Independent random samples of n₁ = 18 and n₂ = 13 observations were selected from two normal populations with equal variances. Sample Size Sample Mean Sample Variance Population 1 2 (a) Suppose you wish to detect a difference between the population means. State the null and alternative hypotheses for the test. Ho: (H₁-H₂) = 0 versus H₂: (#₁ - M₂) > O Ho: (H₁-H₂) < 0 versus H₂: (H₁-H₂) >0 Ho: (H₁-H₂) = 0 versus H₂: (H₁-H₂) # 0 Ho: (H₁-H₂) = 0 versus H₂: (μ₁ −μ₂) <0 Ho: (M₁ - H₂) = 0 versus H₂: (H₁-H₂) = 0 0.010 < p-value < 0.020 0.020 < p-value < 0.050 0.050 < p-value < 0.100 0.100 < p-value < 0.200 18 13 34.9 32.2 4.1 5.4 (b) Find the rejection region for the test in part (a) for a = 0.01. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.) t> t< O p-value < 0.200 (c) Find the value of the test statistic. (Round your answer to three decimal places.) (d) Find the approximate p-value for the test. O p-value < 0.010 (e) Conduct the test and state your conclusions. O Ho is rejected. There is sufficient evidence to conclude that there is a significant difference between the population means. O Ho is not rejected. There is sufficient evidence to conclude that there is a significant difference between the population means. O Ho is rejected. There is insufficient evidence to conclude that there is a significant difference between the population means. O Ho is not rejected. There is insufficient evidence to conclude that there is a significant difference between the