Practice Problems: t-test Answer
A research study was conducted to examine the differences between older and younger adults on perceived life satisfaction. A pilot study was conducted to examine this hypothesis. Ten older adults (over the age of 70) and ten younger adults (between 20 and 30) were give a life satisfaction test (known to have high reliability and validity). Scores on the measure range from 0 to 60 with high scores indicative of high life satisfaction; low scores indicative of low life satisfaction. The data are presented below. Compute the appropriate t-test.
|Older Adults ||Younger Adults|
|45 ||34 |
|38 ||22 |
|52 ||15 |
|48 ||27 |
|25 ||37 |
|39 ||41 |
|51 ||24 |
|46 ||19 |
|55 ||26 |
|Mean = 44.5 ||Mean = 28.1|
|S = 8.682677518 ||S = 8.543353492|
|S2 = 75.388888888 ||S2 = 72.988888888|
- What is your computed answer? tobs = 4.257
- What would be the null hypothesis in this study? The null hypothesis would be that there are no significant differences between younger and older adults on life satisfaction.
- What would be the alternate hypothesis? The alternate hypothesis would be that life satisfaction scores of older and younger adults are different.
- What probability level did you choose and why? .05 - if one makes either a Type I or a Type II error, there will be no major risk involved.
- What is your tcrit? tcrit = 2.101
- Is there a significant difference between the two groups? Yes, the tobs is in the tail. In fact, even if one uses a probability level the t is still in the tail. Thus, we conclude that we are 99.9 percent sure that there is a significant difference between the two groups.
- Interpret your answer. Older adults in this sample have significantly higher life satisfaction than younger adults (t = 4.257, p < .001). As this is a quasi-experiment, we can not make any statements concerning the cause of the difference.
- If you have made an error, would it be a Type I or a Type II error? Explain your answer. If an error was made, it would have to be a Type I error; there really are no differences in life satisfaction between younger and older adults. We just got these results by chance.
Back to Practice Problems: t-tests