Question

a high school principal conducts a survey on whether or not students would be interested in an elective art course. the principal knows that it would be too time - consuming to survey all 482 students in the high school, so he decides to ask the 98 students currently in the cafeteria. one of the students states that this survey cannot be used to make an inference about the entire high school.
which of the following statements best justifies the student’s interpretation of the survey?

a. the survey sample was too small.

b. an art teacher should have conducted the survey.

c. the survey method was flawed since the sample was not random.

d. an observational study, rather than a sample survey, should have been used.

Explanation:

To determine the best justification, we analyze each option:

• Option A: The sample size of 98 out of 482 isn't necessarily too small (e.g., a sample can be representative with proper randomization), so this is incorrect.
• Option B: Who conducts the survey (principal vs. art teacher) doesn't affect the validity of the sample for inference, so this is irrelevant.
• Option C: The principal surveyed only students in the cafeteria, which is a non - random sample (not all students have an equal chance to be selected). A non - random sample can lead to bias and make it inappropriate for inferring about the entire high school, so this is correct.
• Option D: A sample survey is appropriate here to gather students' opinions, and an observational study is not the right method for this type of question, so this is incorrect.

Answer:

C. The survey method was flawed since the sample was not random.