Test the claim about the difference between two population means 1 and 2 at the level of significance a. Assume the samples are

Test the claim about the difference between two population means μ₁ and μ₂ at the level of significance a. Assume the samples are random and independent, and the populations are normally distributed.

Claim: μ₁ = μ2; α = 0.01. Assume σ¹₂ = σ²₂

Sample statistics: x̅₁ = 33.7, s₁ = 3.5, n₁ = 12 and

x₂ = 35.5, s₂ = 2.2, n₂ = 17