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.

1. 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:
   
   

   • H₀: μ₁ = μ₂ = μ₃

     H_a: μ₁, μ₂, μ₃, are not all equal

   • H₀: μ₁, μ₂, μ₃, are not all equal

     H_a: μ₁ = μ₂ = μ₃

   • H₀: μ₁ = μ₂ = μ₃

     H_a: μ₁ ≠ μ₂ ≠ μ₃

   • H₀: μ₁ ≠ μ₂ ≠ μ₃

     H_a: μ₁ = μ₂ = μ₃

   • None of the above are correct.

2. 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?
   
   

   • Yes, because 14.18 - 11.71 < 2.
   • Yes, because 14.18/11.71 < 2.
   • No, because the standard deviations are not equal.
   • Unable to determine from the information provided.

3. The analysis was run on the data and the following output was obtained:
   
   
   Based on this information, we :
   
   

   • 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.
   • 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.
   • 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.
   • 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.