Question

A researcher is interested in determining whether the mean of group 1 is 10 units larger than the mean of group 2. Which of the following represents the alternative hypothesis for testing the researcher's theory?

a. Ha: µ1 – µ2 ≤ 10
b. Ha: µ1 = µ2
c. Ha: µ1 – µ2 ˃ 10
d. Ha: µ1 – µ2 = 0

Answer 1

c. Ha: µ1 – µ2 ˃ 10

Explanation:

given that a researcher is interested in determining whether the mean of group 1 is 10 units larger than the mean of group 2.

There are two groups with different means.

We want to check whether the difference of mean 1 - mean 2 is greater than 10 units

For this we set up hypotheses with null as difference equal to 10 and alternate as difference large than 10

Hence the hypotheses would be

H0: Mean 1 - Mean 2 =10

Ha: Mean 1 -Mean 2 >10

In notations this would be

c. Ha: µ1 – µ2 ˃ 10