To determine whether there is a relationship between the type of school attended

Question

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: ?1 = ?2 = ?3

Ha: ?1, ?2, ?3, 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?

A. 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.

B. 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.

C. 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.

D. 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.

Explanation / Answer

he following hypotheses were tested:

H0: 1 = 2 = 3

Ha: 1, 2 and 3, are not all equal

Since p-value < 0.0001, reject null hypothesis.

The correct option is:

D. 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.

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