Independent random samples of n = 15 and n = 13 observations were selected from two...

 

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Independent random samples of n₁ = 15 and n₂ = 13 observations were selected from two normal populations with equal variances. Population Sample Size Sample Mean Sample Variance 1 2 15 13 34.9 32.2 4.8 5.8 (a) Suppose you wish to detect a difference between the population means. State the null and alternative hypotheses for the test. O Ho: (₁H₂) = 0 versus H₂: (H₁-H₂) > 0. Ho: (14₁ - 1₂) = 0 versus H₂: (11₁ 11₂) * 0 Hoi (₁H₂) = 0 versus H₂: (H₁-H₂) = 0 Ho: (11-1₂) < 0 versus Ha: (₁-1/₂) > 0 Ho: (1-₂) = 0 versus H₁: (₁ 14₂) <0. (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> (c) Find the value of the test statistic. (Round your answer to three decimal places.) t = (d) Find the approximate p-value for the test. O p-value < 0.010 O 0.010 < p-value < 0.020 O 0.020 < p-value < 0.050 O 0.050 < p-value < 0.100 O 0.100 < p-value < 0.200 O p-value < 0.200 (e) Conduct the test and state your conclusions. O Ho is rejected. There is insufficient evidence to conclude that there is a significant difference between the population means. 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 insufficient evidence to conclude that there is a significant difference between the population means. OH is not rejected. There is sufficient evidence to conclude that there is a significant difference between the population means. Independent random samples of n₁ = 15 and n₂ = 13 observations were selected from two normal populations with equal variances. Population Sample Size Sample Mean Sample Variance 1 2 15 13 34.9 32.2 4.8 5.8 (a) Suppose you wish to detect a difference between the population means. State the null and alternative hypotheses for the test. O Ho: (₁H₂) = 0 versus H₂: (H₁-H₂) > 0. Ho: (14₁ - 1₂) = 0 versus H₂: (11₁ 11₂) * 0 Hoi (₁H₂) = 0 versus H₂: (H₁-H₂) = 0 Ho: (11-1₂) < 0 versus Ha: (₁-1/₂) > 0 Ho: (1-₂) = 0 versus H₁: (₁ 14₂) <0. (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> (c) Find the value of the test statistic. (Round your answer to three decimal places.) t = (d) Find the approximate p-value for the test. O p-value < 0.010 O 0.010 < p-value < 0.020 O 0.020 < p-value < 0.050 O 0.050 < p-value < 0.100 O 0.100 < p-value < 0.200 O p-value < 0.200 (e) Conduct the test and state your conclusions. O Ho is rejected. There is insufficient evidence to conclude that there is a significant difference between the population means. 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 insufficient evidence to conclude that there is a significant difference between the population means. OH is not rejected. There is sufficient evidence to conclude that there is a significant difference between the population means.