# Inference from Sample Statistics and Margin of Error on the SAT: Examples & Practice Source: https://1600.now/sat-skill/sample-statistics-margin-of-error --- Math · Problem-Solving and Data Analysis ## Inference from Sample Statistics and Margin of Error A sample estimates a population quantity. A margin of error describes uncertainty around that estimate; a larger comparable random sample generally gives a narrower interval. Written by [Luke Finigan](https://1600.now/about) 2 min read Updated Oct 2, 2026 ### Build the interval around the estimate A survey estimates support at 52% with a margin of error of 4 percentage points. Its interval runs from 48% to 56%: subtract and add 4 to the reported estimate. This is uncertainty about the population proportion, not a claim that every individual answer is within 4% of something. The interval also does not prove support exceeds 50%, since values below 50% remain within it. ### Identify the population the sample represents A random sample of a city's registered voters can estimate that city's registered voters' opinions. It does not automatically represent all residents, all voters in a state, or people who were excluded from the sampling process. Read how the sample was obtained. A large voluntary poll on a website can remain biased if its participants differ systematically from the target population. ### Compare sample sizes under the same conditions For comparable random samples at the same confidence level, a larger sample generally reduces margin of error. The approximate relationship is inverse to the square root of sample size: quadrupling the sample roughly halves the margin. This comparison holds other features of the survey fixed. Increasing the sample size does not by itself repair a biased sampling method or a leading question. ### Interpret estimates without promising certainty If two intervals overlap, the reported intervals alone do not force a conclusion that the population values differ. Compare the possible ranges before asserting that one group definitely has the larger percentage. Confidence describes the estimation procedure across repeated random samples. Do not reinterpret a reported confidence level as the percentage of respondents who answered accurately. ### Check your understanding Try it yourself A poll estimates 38% with a margin of error of 3 percentage points. What is the reported interval? A 3% to 38% B 35% to 41% C 38% to 41% D 37.7% to 38.3% ### Sample inference from sample statistics and margin of error questions Inference from Sample Statistics and Margin of Error · Easy A landscaping company studied a random sample of 24 lawns in a small town. The company found that 6 of these lawns contain fertilizer. If there are 288 lawns in the town, which of the following is the best estimate of the number of lawns that contain fertilizer? A 5 B 4 C 12 D 72 - [Open the question and explanation](https://1600.now/bank/math/e77e6662) Inference from Sample Statistics and Margin of Error · Easy A district school board in a certain state is considering changing the starting time for all high schools in the district. A sample of 368 high school students was selected at random from all high school students in the district. The selected students were asked whether they approved of the proposed change, and 295 students responded that they did not approve. Which of the following is the largest population to which the survey results can be generalized? A All high school students in the district B The 368 students who were surveyed C The 295 students who responded that they did not approve of the proposed change D All high school students in the state - [Open the question and explanation](https://1600.now/bank/math/b118adc2) Inference from Sample Statistics and Margin of Error · Medium A group of 90 employees selected at random from all the employees at a company were surveyed about the number of books they read last year. From the data collected, it was estimated that the mean number of books employees at the company read last year is 8, with an associated margin of error of 1.4. Which of the following is the most appropriate conclusion? A It is plausible that the actual mean number of books employees at the company read last year is less than 6.6. B It is plausible that the actual mean number of books employees at the company read last year is between 6.6 and 9.4. C It is plausible that every employee at the company read between 8 and 12.2 books last year. D It is plausible that the actual mean number of books employees at the company read last year is greater than 9.4. - [Open the question and explanation](https://1600.now/bank/math/c6b63c52) ### Practice this skill 1. Write the lower and upper endpoints with their units. 2. Name the target population and sampling method. 3. Separate uncertainty from sampling bias when reviewing a missed question. [Practice inference from sample statistics and margin of error](https://1600.now/bank/math/skill/Inference%20from%20sample%20statistics%20and%20margin%20of%20error) [Print the inference from sample statistics and margin of error worksheet and worked answers](https://1600.now/sat-sample-statistics-margin-of-error-worksheet). Then use a [mixed practice module](https://1600.now/modules) to check whether you can choose this method among other question types. ### Source and question labels The bank label for this guide is "Inference from sample statistics and margin of error" in Problem-Solving and Data Analysis. The worked examples above are written for this guide. - [College Board: Types of Math tested](https://satsuite.collegeboard.org/sat/whats-on-the-test/math/types) ### Related skills - **[Evaluating Statistical Claims](https://1600.now/sat-skill/evaluating-statistical-claims)** Check two separate permissions: random sampling supports generalizing to a population, while random assignment in a well-designed experiment supports a causal comparison. - **[One-Variable Data: Distributions and Measures](https://1600.now/sat-skill/one-variable-data)** Use the mean for the arithmetic average, the median for the middle of ordered data, and measures of spread to compare variability. - **[Probability and Conditional Probability](https://1600.now/sat-skill/probability)** Probability compares favorable outcomes with the eligible outcomes.