A researcher claims that students in a private school have exam scores that are at most 8 points higher than those of students in public schools. Random samples of 60 students from each type of school are selected and given an exam. The results are shown. At α = 0.05, test the claim.

Private school                Public school
x̅₁ = 110......................................x̅₂ = 104
σ₁ = 15.........................................σ₂ = 15
n₁ = 60.........................................n₂ = 60