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 analysis was run on the data and the following output was obtained: Based on this information, we : A. Fail to reject the 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 the 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 the 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 the 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

The mean scores of students studying in diffrent type of schools are signoficantly diffrent as visible from the numbers 16,115,140.

The null hypothesis states that there is no significant diffrence in means of scores of students studying in different schools.

Alternative Hypothesis states that there is a diffrence in mean scores of atleast one pair.

We see that , there is large diffrence in scores 16 and 140 , which asks us to reject Null Hypothesis Ho, 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

Also, if 16, 115,140 are scores of primary, vocational and secondary respectively, (the order is not clear in question)

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

HOLDS TRUE

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