Tukey's 100(1 − α)% confidence interval for the difference between two population means μ_i - μ_j for balanced data is given by ________. A) ( _{i -} _j) ± B) ( _{i -} _j) ± C) ( _{i -} _j) ± D) ( _{i -} _j) ±

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Quizplus · Accepted Answer

Tukey's 100(1 − α)% confidence interval for the difference between two population means is given by (x̄i − x̄j) ± qα,N-k × SE, where x̄i and x̄j are the sample means, qα,N-k is the critical value from the Studentized range distribution, and SE is the standard error of the difference between two sample means. For balanced data, we have N = k × n, where N is the total sample size, k is the number of groups, and n is the sample size per group. Therefore, the standard error can be computed as SE = s√(2/n), where s is the pooled standard deviation computed from the two samples. Substituting the values given in the answer choices, only option B gives the correct formula for the confidence interval with the correct values of the sample means, pooled standard deviation, and critical value.

Tukey's 100(1 − α)% Confidence Interval for the Difference Between