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 right-tailed area.
