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 “contribu- tion 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: Gender Bonus Percentage F 9.2 7.7 11.9 6.2 9.0 8.4 6.9 7.6 7.4 F 8.0 9.9 6.7 8.4 9.3 9.1 8.7 9.2 9.1 F 8.4 9.6 7.7 9.0 9.0 8.4 M 10.4 8.9 11.7 12.0 8.7 9.4 9.8 9.0 9.2 M 9.7 9.1 8.8 7.9 9.9 10.0 10.1 9.0 11.4 M 8.7 9.6 9.2 9.7 8.9 9.2 9.4 9.7 8.9 M 9.3 10.4 11.9 9.0 12.0 9.6 9.2 9.9 9.0 Are the datasets for FEMALE and MALE normally distributed? Perform the Shapiro-Wilk test of normality for both genders and write them up. You should have found that one of the gender’s data was not normally distributed . Now you must make a choice: Should you use an independent samples t-test or U-test Compare FEMALE and MALE using the independent samples t-test and U-test (or rank-sum test): Write up the tests using the templates appearing in Appendix A. State which test should be believed given what you figured out in part (b). Compare the tests and see whether they agree or disagree. Share any thoughts you may have about the importance of the Shapiro-Wilk test of normality.
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 “contribu- tion 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:
Gender Bonus Percentage
F 9.2 7.7 11.9 6.2 9.0 8.4 6.9 7.6 7.4
F 8.0 9.9 6.7 8.4 9.3 9.1 8.7 9.2 9.1
F 8.4 9.6 7.7 9.0 9.0 8.4
M 10.4 8.9 11.7 12.0 8.7 9.4 9.8 9.0 9.2
M 9.7 9.1 8.8 7.9 9.9 10.0 10.1 9.0 11.4
M 8.7 9.6 9.2 9.7 8.9 9.2 9.4 9.7 8.9
M 9.3 10.4 11.9 9.0 12.0 9.6 9.2 9.9 9.0
Are the datasets for FEMALE and MALE
You should have found that one of the gender’s data was not normally distributed . Now you must make a choice: Should you use an independent samples t-test or U-test
Compare FEMALE and MALE using the independent samples t-test and U-test (or rank-sum test):
-
- Write up the tests using the templates appearing in Appendix A.
- State which test should be believed given what you figured out in part (b).
- Compare the tests and see whether they agree or disagree. Share any thoughts you may have about the importance of the Shapiro-Wilk test of normality.
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