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.]

If we let µ1, µ2, and µ3 be the mean verbal reasoning scores for students who attended secondary school, vocational school, and primary school only, respectively, the appropriate hypotheses in this case are:

A. H0: 1 = 2 = 3, Ha: 1, 2, 3, are not all equal

B. H0: 1, 2, 3, are not all equal,

Ha: 1 = 2 = 3

C. H0: 1 = 2 = 3,

Ha: 1 2 3

D. H0: 1 2 3,

Ha: 1 = 2 = 3

E. None of the above are correc

A. H0: 1 = 2 = 3, Ha: 1, 2, 3, are not all equal

B. H0: 1, 2, 3, are not all equal,

Ha: 1 = 2 = 3

C. H0: 1 = 2 = 3,

Ha: 1 2 3

D. H0: 1 2 3,

Ha: 1 = 2 = 3

E. None of the above are correc

Explanation / Answer

To determine whether there is a relationship between the type of school attended and verbal reasoning scores for Irish students, we need to test whether the mean verbal reasoning scores for students who attended secondary school, vocational school, and primary school only are equal or atleast one of the mean verbal reasoning scores is not equal to other two scores.

So, the null and alternative hypothesis would be,

A. H0: 1 = 2 = 3, Ha: 1, 2, 3, are not all equal

So, option A is correct.

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