Question

to find how high school students feel about hot lunches, adam walks to the nearest high school and gives a survey postcard to every twentieth student that enters the building. he asks the students to mail the postcard in if they choose to participate in the study.

why might the method used be biased?

asking every twentieth student does not accurately represent the student population.
it is likely that student opinions in one particular high school do not accurately represent the opinions of all high school students.
students that take the time to complete the survey and mail it in probably feel strongly about hot lunches.

Explanation:

Analyze the target population and sampling method

The goal is to find how high school students (broadly) feel about hot lunches.
Adam's sampling method involves:

1. Walking to the nearest high school (convenience location).
2. Giving a postcard to every twentieth student entering (systematic sampling at that school).
3. Asking them to mail the postcard back if they choose to participate (voluntary response).

Evaluate the first option

Option 1: "Asking every twentieth student does not accurately represent the student population."
Using Systematic Sampling (every twentieth student) is generally a valid, random-like method to get a representative sample of that specific school's student body. This is not the primary source of bias.

Evaluate the second option

Option 2: "It is likely that student opinions in one particular high school do not accurately represent the opinions of all high school students."
Since the target population is "high school students" in general, sampling only from the nearest single high school introduces convenience bias. Opinions at one school may not represent all schools. However, we must compare this with the bias introduced by the voluntary mail-in method.

Evaluate the third option

Option 3: "Students that take the time to complete the survey and mail it in probably feel strongly about hot lunches."
This describes Voluntary Response Sampling bias. When participants must actively choose to mail back a postcard, those with strong opinions (either highly positive or highly negative) are far more likely to respond than those with neutral feelings. This is a classic and severe form of sampling bias that directly skews the survey results.

Determine the best fit

In many statistics curricula, a self-selected mail-in survey is the textbook definition of voluntary response bias, where respondents typically hold strong opinions. Thus, the third option directly explains why the voluntary mail-in method leads to bias.

Answer:

• Asking every twentieth student does not accurately represent the student population.
• It is likely that student opinions in one particular high school do not accurately represent the opinions of all high school students.
• Students that take the time to complete the survey and mail it in probably feel strongly about hot lunches. (Correct answer)