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    Employers sometimes seem to prefer executives who appear physically fit...Here are the data...c) You should also hesitate to conclude that increasing fitness causes an increase in ego strength. Explain why?

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    A. 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 was divided into low-fitness groups based on a physical examination. The subjects then took the Cattell Sixteen Personality Factor Questionnaire. Here are the data for the "ego strength" personality factor:

    Low Fitness 4.99 4.24 4.74 4.93 4.16 5.53 4.12 5.10 4.47 5.30 3.12 3.77 5.09 5.40
    High Fitness 6.68 6.42 7.32 6.38 6.16 5.93 7.08 6.37 6.53 6.68 5.71 6.20 6.04 6.51

    (a) Is the difference in mean ego strength significant at the 5% level? At the 1% level? Be sure to state H0 and Ha.
    Denote the mean ego strength for Low Fitness by and denote the mean ego strength for High Fitness by . Then we can set up null hypothesis H0 and Ha as follows.
    H0: = ;
    Using Excel, we got the following table

    t-Test: Two-Sample Assuming Equal Variances

    Variable 1 Variable 2
    Mean 4.64 6.429286
    Variance 0.476385 0.185269
    Observations 14 14
    Pooled Variance 0.330827
    Hypothesized Mean Difference 0
    df 26
    t Stat -8.23054
    P(T<=t) one-tail 5.17E-09
    t Critical one-tail 2.478628
    P(T<=t) two-tail 1.03E-08
    t Critical two-tail 2.778725

    By the above table, we know that p-value=1.03E-08= which is less than 5% and 1%. So, at the 5% level or at the 1% level, we should reject the null hypothesis H0: = . We conclude that the difference in mean ego strength is ...

    Solution Summary

    The expert examines the increasing fitness causes as it increase ego strengths.