The alpha level is the set of analysis of the data. Identify the boundaries that separate the extreme samples from the samples that are more obviously consistent with the null hypothesis. Assume the null hypothesis is nondirectional, meaning that the critical region is split across both tails of the distribution. The z-score boundaries at an alpha level α = .05 are:

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The z-score boundaries at an alpha level α = .05 are:

When critical region is split across both tails of the distribution.

Then our alpha level is also divided by two and the Zscore of the probability obtained is looked up on the z table.

α = .05

Since critical region is split into 2, alpha will be divided by two to obtain the probability value ;

α/2 = 0.05 / 2

α/2 = 0.025

Zα/2 = Z.025

From the z table, probability of 0.025 corresponds to a Zscore of - 1.96 ( negative tail)

Also, (1 - 0.025) = 0.975 corresponds to a Zscore of - 1.96 ( positive tail)

Z.025 = ±1.96

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