Question

Consider the following hypothesis test.

Ha: μ₁-μ₂=0
H₁: μ₁-μ₂>0

The following results are from independent samples taken from two populations:
Sample 1:
n₁=35
X₁=13.6
S₁=5.6

Sample 2:
n₂=40
X₂=10.1
S₂=8.7

What is the value of the test statistic (to 2 decimals)?

Answer 1

The value of the test statistic is approximately 2.34.

Step-by-step explanation:

To find the test statistic, we first need to calculate the standard error, which is the standard deviation of the difference between the sample means.

The formula for the standard error is:

SE = sqrt((S1^2 / n1) + (S2^2 / n2))

Plugging in the given values, we get:

SE = sqrt((5.6^2 / 35) + (8.7^2 / 40))

≈ 1.499

Next, we calculate the test statistic, which is the difference between the sample means divided by the standard error:

Test Statistic = (X1 - X2) / SE

Plugging in the given values, we get:

Test Statistic = (13.6 - 10.1) / 1.499

≈ 2.34