Question

An ambitious statistical-education researcher wants to analyze the typical statistical skills of STEM (science, technology, engineering, and math) majors across the country. They have an exam they plan on giving to sampled college students who are majoring in a STEM field, but they need to choose how to sample college students. Which of the following are considered good sampling methods?

Select one or more:

a. The researcher can go to their local university and get all the STEM majors there to take the exam.

b. The researcher can randomly pick 10 universities and get all the STEM majors at those randomly chosen universities to take the exam.

c. Assuming the researcher can get such a list, they can sort STEM majors into those attending private or public universities. They can then pick 30 randomly chosen students from those attending private universities and 30 from public universities.

d. Assuming the researcher can get such a list, they can sort STEM majors into those whose last names start with an A-K and those whose last names start with an L-Z. They can then randomly pick 30 students from each list.

e. Assuming the researcher can get such a list, they can randomly pick 60 STEM majors from across the country.

Answer 1

Solution: Option (b), (c) and (e) are correct alternatives

• Option (a) is not appropriate because it will introduce bias since the selection is neither random nor systematic.
• Option (b) is appropriate because this is an example of Simple random sampling where random universities are chosen to remove bias.
• Option (c) is correct because this is an example of Stratified sampling where two homogenous groups (private and public universities are considered) and samples are chosen at random to remove bias
• Option (d) is not appropriate because here each element of the sample does not have an equal chance of being selected.
• Option (e) is correct because this again is an example of Simple random sampling where 60 random STEM majors are chosen at random.