In exercises that call for two-sample procedures, you may use either of the two approximations for the degrees of freedom that we have discussed: the value given by your software or the smaller of and . Be sure to state clearly which approximation you have used.

Question 7.63

7.63 Fitness and ego.

Employers sometimes seem to prefer executives who appear physically fit, despite the legal troubles that may result. Employers may also favor certain personality characteristics. Fitness and personality are related. In one study, middle-aged college faculty who had volunteered for a fitness program were divided into low-fitness and high-fitness groups based on a physical examination. The subjects then took the Cattell Sixteen Personality Factor Questionnaire.31 Here are the data for the “ego strength” personality factor:

ego

Low fitness High fitness
4.99 5.53 3.12 6.68 5.93 5.71
4.24 4.12 3.77 6.42 7.08 6.20
4.74 5.10 5.09 7.32 6.37 6.04
4.93 4.47 5.40 6.38 6.53 6.51
4.16 5.30 6.16 6.68
  1. Is the difference in mean ego strength significant at the 5% level? At the 1% level? Be sure to state and .
  2. Can you generalize these results to the population of all middle-aged men? Give reasons for your answer.
  3. Can you conclude that increasing fitness causes an increase in ego strength? Give reasons for your answer.

7.63

(a) . The data are significant at both the 5% and 1% levels, and there is evidence the two groups are different in mean ego strength. (b) No, they were all college faculty who volunteered and would not represent all middle-aged men. (c) No, the study was observational; we would need an experiment to show causation.