Appendix A.35

Two Proportions Hypothesis Test

Test whether two population proportions are equal or compare them directionally.

Two-Proportion Z-Test Calculator

Compare two population proportions from independent samples

Sample 1

p̂₁ = 0.2250

Sample 2

p̂₂ = 0.1667

Hypotheses

Null:
Alternative:

Requirements Met

Calculations

Pooled Proportion
Standard Error
Difference
Test Statistic

Standard Normal Distribution

-1.961.960z₀ = 1.43RejectRejectFail to Reject

Classical Approach

Critical Region: z < -1.960 or z > 1.960
z₀ = 1.4265 is NOT in rejection region

P-Value Approach

P-value = 0.1537
P-value ≥ α = 0.05

Fail to Reject H₀

At the α = 0.05 significance level, there is insufficient evidence to conclude that the two population proportions are different.