Choosing a sample size
Decide how many people to include so results are trustworthy, and see why a t-test asks whether two group means differ more than chance.
- Sample vs. population: A sample is the people actually measured; choosing its size only makes sense once you know it stands in for a larger population.
- Variability (spread) in data: More spread among people means you need more of them to see a real difference, so understanding spread comes first.
Prerequisites are inferred: pending teacher review.
Re-learn the skill with worked practice and clear examples.
A larger, well-chosen sample gives more trustworthy results because it represents the whole group better and is less swayed by one unusual person.
A team tests whether a sports drink lowers heart rate. Plan A measures 4 people; Plan B measures 40 people. Why is Plan B's result more trustworthy?
Reviewed- A.Because measuring more people makes the drink work better
- B.Because a larger sample is less swayed by one unusual reading and better represents the group
- C.Because 40 is an even number and 4 is small
- D.Because a larger sample removes the need to measure heart rate carefully
Show the worked solution ▾
Answer: B. Because a larger sample is less swayed by one unusual reading and better represents the group
- Step 1: Picture one odd person: In a group of 4, one strange reading is a quarter of the data and can flip the result.
- Step 2: Scale it up: In a group of 40, that same odd reading is diluted, so the result better reflects the whole group.
Why it's right: A larger sample is less affected by any single unusual reading and represents the group better, so Plan B's result is more trustworthy.
- A: Sample size changes how trustworthy the result is, not whether the drink itself works.
- C: Whether the count is even or odd has nothing to do with trustworthiness.
- D: A bigger sample still requires careful measurement; it does not replace it.
Aligned to BI 2.1: sample size and reliability · reading level ~grade 9
- A device trial enrolls dozens of patients rather than a handful so reviewers will believe the measured difference is real and not luck.
Fill these in as you work through the lesson.
- Sample size (how many people you measure):
- Sample (the measured stand-in for the whole group):
- t-test (checks if a gap between two means is bigger than random luck would give):
- Statistical significance (when a difference is too big to be explained by random luck alone):
A sample gives more trustworthy results because it represents the whole group better. A t-test asks whether two means differ more than would happen just by .
- A team tests a breathing exercise on 4 people and finds a difference. Why should they be cautious about that result?
- In plain words, what question does a t-test try to answer about two groups?
- If two groups' means are very close together, is a t-test more or less likely to call the difference real?
A team compares resting heart rate before and after caffeine. Explain why measuring 30 people instead of 3 makes the comparison more trustworthy, and state in one sentence what a t-test would check about the two means.