Assumptions:
a) Simple Random Samples and Independent Samples
b) Normal Difference or Large Sample
c) σ1 and σ2 Unknown
d) σ1 ≠ σ2 (Variances are unequal)
Step 1: Set up null and alternative hypotheses.
H0: μ1 = μ2
(Note: H0: μ1 = μ2 ⇔ H0: μ1 - μ2 = 0)
H1: μ1 ≠ μ2
(Note: H1: μ1 ≠ μ2 ⇔ H1: 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, s1, s2,
n1, and n2; and then calculate test statistic
x̅1 for population 1:
s1 (population 1 standard deviation) =
n1 (sample size 1) =
(x̅2) for population 2:
s2 (population 2 standard deviation) =
n2 (sample size 2) =
(Note: From Step 1, we have H0: μ1 = μ2 ⇔ H0: μ1 - μ2 = 0; therefore, μ1 - μ2 = 0)
Step 4: Determine P-value
Using the test statistic in Step 3 as a t-score, we will find the left-tailed area and right-tailed area corresponding to this t-score.
(Note: We use the t-distribution since the population stanadard deviations (σ1 and σ2) are unknown.)