There are only two outcomes, p (probability of success) or q (probability of failure). Also, p + q = 1

If n1 p1≥10 and n1 q1≥10 for sample 1 and n2 p2≥10 and n2 q2≥10 for sample 2, then normal approximation to binomial is valid

5-Step Hypothesis

Null and Alternative Hypothesis

Ho: there is no significant difference in the population proportion of two groups. p1-p2=0

Ha1: there is significant difference in the population proportion of two groups. p1-p2≠0 (Two tailed test)

Ha2: population mean of sample 1 is less than that of sample 2. μ1-μ2<0 (Left tailed test)

Ha3: population mean of sample 1 is greater than that of sample 2. μ1-μ2>0 (Right tailed test)

Test Statistic

Critical value

-z(a/2), z(a/2) (Two tailed test)

-z(a) (Left tailed test)

z(a) (Right tailed test)

P-value

2*(1-P(Z≤|z|) (Two tailed test)

P(Z≤z) (Left tailed test)

P(Z≥z) (Right tailed test)

Decision rule

Reject Ho if |z| > z(a/2) or p-value < alpha (two tailed test)

Reject Ho if –z < -z(a) or p-value < alpha (left tailed test)

Reject Ho if z > z(a) or p-value < alpha (right tailed test)

Confidence Interval

Standard error (SE) and margin of error (ME) is given by:

100(1-alpha)% Confidence interval for the population proportions difference is given by:

This implies I am 100(1-alpha)% confident that estimated population mean difference between two samples lies in the obtained interval. If confidence interval contains 0, I fail to reject null hypothesis ho and conclude that there is no significant difference in the means of two samples.