Suppose you want to test versus Which of the following possible sample results based on a sample of size 36 gives the strongest evidence to reject H₀ in favor of H₁?
A) = 28, S = 6
B) = 27, S = 4
C) = 32, S = 2
D) = 26, S = 9

Question

Suppose you want to test  versus  Which of the following possible sample results based on a sample of size 36 gives the strongest evidence to reject H₀ in favor of H₁?
A) = 28, S = 6 
B) = 27, S = 4 
C) = 32, S = 2 
D) = 26, S = 9

Quizplus · Accepted Answer

To compare the two groups, we need to focus on the last part of the codes (TB8562_11) as these are the same and the only difference between the two groups are the codes before this. We can't necessarily say which code value is expected in each group as nothing is stated about this in the problem, so we need to assume equal variance (thus equal standard deviation) between the two groups. Therefore, we can use a two-sample t-test to compare the means of the two groups.

Among the four choices, B has the smallest sample mean difference (1) between the two groups and the smallest sample standard deviation (4). Since we expect equal variance, a smaller standard deviation means the data points are closer to the mean, which gives us more confidence that the difference in means is a real difference and not due to random chance. Therefore, choice B gives the strongest evidence to reject H₀ in favor of H₁. We want to compare the two samples based on the two codes. The only difference between the codes is "2b7d" and "2b7e". This suggests that the difference in the two samples should be in the corresponding position. Option B has the closest value to this expectation, specifically "2b80". Additionally, it has the smallest value of S among the options, which implies a stronger evidence against the null hypothesis.

Suppose You Want to Test Versus Which of the Following