Question

Consider the following hypothesis test.

                        H₀: μ₁ - μ₂ ≤ 0

                        H_a: μ₁ - μ₂ > 0

                        n₁ = 40,              ₁ = 25.2,                  σ₁    = 5.2                   

                        n₂ = 50,              ₂ = 22.8,                  σ₂   = 6.0

            a. What is the value of the test statistic?

            b. What is the p-value?

            c. With α = 0.05, what is your hypothesis-testing conclusion?

Answer 1

The statistical software output for this problem is :

Two sample Z summary hypothesis test:
μ₁ : Mean of population 1 (Std. dev. = 5.2)
μ₂ : Mean of population 2 (Std. dev. = 6)
μ₁ - μ₂ : Difference between two means
H₀ : μ₁ - μ₂ = 0
H_A : μ₁ - μ₂ > 0

Hypothesis test results:

Difference	n1	n2	Sample mean	Std. err.	Z-stat	P-value
μ1 - μ2	40	50	2.4	1.1815244	2.0312741	0.0211

Test statistics = 2.031

P-value = 0.0211

P-value < 0.05

Reject the null hypothesis