Nonparametric tests and a longitudinal study of mathematically gifted teenagers: Researchers studied male and female teenagers who had scored in the top 1% on mathematical reasoning measures (Lubinski, Benbow, & Kell, 2014). The researchers were able to follow the participants’ progression over the next 40 years. They tracked two groups, or cohorts, of participants on a number of variables, including career-related variables. They reported “pronounced and significant sex differences in the percentage of participants who were working full time (Cohort 1: 89% of males and 69% of females; Cohort 2: 90% of males and 59% of females), χ 2 (1, N = 1,131) = 67.56, p < .001, and χ 2 (1, N = 481) = 68.55, p < .001.” So, the researchers looked at income only among those who were employed full time. For example, for one cohort they reported median incomes of $150,000 for men and $101,000 for women. This gender difference was statistically significant for both groups: “Mann–Whitney U test, zs ≥ 5.09, ps < .001.” 

a. Explain why the researchers conducted a chi-square test for their data on whether participants were working full time. 

b. Explain the findin g on full-time work in your own words.

c. Explain why the researchers conducted a Mann– Whitney U test for their data on incomes. 

d. Explain the finding on incomes in your own words. 

e. Why did the researchers report median income rather than mean income?