Consider the hypothesis test H 0 : 1 = 2 against H 1 :

Consider the hypothesis test H₀: μ₁ = μ₂ against H₁: μ₁ = μ₂. Suppose that sample sizes n₁ = 15 and n₂ = 15, that x̅₁ = 6.2 and x̅₂ = 7.8, and that s²₁ = 4 and s²₂ = 6.25. Assume that σ²₁ = σ²₂ and that the data are drawn from normal distributions. Use α = 0.05.

(a) Test the hypothesis and find the P-value.

(b) Explain how the test could be conducted with a confidence interval.

(c) What is the power of the test in part (a) if μ₁ is 3 units less than μ₂?

(d) Assume that sample sizes are equal. What sample size should be used to obtain β = 0.05 if μ₁ is 2.5 units less than μ₂? Assume that α = 0.05.