In which one of the following situations would it be most appropriate to use an ANOVA to analyze the data?

1.  A researcher is interested in determining the most effective format for advertising. He randomly assigns 60 people to one of three groups: (1) television commercial, (2) radio commercial, or (3) magazine advertisement. Group members review the commercial and then report whether or not they would buy the product.
2.  In order to determine the effectiveness of different diet plans, 90 people are randomly assigned to one of three groups: (1) low calorie diet, (2) low-fat diet, or (3) low-carb diet. At the end of 60 days, the number of pounds lost was recorded for each of the participants.

To determine whether there is a relationship between the type of school attended and verbal reasoning scores for Irish students, three samples with 25 students, in each group, were randomly selected from data used by Raferty and Hout (1985). One group of students attended secondary school, the second group of students attended vocational school, and the third group consisted of students who attended only primary school.

Raftery, A. E. and Hout, M. (1985). "Does Irish education approach the meritocratic ideal? A logistic analysis." Economic and Social Review, 16, 115-140.

Let µ1, µ2, and µ3 be the mean verbal reasoning scores for students who attended secondary school, vocational school, and primary school only, respectively.

Which of the following are the appropriate null and alternative hypotheses?

1. H0: μ1 = μ2 = μ3

   Ha: μ1, μ2, μ3, are not all equal

2. H0: μ1, μ2, μ3, are not all equal

   Ha: μ1 = μ2 = μ3

3. H0: μ1 = μ2 = μ3

   Ha: μ1 ≠ μ2 ≠ μ3

4. H0: μ1 ≠ μ2 ≠ μ3

   Ha: μ1 = μ2 = μ3

To determine whether there is a relationship between the type of school attended and verbal reasoning scores for Irish students, three samples with 25 students, in each group, were randomly selected from data used by Raferty and Hout (1985). One group of students attended secondary school, the second group of students attended vocational school, and the third group consisted of students who attended only primary school.

Raftery, A. E., and Hout, M. (1985). Does Irish education approach the meritocratic ideal? A logistic analysis. Economic and Social Review, 16, 115-140.

Here are the three sample standard deviations for the verbal reasoning scores for the three groups (secondary school, vocational school, and primary school only):

Based on this information, do the data meet the condition of equal population standard deviations for the use of the ANOVA?

1.  Yes, because 14.18 - 11.71 < 2.
2.  Yes, because 14.18/11.71 < 2.
3.  No, because the standard deviations are not equal.

To determine whether there is a relationship between the type of school attended and verbal reasoning scores for Irish students, three samples with 25 students, in each group, were randomly selected from data used by Raferty and Hout (1985). One group of students attended secondary school, the second group of students attended vocational school, and the third group consisted of students who attended only primary school.

Raftery, A.E., and Hout, M. (1985). Does Irish education approach the meritocratic ideal? A logistic analysis. Economic and Social Review, 16, 115-140.

The following hypotheses were tested:

H0: μ1 = μ2 = μ3

Ha: μ1, μ2, μ3, are not all equal

The analysis was run on the data and the following output was obtained:

Which of the following is an appropriate conclusion based on the output?

1.  Fail to reject H0 and conclude that the data provide strong evidence that the three mean verbal reasoning scores (representing the three types of schools attended) are not all equal.
2.  Fail to reject H0 and conclude that the data do not provide sufficient evidence that there is a relationship between the type of school attended and verbal reasoning scores for Irish students.
3.  Reject H0 and conclude that the data provide strong evidence that there is a relationship between the type of school attended and verbal reasoning scores for Irish students.
4.  Reject H0 and conclude that the data provide strong evidence that verbal reasoning scores are related to type of school in the following way: the mean verbal reasoning score for Irish students who attended secondary school is higher than the mean verbal reasoning score for Irish students who attended vocational school, which in turn is higher than that of Irish students who attended only primary school.