Question

Explain how to perform a​ two-sample z-test for the difference between two population means using independent samples with sigma 1 and sigma 2 known.

Answer 1

Answer:

Step-by-step explanation:

In the two independent samples application, it involves the test of hypothesis that is the difference in population means, μ1 - μ2. The null hypothesis is always that there is no difference between groups with respect to means.

Null hypothesis: ∪₁ = ∪₂. where ∪₁ represent the mean of sample 1 and ∪₂ represent the mean of sample 2.

A researcher can hypothesize that the first mean is larger than the second (H1: μ1 > μ2 ), that the first mean is smaller than the second (H1: μ1 < μ2 ), or that the means are different (H1: μ1 ≠ μ2 ). These ae the alternative hypothesis.

Thus for the z test:

    if n₁ > 30 and n₂ > 30

     z = X₁ - X₂ / {Sp[√(1/n₁ + 1/n₂)]}

where Sp is √{ [(n₁-1)s₁² + (n₂-1)s₂²] / (n₁+n₂-2)}