Question: The one-sample t-test requires that you know the population mean. It is unusual to have this information, so most studies compare two samples. Each sample measures a different condition of the independent variable. For example before conducting a study, it is important to know if you would need to conduct a related-samples t-test or an independent-samples t-test. Independent samples are groups that are not related to each other. One group has been randomly selected without worrying about who is in the other group. Related samples are groups that are deliberately selected to be similar to each other. For example, you might want to select two groups that have similar heights. If height could affect the experiment, it’s best to match the groups on that variable.

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

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 t_obt = 1.49. Report the statistical results using the correct format.

? What should Martha conclude?