Final answer:
The study looking into the relationship between the gender of mayors and employment statistics for women in labor is categorized as an observational study with characteristics of a matched-pairs design due to the comparison of each city to itself over time.
Therefore, the correct answer is: option 'III only'.
Step-by-step explanation:
The design of the study that collected data in twenty major urban cities on the percent of women in the labor force and examined the impact of mayoral gender on employment statistics is best described as an observational study.
A matched-pairs design would suggest that each city is compared to itself at different points in time, which fits the description of the data collection.
It is not explicitly stated that the cities were paired or 'blocked' based on certain variables to control for variation, nor is it stated that any randomization procedure was utilized.
Thus, option III, An observational study, is the accurate choice since the study observes and compares pre-existing conditions without imposing any treatments or randomization.