Problem-Solving and Data Analysis · Math

Sample statistics and margin of error

Using a sample to estimate a population, and interpreting a margin of error.

8 questions in the bank · 2 easier · 4 medium · 2 harder · this domain is ≈15% of the section

Learn it in the Guide

What to watch for

A margin of error describes uncertainty about the population value from this one sample. It is not a claim about future samples, and it is not an error rate in the data.

How the question is worded

These are the actual stems used in the bank — the SAT reuses a small set of wordings, and recognising them saves time on test day.

  • A random sample of residents were surveyed about a proposed park. An estimated 32% supported the proposal, with a margin of error of 5%. Which of the following is the best interpretation of this result?
  • A random sample of residents were surveyed about a proposed park. An estimated 62% supported the proposal, with a margin of error of 4%. Which of the following is the best interpretation of this result?
  • A random sample of residents were surveyed about a proposed park. An estimated 47% supported the proposal, with a margin of error of 3%. Which of the following is the best interpretation of this result?
  • A random sample of residents were surveyed about a proposed park. An estimated 41% supported the proposal, with a margin of error of 3%. Which of the following is the best interpretation of this result?

Worked examples

easyIn a random sample of 60 students from a school of 1200 students, 15 said they…

In a random sample of 60 students from a school of 1200 students, 15 said they use the library weekly. Based on the sample, what is the best estimate of the number of students in the whole school who use the library weekly?

Answer: 300

Explanation

The sample proportion is 15/60. Applied to the population: (15/60) × 1200 = 300. Random sampling is what justifies scaling the proportion up — the estimate inherits the sample's uncertainty.

mediumA random sample of residents were surveyed about a proposed park. An estimated…

A random sample of residents were surveyed about a proposed park. An estimated 32% supported the proposal, with a margin of error of 5%. Which of the following is the best interpretation of this result?

  • A. 5% of the survey responses were recorded incorrectly.
  • B. Every additional survey would give a result between 27% and 37%.
  • C. It is plausible that the percent for the full population is between 27% and 37%.
  • D. Exactly 32% of the full population has this preference.

Answer: C. It is plausible that the percent for the full population is between 27% and 37%.

Explanation

A margin of error gives a plausible range for the POPULATION value: 32% ± 5% → 27% to 37%. It does not mean the sample was mis-recorded, and it does not promise where future samples will land — it quantifies uncertainty about the population from this one sample.

hardA random sample of residents were surveyed about a proposed park. An estimated…

A random sample of residents were surveyed about a proposed park. An estimated 47% supported the proposal, with a margin of error of 3%. Which of the following is the best interpretation of this result?

  • A. Every additional survey would give a result between 44% and 50%.
  • B. It is plausible that the percent for the full population is between 44% and 50%.
  • C. 3% of the survey responses were recorded incorrectly.
  • D. Exactly 47% of the full population has this preference.

Answer: B. It is plausible that the percent for the full population is between 44% and 50%.

Explanation

A margin of error gives a plausible range for the POPULATION value: 47% ± 3% → 44% to 50%. It does not mean the sample was mis-recorded, and it does not promise where future samples will land — it quantifies uncertainty about the population from this one sample.