You have a random sample of 10 Population 1 members and a sample of 13 Population 2 members, and you want to set up a test using the following hypotheses: H₀: μ₁ – μ₂ < 0 (The mean of Population 1 is no greater than the mean of Population 2.) H_a: μ₁ – μ₂ > 0 (The mean of Population 1 is greater than the mean of Population 2.) Assume that the two population distributions are normal and that the population standard deviations are equal. 

a. Using a significance level of .01, find the critical t_score for the test and state your decision rule.

b. Suppose the sample results are x₁ = 98 and x₂ = 90. Compute the appropriate test statistic, t stat , and report your decision. The sample standard deviations are s₁ = 6.2 and s₂ = 5.6. 

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.