Question

A college professor wants to survey a sample of students taking his course. Here are some details about his course: he teaches [5] sections of the course. There are [250] total students across those sections. There are [50] graduate students and [200] undergraduate students taking the course. Each section has about [50] students (some graduate and some undergraduate). The professor wants to take a sample of [30] students for a survey. He suspects that opinions on the survey may differ the most based on student type (graduate or undergraduate), so he wants to design his sample to take that into account. Which of these strategies will accomplish his intended design?

1) Randomly select 15 graduate students and 15 undergraduate students for the survey
2) Randomly select 30 students from the total student population for the survey
3) Randomly select 10 graduate students and 20 undergraduate students for the survey
4) Randomly select 20 graduate students and 10 undergraduate students for the survey

Answer 1

The professor should use stratified sampling to ensure that the sample reflects the proportion of graduate and undergraduate students in the course. Option 3, which involves selecting 10 graduate students and 20 undergraduate students, provides the best representation of the student distribution for the survey.

Step-by-step explanation:

The college professor interested in surveying students based on their status as graduate or undergraduate students can achieve his intended design by utilizing stratified sampling. One effective method to reflect the distribution of student types in the survey is to take an equal or proportionate random sample from each subgroup. Considering that there are 50 graduate students and 200 undergraduate students in the course:

• Option 1 suggests selecting 15 graduate students and 15 undergraduate students for the survey, which does not reflect the actual proportions in the population.
• Option 2 entails selecting 30 students randomly from the total population, but this may not ensure the distribution of student types is accounted for in the sample.
• Option 3 involves selecting 10 graduate and 20 undergraduate students, representing a ratio closer to the actual distribution.
• Option 4 indicates selecting 20 graduate students and 10 undergraduate students, which inverts the actual ratio in the population.

Therefore, Option 3 (randomly selecting 10 graduate students and 20 undergraduate students for the survey) is the most suitable strategy to take into account the proportion of graduate and undergraduate students in the course and reflect their opinions accurately in the survey results.