You have a random sample of 100 population members from each of two populations. You intend to use sample results to test the following hypotheses: H₀: μ₁ – μ₂ < 0 H_a: μ₁ – μ₂ > 0 

a. Suppose the sample results are x̅₁ = 85 and x̅₂ = 82. Compute the sample test statistic, z stat. Assume the population standard deviations are σ₁ = 9 and σ₂ = 11.

b. Using a significance level of .01, show the critical z-scores, z_c , for the test and state your decision rule. Report your decision.