Martha believes that a relaxation technique involving visualization will help people with mild insomnia fall asleep faster. She randomly selects a sample of 20 participants from a group of mild insomnia patients and randomly assigns 10 to receive visualization therapy. The other 10 participants receive no treatment. Each participant is then measured to see how long (in minutes) it takes him or her to fall asleep. Martha's data are below. The numbers represent the number of minutes each participant took to fall asleep.

No Treatment (X1) Treatment (X2)

22 19
18 17
27 24
20 21
23 27
26 21
27 23
22 18
24 19
22 22

The assignment (1–2 pages):

Please respond to the following questions related to the research study and data presented in the "To Prepare" section.

Should Martha use an independent-samples t-test or a related samples t-test? Explain your answer.


What are the independent and dependent variables?


Using the fact that Martha believes the treatment will reduce the amount of time to fall asleep, state the null and alternate hypotheses.


Would you use a one-tailed or two-tailed test? Explain your response.


What is the df?


Consider that a = .05. Then use Appendix B, Table 2 to determine the critical value, state the value, and how you found it.


Consider that tobt = 1.49. Report the statistical results using the correct format.


What should Martha conclude?

I am very confused, the last paper I did it all wrong. Help please

dependent variable


One tail
df = 9
t = (dbar-mud)/sd/sqrt(n)
t = (2-0)/2.9439/sqrt(10)
t = 2.15
test statistic = 2.15

No problem! I'll help you go through each question step by step.

1. Should Martha use an independent-samples t-test or a related samples t-test? Explain your answer.
In this study, Martha has two groups of participants: one group receiving visualization therapy and the other group receiving no treatment. Since the participants in each group are different and independent from each other, Martha should use an independent-samples t-test. This test compares two independent groups to determine if there is a significant difference between their means.

2. What are the independent and dependent variables?
The independent variable is the type of treatment (visualization therapy or no treatment) that the participants receive. The dependent variable is the time it takes for each participant to fall asleep, as measured in minutes.

3. Using the fact that Martha believes the treatment will reduce the amount of time to fall asleep, state the null and alternate hypotheses.
The null hypothesis (H0) states that there is no significant difference in the mean time to fall asleep between the visualization therapy group and the no treatment group. The alternate hypothesis (H1) states that there is a significant difference in the mean time to fall asleep between the two groups, with the visualization therapy group taking less time to fall asleep.

4. Would you use a one-tailed or two-tailed test? Explain your response.
In this case, we should use a one-tailed test because Martha believes that the treatment will reduce the time to fall asleep compared to the no treatment group. By using a one-tailed test, we are only looking for a significant difference in one direction (specifically, that the visualization therapy group takes less time to fall asleep).

5. What is the df?
The degrees of freedom (df) in an independent-samples t-test is calculated by subtracting 1 from the sum of the sample sizes of the two groups. In this case, the sample sizes are both 10, so the df would be 10 + 10 - 1 = 19.

6. Consider that a = .05. Then use Appendix B, Table 2 to determine the critical value, state the value, and how you found it.
To find the critical value from Table 2 in Appendix B, you need to consider the degrees of freedom (df) and the desired level of significance (alpha, denoted as a). Since our df is 19 and the desired level of significance is a = .05, we can find the critical value under the column "α = .05, One-Tailed" for df = 19. The critical value is 1.734.

7. Consider that tobt = 1.49. Report the statistical results using the correct format.
To report the statistical results, you need to compare the obtained t-value (tobt) with the critical value from the previous question. Since tobt = 1.49 is less than the critical value of 1.734, this means that the obtained t-value is not significant. Therefore, there is not enough evidence to reject the null hypothesis.

8. What should Martha conclude?
Based on the statistical analysis, Martha should conclude that there is not enough evidence to support her belief that visualization therapy reduces the time to fall asleep for people with mild insomnia. The data does not show a significant difference in the mean time to fall asleep between the visualization therapy and no treatment groups. Martha may need to explore other factors or treatments to help mild insomnia patients fall asleep faster.