Math · Problem-Solving and Data Analysis

    Inference from Sample Statistics and Margin of Error

    Use sample results and margins of error to estimate population values.

    What the SAT Tests

    These questions give you a sample statistic (mean or proportion) with a margin of error and ask what that implies for the full population. You need to build confidence intervals and interpret them in plain English.

    Key Tips for Inference from Sample Statistics and Margin of Error

    • Confidence interval = point estimate ± margin of error.
    • A larger sample shrinks the margin of error — tests love this relationship.
    • Beware answers that extend conclusions beyond the sampled population.

    Sample Inference from Sample Statistics and Margin of Error Questions

    These are real practice questions pulled from our Digital SAT bank. Try each one before reading the highlighted correct answer.

    1. Question 1 · Medium
      A market researcher collected data on the price of a hot dog at 59 locations selected at random in a state. The mean price of a hot dog in the state was estimated to be $3.28, with an associated margin of error of $0.06. Which of the following is a plausible statement about the mean price of a hot dog for all locations that sell this product in the state?
      • A. It is between $3.22 and $3.34.Correct
      • B. It is either less than $3.22 or greater than $3.34.
      • C. It is less than $3.22.
      • D. It is greater than $3.34.
    2. Question 2 · Medium
      A group of 80 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 7, with an associated margin of error of 1.6. 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 5.4.
      • B. It is plausible that the actual mean number of books employees at the company read last year is between 5.4 and 8.6.Correct
      • C. It is plausible that every employee at the company read between 7 and 11.8 books last year.
      • D. It is plausible that the actual mean number of books employees at the company read last year is greater than 8.6.
    3. Question 3 · Medium
      A group of 40 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 6.8, with an associated margin of error of 1.1. 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 5.7.
      • B. It is plausible that the actual mean number of books employees at the company read last year is between 5.7 and 7.9.Correct
      • C. It is plausible that every employee at the company read between 6.8 and 10.1 books last year.
      • D. It is plausible that the actual mean number of books employees at the company read last year is greater than 7.9.

    Practice Inference from Sample Statistics and Margin of Error Questions

    Drill inference from sample statistics and margin of error questions in the Digital SAT Math question bank, or take a full-length practice module to see how this skill appears under test conditions.

    FAQs

    What is Inference from Sample Statistics and Margin of Error on the Digital SAT?

    These questions give you a sample statistic (mean or proportion) with a margin of error and ask what that implies for the full population. You need to build confidence intervals and interpret them in plain English.

    How hard are inference from sample statistics and margin of error questions?

    Inference from Sample Statistics and Margin of Error questions appear at every difficulty level on the Digital SAT Math section. The hardest versions gate access to the top scaled scores in the hard Module 2.

    How do I practice inference from sample statistics and margin of error?

    Use the 1600.now question bank to filter for inference from sample statistics and margin of error questions, solve at least 20 in a row, and review every miss with the written explanation.

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