A researcher compares mean birth weights across four ethnic groups using multiple pairwise t-tests (6 comparisons). The probability of committing at least one Type I error across all comparisons, assuming α = 0.05 per test, is approximately:

• A 0.05
• B 0.26 ✓
• C 0.10
• D 0.30

Explanation

The familywise Type I error rate for k independent comparisons is 1 − (1 − α)^k. For 6 comparisons at α = 0.05: 1 − (0.95)^6 ≈ 1 − 0.735 = 0.265, approximately 26%. This is why one-way ANOVA followed by post-hoc tests (e.g., Tukey's, Bonferroni correction) is the correct approach for comparing means across >2 groups, rather than multiple pairwise t-tests.

Reference: Park's Textbook of Preventive and Social Medicine, 27th ed.

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