(SAT) Select plausible population values given a sample statistic and margin of error.
Check whether a population value falls inside the statistic ± margin of error interval.
核心知识
Given a sample statistic and margin of error, a population value is plausible if and only if it falls within the interval formed by statistic ± margin of error.
深入理解
This is the most common way the SAT packages these ideas into a question. You're given a result — say, a sample mean of 72 with a margin of error of 5 — and asked which population mean is plausible. Build the interval: 67 to 77. Any value inside that range is a plausible answer; any value outside it is not.
The check is mechanical:
Some questions flip the framing: instead of asking "which value is plausible," they ask "which value can be ruled out." Same interval, opposite logic — if the value is outside the interval, it can be ruled out.
Boundary values count as plausible. If the interval is 67 to 77, then 67 and 77 are both plausible.
分步讲解
- Find the sample statistic and the margin of error in the problem.
- Calculate: lower bound = statistic − margin of error.
- Calculate: upper bound = statistic + margin of error.
- Check each answer choice: if the value is between the lower and upper bounds (inclusive), it's plausible.
- Select the answer that falls inside (or outside) the interval, depending on what the question asks.
常见误解
- Excluding boundary values — a value exactly at the edge of the interval is still plausible.
- Mixing up 'plausible' and 'not plausible' — read carefully whether the question asks for a value that could be the true value or one that can be ruled out.
- Forgetting to subtract the margin of error and only checking the upper end of the interval.
示例解析
A random sample of 250 trees in a national forest had a mean height of 34 feet, with a margin of error of 3 feet. Which of the following is a plausible value for the mean height of all trees in the forest?
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