SE = √(p̂1(1-p̂1)/n1 + p̂2(1-p̂2)/n2)

(p̂1 - p̂2) ± z* * √(p̂1(1-p̂1)/n1 + p̂2(1-p̂2)/n2)

p̂1 - p̂2

(p̂1 - p̂2) - z* * √(p̂1(1-p̂1)/n1 + p̂2(1-p̂2)/n2)

(p̂1 - p̂2) + z* * √(p̂1(1-p̂1)/n1 + p̂2(1-p̂2)/n2)

Both samples must be random samples to generalize findings to the population.

Each population should be at least 10 times larger than its respective sample size (10% condition), or random assignment is used.

Both samples must have at least 10 expected successes and 10 expected failures: n₁p̂₁ ≥ 10, n₁(1-p̂₁) ≥ 10, n₂p̂₂ ≥ 10, and n₂(1-p̂₂) ≥ 10.

Checking conditions ensures the validity of the inference and that the results can be reliably generalized.

We are [confidence level]% confident that the true difference in [context] is between [lower bound] and [upper bound].

A confidence interval used to estimate the difference between two population proportions for a categorical variable.

The difference between the two sample proportions: p̂1 - p̂2.

The 'buffer zone' around the point estimate, calculated using the critical value (z-score) and standard error.

A measure of the variability of the difference between two sample proportions.

It suggests there might not be a significant difference between the two population proportions.