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
6 practice questions
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 \(62\pm4\), 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. Every answer here was re-checked independently by computer before it was published.

Question 1

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?

\(67\%\)
\(60\%\)
\(56\%\)
\(71\%\)

Show the answer and solution

Answer: B: \(60\%\)

Plausible values lie within \(62\pm3\), from 59% to 65%. Only 60% is in that interval.

Question 2

In a random sample of residents, 38% support a new park. The margin of error for this estimate is 5 percentage points. Which of the following is a plausible value for the percentage of all residents who support the park?

\(36\%\)
\(49\%\)
\(31\%\)
\(44\%\)

Show the answer and solution

Answer: A: \(36\%\)

Plausible values lie within \(38\pm5\), from 33% to 43%. Only 36% is in that interval.

Question 3

In a random sample of residents, 38% 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?

\(43\%\)
\(36\%\)
\(47\%\)
\(33\%\)

Show the answer and solution

Answer: B: \(36\%\)

Plausible values lie within \(38\pm3\), from 35% to 41%. Only 36% is in that interval.

Question 4

In a random sample of residents, 70% support a new park. The margin of error for this estimate is 5 percentage points. Which of the following is a plausible value for the percentage of all residents who support the park?

\(76\%\)
\(74\%\)
\(62\%\)
\(81\%\)

Show the answer and solution

Answer: B: \(74\%\)

Plausible values lie within \(70\pm5\), from 65% to 75%. Only 74% is in that interval.

Question 5

In a random sample of residents, 55% 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?

\(60\%\)
\(65\%\)
\(48\%\)
\(57\%\)

Show the answer and solution

Answer: D: \(57\%\)

Plausible values lie within \(55\pm4\), from 51% to 59%. Only 57% is in that interval.

Keep going

Previous topic: Probability and conditional probability
Next topic: Evaluating statistical claims
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