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

Independent t-test

  1. What is your computed answer? tobs = 4.257

  2. 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.

  3. What would be the alternate hypothesis? The alternate hypothesis would be that life satisfaction scores of older and younger adults are different.

  4. 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.

  5. What is your tcrit? tcrit = 2.101

  6. 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.

  7. 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.

  8. 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