Critical Z Score Calculator

α (Significance Level)

A value between 0 and 1, e.g. 0.05 for a 5% significance level.

About This Test

What Is a Critical Z-Score?

The critical z-score is the cutoff on the standard normal distribution that separates "likely due to chance" from "statistically significant." If your calculated z-statistic goes past this cutoff, you reject the null hypothesis.

When to Use It

Any hypothesis test or confidence interval based on the standard normal distribution
Large-sample tests where the normal approximation applies
Proportion tests, where the sampling distribution is approximately normal

The Concept

\[ P(Z > z_{\alpha}) = \alpha \]

Worked Example

At α = 0.05, what are the critical z-values?

Two-tailed: \( z_{0.025} \approx \pm 1.96 \) — probably the single most-cited number in statistics.
One-tailed (right): \( z_{0.05} \approx 1.645 \)
One-tailed (left): \( z_{0.05} \approx -1.645 \)

Your Results

Shaded regions show the two-tailed rejection zone. Dashed lines mark the one-tailed (left and right) critical values.

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Calculating Z-Score in Business Analytics

Practical guide with real-world business examples.

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