Here is the scenario:
Suppose we hypothesize that there is a negative (inverse) relationship between treatment and depression. We'd like to test this hypothesis, so we obtain two samples. Sample 1 is drawn from a population of depressed persons who have not received any type of treatment. Sample 2 is drawn from a population of depressed people who HAVE received treatment for depression. No subject in either group has ever interacted with any other subject in either group. Each subject in each group has been administered the MMPI-2. The mean T score of Scale 2 for group 1 is 75, while it is 63 for group 2. The scores, in the population, for both groups are distributed normally. Sample 1 is made up of 20 people, and their Scale 2 scores have a standard deviation of 10. Sample 2 also has 20 people with a Scale 2 standard deviation of 10, as well.
Here is the question:
What is the null hypothesis for the t-test in this problem?
(Please state your answer symbolically, rather than as a sentence.)
(It is OK to spell out the Greek letters.)
Ho: mu1 < mu2 --Answer
mu1 = <X1> +or- t*S1/sqrt(20) = mean ...
The solution answers the question(s) below.