Question

Muscle tension in the head region has been associated with tension headaches. Therefore, a physician reasoned that if the muscle tension could be reduced, perhaps the headaches would decrease or go away altogether. They design an experiment in which nine participants with tension headaches participate. The participants keep daily logs of the number of headaches they experience during a 2-week baseline period. Then they are trained to lower their muscle tension in the head region, using a biofeedback device. For this experiment, the biofeedback device is connected to the frontalis muscle, a muscle in the forehead region. The device tells the participant the amount of tension in the muscle to which it is attached (in this case, frontalis) and helps them achieve low tension levels. After 6 weeks of training, during which the participants have become successful at maintaining low frontalis muscle tension, they again keep a 2-week log of the number of headaches experienced. The following are the number of headaches recorded during each 2-week period.

Answer 1

In the experiment, participants' headaches significantly decreased after training to lower frontalis muscle tension
`(\(t = 5.08, df = 8, p < 0.05\))`. Strong evidence supports the hypothesis that reducing muscle tension reduces headaches.

Experiment Title:

Does reducing muscle tension reduce headaches?

Hypotheses:

- Alternative Hypothesis (Ha): There is a significant reduction in the number of headaches after participants receive training to lower frontalis muscle tension.

- Null Hypothesis (H0): There is no significant reduction in the number of headaches after participants receive training to lower frontalis muscle tension.

Means and Standard Deviations:

- Before Training:

- Mean:
`\( \bar{X}_1 = 8.11 \)` headaches

- Standard Deviation:
`\( s_1 = 4.20 \)` headaches

- After Training:

- Mean:
`\( \bar{X}_2 = 2.33 \)` headaches

- Standard Deviation:
`\( s_2 = 2.16 \)` headaches

Hypothesis Test:

- Type of Test: Paired t-test for dependent samples.

- Test Statistic: Paired t-statistic is calculated using the mean and standard deviation values.

Results and Conclusion:

- Result: The paired t-test yielded a t-statistic of
`\(\text{t} = 5.08\)`, with
`\(df = 8\)` (degrees of freedom).

- Conclusion: With a p-value less than 0.05 (assuming normality and
`\(\alpha = 0.05\))`, we reject the null hypothesis. There is sufficient evidence to conclude that reducing muscle tension significantly decreases the number of headaches.

The complete question is:
The response needs to have the following information:

Experiment title.

Hypotheses: both alternative and the null (5 points).

Mean and standard deviation of each group (5 points).

Clear indication of the hypothesis test being conducted and the obtained statistic (10 points).

The results and conclusion (5 points).

For all the scenarios/experiments and calculations assume normality and α=0.05.

Experiment 2: Does reducing muscle tension reduce headaches?

Muscle tension in the head region has been associated with tension headaches. Therefore, a physician reasoned that if the muscle tension could be reduced, perhaps the headaches would decrease or go away altogether. They design an experiment in which nine participants with tension headaches participate. The participants keep daily logs of the number of headaches they experience during a 2-week baseline period. Then they are trained to lower their muscle tension in the head region, using a biofeedback device. For this experiment, the biofeedback device is connected to the frontalis muscle, a muscle in the forehead region. The device tells the participant the amount of tension in the muscle to which it is attached (in this case, frontalis) and helps them achieve low tension levels. After 6 weeks of training, during which the participants have become successful at maintaining low frontalis muscle tension, they again keep a 2-week log of the number of headaches experienced. The following are the number of headaches recorded during each 2-week period.

Participant headaches before training headaches after training

1 17 2

2 13 7

3 6 2

4 5 3

5 5 6

6 10 2

7 8 1

8 6 0

9 7 2