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Hypothesis Test for a Proportion — One-Sample z-Test

z = (p̂ − p₀) / √(p₀(1−p₀)/n). Use p₀ in the SE (not p̂), because H₀ specifies p = p₀.

StatisticsCommon Core VAR-6.DINFVerified correct ✓

Worked examples

In a sample of n = 200 individuals, x = 82 have the attribute of interest, giving p̂ = 0.4100. The null hypothesis is H₀: p = 0.5. Compute the z-test statistic.
Answer: -2.5456
In a sample of n = 200 individuals, x = 50 have the attribute of interest, giving p̂ = 0.2500. The null hypothesis is H₀: p = 0.3. Compute the z-test statistic.
Answer: -1.543

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Confidence Interval for a Population Proportion (z-interval)

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