Answer and explanation:
First, let's understand the difference between categorical and quantitative variables. A quantitative variable can also be called a numerical variable. As this name suggests, it involves numbers. It can be measured numerically and be used in calculations - this is important, because not everything that has numbers is used in calculations; take the zip code as an example. On the other hand, a categorical variable cannot be expressed numerically in the same way described above. It is related to a certain quality or characteristic of something. For instance, you can attribute the number one to a person who is sick and the number two to a person who is not sick. The numbers are just a representation of the qualities; they won't be used in calculations. Now, we can safely judge the options given:
The price in dollars of statistics textbooks. --> quantitative
The working status of a computer part (working/not working). --> categorical
The gender of faculty in the mechanical engineering department. --> categorical
The number of miles until failure of a certain brand of tires. --> quantitative
The political party affiliation of students at OSU. --> categorical
The time to complete an exam. --> quantitative
The shirt sizes of a running club. --> categorical
