2 = 3

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 = μ3Ha: μ1, μ2, and μ3 are not all equalThe 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. The data provide strong evidence that SAT scores are related to learning strategy. 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. The data provide strong evidence that the three mean SAT scores (representing the three learning strategies) are not all equal. The data do not provide sufficient evidence that SAT scores are related to learning strategy.

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.One 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? No, since the three sample standard deviations are not all equal. No, since the population standard deviations are not given, so we cannot check this condition. Yes, since 5.7 − 4.9 < 2. Yes, since 5.7/4.9 < 2.

A teacher is experimenting with a new computer-based instruction and conducts a study to test its effectiveness. In which situation could the teacher use the two-sample t-test for comparing two population means? The teacher randomly divides the class into two groups. One of the groups receives computer-based instruction and the other group receives traditional instruction without computers. After instruction, each student takes a test and the teacher wants to compare the test scores of the two groups. The teacher uses a combination of traditional methods and computer-based instruction. She asks students which they liked better. She wants to determine if the majority prefer the computer-based instruction. The teacher gives each student in the class a pretest. Then she teaches a lesson using a computer program. Afterwards, she gives each student a post-test. The teacher wants to compare test scores for each student to see whether the data will show an improvement.