SAT Math: Margin of error and inference

Inference from sample statistics and margin of error.

Problem-Solving and Data Analysis · Inference from sample statistics and margin of error
Both modules
8 practice questions · 2 with free solutions
Calculator allowed (Desmos)

Practise margin of error and inference →Adaptive SAT module

What the test covers

Estimate +/- margin of error as a plausible interval
Effect of sample size

Key ideas

A sample estimate $\pm$ the margin of error gives a range of plausible values for the population.
Larger random samples give smaller margins of error.
Conclusions only apply to the population that was randomly sampled.

Common mistakes

A plausible value lies inside the interval, including its ends.
A margin of error does not describe individual people.

Do it in Desmos

Just arithmetic: estimate minus and plus the margin.

Worked example

In a random sample of voters, 62% support a proposal. The margin of error for this estimate is 4 percentage points. Which of the following is a plausible value for the percentage of all voters who support the proposal?

$67 %$
$60 %$
$70 %$
$57 %$

Answer: B: $60 %$

Plausible values lie within $62 \pm 4$ , from 58% to 66%. Only 60% is in that interval.

Practice questions

Try each question before opening the solution. Desmos or your own calculator is allowed on every SAT Math question. Solutions to the first 1 are open to everyone; the rest need only a free account. Every answer here was checked independently before it was published.

Question 1

In a random sample of residents, 38% support a new park. The margin of error for this estimate is 4 percentage points. Which of the following is a plausible value for the percentage of all residents who support the park?

$43 %$
$48 %$
$41 %$
$32 %$

Show the answer and solution

Answer: C: $41 %$

Plausible values lie within $38 \pm 4$ , from 34% to 42%. Only 41% is in that interval.

Question 2

In a random sample of residents, 62% support a new park. The margin of error for this estimate is 3 percentage points. Which of the following is a plausible value for the percentage of all residents who support the park?

$67 %$
$60 %$
$56 %$
$71 %$