Consider the hypothesis test H 0 : 1 = 2 against H 1 : 1 > 2 with known variances

Consider the hypothesis test H₀: μ₁ = μ₂ against H₁: μ₁ > μ₂ with known variances σ₁ = 10 and σ₂ = 5. Suppose that sample sizes n₁ = 10 and n₂ = 15 and that x₁ = 24.5 and x₂ = 21.3. Use α = 0.01.

(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 2 units greater than μ₂?

(d) Assume that sample sizes are equal. What sample size should be used to obtain β = 0.05 if μ₁ is 2 units greater than μ₂? Assume that α = 0.05.