A study compared the average number of courses taken by a random sample of freshmen at a university with the average number of courses taken by a separate random sample of freshmen at a community college. Which of the following combinations would lead to a test with the highest power? A) n₁ = 50, n₂ = 100 and $\mu$₁ -$\mu$₂ = 1.2 B) n₁ = 70, n₂ = 120 and $\mu$₁ - $\mu$₂ = 1.2 C) n₁ = 50, n₂ = 100 and $\mu$₁-$\mu$₂ = 0.8 D) n₁ = 70, n₂ = 120 and $\mu$₁ -$\mu$₂ = 0.8

Question

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The power of a test increases with larger sample sizes and larger differences between the means. Option B has the largest sample sizes and maintains the larger mean difference of 1.2, leading to the highest power.

A Study Compared the Average Number of Courses Taken by a Random