Concept 2

Use sample proportion to estimate population proportion.

Use a random sample proportion as the best estimate for the population proportion.

Core Idea

The proportion observed in a random sample is the best single-number estimate for the proportion in the whole population.

Understanding

Proportions work just like means: measure a random part, use the result to estimate the whole. If 84 out of 300 randomly selected voters favor a proposal, the sample proportion is 84300 =0.28, or 28%. That 28% is the estimate for the proportion of all voters who favor the proposal.

The logic is identical to sample means, but the quantity is a fraction rather than an average. SAT questions usually express proportions as percentages.

Watch what population the sample actually represents. If only registered voters in one district were surveyed, the 28% estimates the proportion for that district — not the entire state.

Step by Step

  1. Confirm the sample was randomly selected.
  2. Calculate the sample proportion: divide the count with the characteristic by the total sample size.
  3. Use that proportion as the estimate for the population proportion.
  4. Make sure the conclusion references the correct population — the one the sample was drawn from.

Misconceptions

  • Confusing count with proportion — 84 out of 300 is 28%, not 84%.
  • Applying the result to a broader population than the one actually sampled.
  • Assuming the sample proportion is exact — it's still an estimate subject to sampling variability.
Question

Worked Example

A random sample of 500 employees at a large company found that 35% prefer remote work. Based on this sample, what is the best estimate of the percentage of all employees at the company who prefer remote work?

Select an answer to see the explanation