Assumptions: a) Simple Random Sample
b) Normal Difference or Large Sample
c) σ1 and σ2 Known.
Step 1: Set up null and alternative hypotheses.
Ho: μ1 = μ2
(Note: Ho: μ1 = μ2 ⇔ Ho: μ1 - μ2 = 0)
Ha: μ1 ≠ μ2
(Note: Ha: μ1 ≠ μ2 ⇔ Ha: μ1 - μ2 ≠ 0)
Step 2: Input α (level of significance of hypothesis test).
α =
(Note: α = level of significance of hypothesis test
= probability of making Type I error.)
Step 3: Input x̅1, x̅2, σ1, σ2,
n1, and n2; and then calculate test statistic
x̅1 (sample mean 1):
s1 (sample standard deviation 1) =
n1 (sample size 1) =
x̅2 (sample mean 2):
s2 (sample standard deviation 2) =
n2 (sample size 2) =
(Note: From Step 1, we have H0: μ1 = μ2 ⇔ H0: μ1 - μ2 = 0; therefore, μ1 - μ2 = 0)
Step 4: Find Critical Values
Since the population standard deviations (σ1 and σ2) are unknown, we will use the t-distribution to find the critical values.
-tα/2 is the t-score corresponding to the left-tailed area.
tα/2 is the z-score corresponding to the right-tailed area.
Degrees of Freedom = smaller of (n1 - 1) or (n2 - 1)