3. Level of significance (be careful as to one-tailed or two-tailed)

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The prompt asks about the level of significance and cautions about one-tailed vs two-tailed tests. In a two-tailed test with an overall alpha of 0.05, the probability in each tail must sum to 0.05, so you split it evenly between the two extremes. That gives 0.025 in the left tail and 0.025 in the right tail. Therefore, the critical region for each tail corresponds to alpha/2 = 0.05/2 = 0.025. If instead you were conducting a one-tailed test, you would place the entire 0.05 in a single tail (left or right depending on the alternative hypothesis). The diagram also shows a null hypothesis of no difference (μ1 − μ2 = 0), which is tested against the alternative that there is a difference; in such a two-tailed framework, the rejection regions are at the two tails with 0.025 in each. In short, for a two-tailed test with alpha = 0.05, the per-tail significance level is 0.025. If the problem were one-tailed, you would use 0.05 in the single tail instead.

BSTA011 Hypothesis Testing of 2 populations ( Population Mean )

3. Level of significance (be careful as to one-tailed or two-tailed)

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