Use sample proportion to estimate population proportion.
Use a random sample proportion as the best estimate for the population proportion.
核心知识
The proportion observed in a random sample is the best single-number estimate for the proportion in the whole population.
深入理解
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
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.
分步讲解
- Confirm the sample was randomly selected.
- Calculate the sample proportion: divide the count with the characteristic by the total sample size.
- Use that proportion as the estimate for the population proportion.
- Make sure the conclusion references the correct population — the one the sample was drawn from.
常见误解
- 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.
示例解析
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?
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