Consider the hypothesis test H 0 1 2 against H 1 1 2 with known variances 1 10 and 2 5 Suppose that sample sizes n 1 10 and n 2 15 and that x 1 4 7 and x 2 7 8 Use 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 th...

a 1 The parameter of interest is the difference in means 1 2 Note that 0 0 ...

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

Question:

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 x̅₁ = 4.7 and x̅₂ = 7.8. 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.

(d) Assume that sample sizes are equal. What sample size should be used to obtain β = 0.05 if the true difference in means is 3? Assume that α = 0.05.

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