Question

Consider the following hypothesis test.

H_{0}: μ_{1} - μ_{2} ≤ 0

H_{a}: μ_{1} - μ_{2} > 0

n_{1} =
40,
_{1} =
25.2,
σ_{1} =
5.2

n_{2} =
50,
_{2} =
22.8,
σ_{2} = 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:

μ_{1} : Mean of population 1 (Std. dev. = 5.2)

μ_{2} : Mean of population 2 (Std. dev. = 6)

μ_{1} - μ_{2} : Difference between two means

H_{0} : μ_{1} - μ_{2} = 0

H_{A} : μ_{1} - μ_{2} > 0

**Hypothesis test results:**

Difference | n_{1} |
n_{2} |
Sample mean | Std. err. | Z-stat | P-value |
---|---|---|---|---|---|---|

μ_{1} -
μ_{2} |
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

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