Interpret margin of error and form a plausible interval estimate. | Inference from sample statistics and margin of error | SAT Math

Turn a sample statistic and margin of error into a plausible population interval.

Core Idea

The margin of error defines a range around the sample statistic — add and subtract it to get the interval where the true population value plausibly falls.

Understanding

A sample statistic on its own is a point estimate — one number. The margin of error turns it into an interval estimate by marking how far the true value could reasonably be from that point.

The formula is straightforward:

P l a u s i b l e i n t e r v a l = s a m p l e s t a t i s t i c \pm m a r g i n o f e r r o r

If a survey finds that 45% of residents support a new park, with a margin of error of 3 percentage points, the plausible range for the true support level is $45 % - 3 % = 42 %$ to $45 % + 3 % = 48 %$ .

The margin of error goes in both directions. A common SAT trap is an answer that only adds or only subtracts the margin of error. You always need both ends of the interval.

Step by Step

Identify the sample statistic (mean or proportion).
Identify the margin of error.
Compute the lower bound: statistic minus margin of error.
Compute the upper bound: statistic plus margin of error.
State the interval: the true population value plausibly lies between the lower and upper bounds.

Misconceptions

Only adding the margin of error (getting just an upper bound) or only subtracting it — the interval extends in both directions.
Thinking the margin of error is a percentage of the statistic rather than an absolute amount to add and subtract.
Believing the true value is guaranteed to be inside the interval — it's plausible, not certain.

Question

Worked Example

A poll of 600 randomly selected adults found that 52% support a new policy, with a margin of error of 4 percentage points. Which of the following is the best interpretation of this result?

Select an answer to see the explanation