Question

question 2 of 6, step 1 of 3
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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 0.10 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 4 4 3 8 4 11 11 6 10 7 5 6
after 3 4 4 4 4 8 10 5 8 7 4 5

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

h₀: μ_d = 0
hₐ: μ_d ______ 0

answer

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options: <, ≠, >

Explanation:

The claim is that participants will lose their tempers less often after the course. Since \( d=\text{(after)} - \text{(before)} \), if they lose their tempers less often after, then \( \text{after}<\text{before} \), so \( d=\text{after}-\text{before}<0 \). The alternative hypothesis \( H_a \) should reflect this claim. So we need to check if \( \mu_d < 0 \).

Step 1: Understand the claim

The anger - management course claims that after the seminar, participants lose their tempers less often. So the number of times after (\( \text{after} \)) is less than the number of times before (\( \text{before} \)).

Step 2: Relate to the paired difference \( d \)

Given \( d=\text{after}-\text{before} \), if \( \text{after}<\text{before} \), then \( d=\text{after}-\text{before}<0 \). The null hypothesis \( H_0:\mu_d = 0 \) (no difference), and the alternative hypothesis \( H_a \) should be \( \mu_d<0 \) to test the claim that after the course, the number of temper - losses is less (so \( d \) is negative on average).

Answer:

\( < \) (corresponding to the option " < ")