Question

an anger - management course claims that, after completing its seminar, participants will lose their tempers less often. always a skeptic, you decide to test this claim. a random sample of 12 seminar participants is chosen, and these participants are asked to record the number of times that they lost their tempers in the two weeks prior to the course. after the course is over, the same participants are asked to record the number of times that they lost their tempers in the next two weeks. the following table lists the results of the survey. using these data, test the claim at the 0.01 level of significance assuming that the population distribution of the paired differences is approximately normal. let d=(participants after completing the anger - management course)−(participants before completing the anger - management course).

number of times temper was lost during a two - week period

before	6	7	10	11	8	12	9	8	3	7	11	12
after	5	5	11	8	8	8	6	9	4	6	9	12

step 1 of 3: state the null and alternative hypotheses for the test. fill in the blank below.

$h_0:mu_d = 0$
$h_a:mu_d$______0

Explanation:

Step1: Understand the claim

The claim is that after the anger - management course, participants lose their tempers less often. So, we expect the mean of the paired differences $\mu_d$ (after - before) to be less than 0.

Step2: Determine the alternative hypothesis

Since we expect $\mu_d<0$ based on the claim, the alternative hypothesis $H_a$ is $\mu_d < 0$.

Answer:

$H_0:\mu_d = 0$
$H_a:\mu_d<0$