Question

Employers sometimes seem to prefer executives who appear physically fit, despite the legal troubles that may result. Employers may also favor certain personality characteristics. Researchers are interested in determining whether fitness and personality are related. In one study, random samples of middle-aged managers 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.

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 5.1 4.47 5.3 3.12 3.77 5.09 5.4

High fitness: 6.68 6.42 7.32 6.38 6.16 5.93 7.08 6.37 6.53 6.68 5.71 6.2 6.04 6.51

Is there a statistically significant difference in mean ego strength for the two fitness groups? Conduct a complete and appropriate hypothesis test at the 2% significance level.

Answer 1

n1 = 14

= 4.64

s1 = 0.6902

n2 = 14

= 6.43

s2 = 0.4304

Claim: There is a difference in mean ego strength for the two fitness groups.

The null and alternative hypothesis is

For doing this test first we have to check the two groups have population variances are equal or not.

Null and alternative hypothesis is

Test statistic is

F = largest sample variance / Smallest sample variances

F = 0.6902*0.6902 / 0.4304*0.4304

F = 0.4764 / 0.1853 = 2.571

Degrees of freedom => n1 - 1 , n2 - 1 => 14 - 1 , 14 - 1 => 13 , 13

Critical value = 3.299   ( Using f table)

Critical value > test statistic so we fail to reject null hypothesis.

Conclusion: The population variances are equal.

So we have to use here pooled variance.

Test statistic is

Degrees of freedom = n1 + n2 - 2 = 14 + 14 - 2 = 26

Critical value = 2.479    ( Using t table)

| t | > critical value we reject null hypothesis.

Conclusion:

There is a difference in mean ego strength for the two fitness groups.