Question

For her statistics project, Freda wants to find the proportion of high school students who believe learning math is necessary, regardless of their future majors. She conducts a survey on her statistics classmates and finds that 82% of them believe it is necessary to learn math. Is Freda's sample a random sample and a good representation of the population in her study? If so, what can Freda conclude about the proportion of high school students who believe leaming math is necessary? If not, propose a random sample on which Freda should be conducting her survey. (4 points)

Answer 1

No — Freda’s sample is a convenience sample of her statistics classmates, not a random sample of high school students, so it is not a good representation of the population she wants to study. Classmates are likely similar in age, interests, course-taking, and background, so the 82% may be biased and cannot be validly generalized to all high school students.

What she should do instead (one good option)
- Define the population clearly (e.g., all high school students in a given city, state, or country).
- Construct a sampling frame (a list of students, or a list of schools with enrollment lists).
- Use a probability method such as
- Simple random sample: randomly pick students from the frame using a random-number generator, or
- Stratified random sample: divide students into strata (grade, school, urban/rural, etc.), then randomly sample within each stratum to ensure representation,
- or two-stage cluster sample: randomly select schools, then randomly select students within those schools.
- Aim for a sufficiently large sample (e.g., n ≥ 100–400 depending on desired margin of error) and try to minimize nonresponse.

If Freda collects a proper random sample, she can use the sample proportion (for example 82% if that were observed in the random sample) as an unbiased point estimate of the population proportion and compute a confidence interval (SE = sqrt[p(1−p)/n]) to quantify the uncertainty.