Assumptions:
a) Simple Random Sampling
b) n1(p̂1)(1 - p̂1) ≥ 10 and n2(p̂2)(1 - p̂2) ≥ 10
c) n1 ≤ 0.05N1 and n2 ≤ 0.05N2
Step 1: Set up null and alternative hypotheses.
H0: p1 = p2
(Note: H0: p1 = p2 ⇔ H0: p1 - p2 = 0)
H1: p1 < p2
(Note: H1: p1 < p2 ⇔ H1: p1 - p2 < 0)
Step 2: Determine level of significance of hypothesis test.
α =
(Note: α = level of significance of hypothesis test
= probability of making Type I error.)
Step 3: Calculate Test Statistic.
For Sample 1:
n1 =
(sample size)
x1 =
(This is the number of successes from sample 1)
p̂1 = x1/n1 =
(This is the sample proportion from sample 1)
For Sample 2:
n2 =
(sample size)
x2 =
(This is the number of successes from sample 2)
p̂2 = x2/n2 =
(This is the sample proportion from sample 1)
p̂ = (x1 + x2)/(n1 + n2)
(Note: From Step 1, we have H0: p1 = p2 ⇔ H0: p1 - p2 = 0; therefore, p1 - p2 = 0)
Step 4: Find Critical Value
zα is the z-score corresponding to the left-tailed area.
