Practice Problems: t-tests
Researchers want to examine the effect of perceived control on health complaints of geriatric patients in a long-term care facility. Thirty patients are randomly selected to participate in the study. Half are given a plant to care for and half are given a plant but the care is conducted by the staff. Number of health complaints are recorded for each patient over the following seven days. Compute the appropriate t-test for the data provided below.
|Control over Plant ||No Control over Plant|
|23 ||35 |
|12 ||21 |
|6 ||26 |
|15 ||24 |
|18 ||17 |
|5 ||23 |
|21 ||37 |
|18 ||22 |
|34 ||16 |
|10 ||38 |
|23 ||23 |
|14 ||41 |
|19 ||27 |
|23 ||24 |
|Mean = 16.6||Mean = 27.066666666|
|S = 7.790103612||S = 7.741047056|
|S2 = 60.68571429 ||S2 = 59.92380952|
- What is your computed answer? tobs = 3.691
- What would be the null hypothesis in this study? Control over a plant will have no impact on the number of health complaints. Whether one has control over the care of a plant or not, the number of health complaints will be the same.
- What would be the alternate hypothesis? The group of individuals who have control over a plant will have either fewer or more health complaints as a group than the group that does not have control over the plants.
- What probability level did you choose and why? .05 Again, I would like to avoid a Type II error. I would like to be able to demonstrate if the plants have any impact on reducing health complaints.
- What are your degrees of freedom? N + N - 2 = 28
- Is there a significant difference between the two groups? Yes, the group that had control over caring for the plants had significantly fewer health complaints. The tobs was not only in the tail for the .05 level but the .01 level as well.
- Interpret your answer. Patients with control over a plant had significantly fewer health complaints than patients with no control over the care of the plant (t = 3.691, p < .01)
- If you have made an error, would it be a Type I or a Type II error? Explain your answer. There is a 1 percent chance that I have made a Type I error. It may be that having control over a plant really has no impact on the number of health complaints of geriatric patients in a long-term care facility.
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