A firm has a generous but rather complicated policy concerning end-of-year bonuses for its lower-level managerial personnel. The policy’s key factor is a subjective judgment of “contribution to corporate goals.” A personnel officer took samples of 24 female and 36 male managers to see whether there was any difference in bonuses, expressed as a percentage of yearly salary. The data are listed here:

a. What are the populations of interest in this study?

b. Is there significant evidence that the mean bonus percentage for males is more than five units larger than the mean bonus percentage for females? Use α = .05.

c. What is the level of significance of your test?
d. Estimate the difference in the mean bonus percentages for males and females using a 95% confidence interval.

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Gender Bonus Percentage 9.2 8.0 8.4 10.4 9.7 8.7 9.3 7.7 11.9 6.7 7.7 8.9 11.7 8.8 9.2 10.4 11.9 6.2 84 9.0 12.0 7.9 9.7 9.0 12.0 9.0 9.3 9.0 8.7 9.9 8.9 8.4 9.1 84 9.4 10.0 10.1 9.2 9.6 69 7.6 9.9 9.6 7.4 9.1 87 9.2 9.8 9.0 9.4 9.7 9.2 9.0 11.4 8.9 9.0 9.1 9.6 9.2 9.9