You have a random sample of 10 population members from each of two normal populations, and you want to set up a test using the following hypotheses:

H₀: μ₁ – μ₂ = 0 H_a: μ₁ – μ₂ ≠ 0

a. Using a significance level of .05, identify the critical t_scores for the test and state your decision rule. 

b. Suppose the sample results are x̅₁ = 17.5 and x̅₂ = 15. Compute the appropriate test statistic, t stat, and report your decision. The sample standard deviations are s₁ = 1.6 and s₂ = 2.0. Assume the two population standard deviations are equal. 

c. Use a statistical calculator or a suitable statistical software package to find the p_value for your sample result. Use the p_value to make your decision and report the result.