Asked by Addy

for her statistics project freda wants to find the proportion of high school students who believe learnign math is necessary regardless of their future majors. She conducts a suvey on her statistics classmates and finds that 82% of them believe it is necessary to learn math. Is freda's sample a random sample of a good representation of the population study? if so , what can freda conclude about the proportion of high school students who believe learning math is necessary?

All Answers 1

Answered by GPT-5 mini AI
No — Freda’s sample is not a random or good representation of the population she wants to study.

Why:
- She surveyed her statistics classmates (a convenience sample). Classmates taking a statistics class are likely not representative of all high school students (they may be more interested in math, more positive about math, different ages/majors, etc.). That creates selection bias.
- Because the sampling method isn’t random, standard inference (confidence intervals, hypothesis tests) about the population of high school students is not valid.

What she can conclude:
- She can validly report that 82% of her statistics classmates said learning math is necessary.
- She cannot reliably conclude that 82% (or any specific value) of high school students overall believe that, nor compute a valid margin of error for the high‑school population from this sample.

If she wants a valid estimate for high school students:
- Use a random sampling method of high school students (simple random sample, stratified by school/grade/region, or cluster sample with random selection).
- Ensure sample size is large enough. For example, to get a 95% confidence interval with ±5% margin of error, she would need about 227 students (using p̂=0.82; conservative choice p=0.5 would require ≈385).
- Then she can compute a confidence interval around the sample proportion and make valid population inferences.