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SAT Sampling and Margin of Error Practice

Decide what a sample can represent and use margin of error to describe a reasonable interval around an estimate.

Practice sampling and margin of error in Dolphin SATPractice questions
12-18 min practice time3 questions on pageProblem Solving and Data Analysis
Practice time12-18 min
Question bank3 questions
Best forProblem Solving and Data Analysis

What this tests

What to know for this SAT skill

Dolphin question bank

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Question 1 of 3Medium
A bag containing 10,000 beads of assorted colors is purchased from a craft store. To estimate the percent of red beads in the bag, a sample of beads is selected at random. The percent of red beads in the bag was estimated to be 15%, with an associated margin of error of 2%. If r is the actual number of red beads in the bag, which of the following is most plausible?
  1. r > 1,700
  2. 1,300 < r < 1,700
  3. 200 < r < 1,500
  4. r < 1,300
Show answer and solution
Correct answerB. 1,300 < r < 1,700

Solution walkthrough

  1. It was estimated that 15% of the beads in the bag are red. Since the bag contains 10,000 beads, it follows that there are an estimated red beads.
  2. It’s given that the margin of error is 2%, or beads. If the estimate is too high, there could plausibly be red beads.
  3. If the estimate is too low, there could plausibly be red beads. Therefore, the most plausible statement of the actual number of red beads in the bag is .
Why the other choices miss
Choices A and D are incorrect and may result from misinterpreting the margin of error. It’s unlikely that more than 1,700 beads or fewer than 1,300 beads in the bag are red. Choice C is incorrect because 200 is the margin of error for the number of red beads, not the lower bound of the range of red beads.
Question 2 of 3Medium
A sample consisting of 720 adults who own televisions was selected at random for a study. Based on the sample, it is estimated that 32% of all adults who own televisions use their televisions to watch nature shows, with an associated margin of error of 3.41%. Which of the following is the most plausible conclusion about all adults who own televisions?
  1. More than 35.41% of all adults who own televisions use their televisions to watch nature shows.
  2. It is plausible that between 28.59% and 35.41% of all adults who own televisions use their televisions to watch nature shows.
  3. Since the sample included adults who own televisions and not just those who use their televisions to watch nature shows, no conclusion can be made.
  4. Since the sample did not include all the people who watch nature shows, no conclusion can be made.
Show answer and solution
Correct answerB. It is plausible that between 28.59% and 35.41% of all adults who own televisions use their televisions to watch nature shows.

Solution walkthrough

  1. It's given that based on a sample selected at random, it's estimated that 32% of all adults who own televisions use their televisions to watch nature shows, with an associated margin of error of 3.41%.
  2. Subtracting the margin of error from the estimate and adding the margin of error to the estimate gives an interval of plausible values for the true percentage of adults who own televisions who use their televisions to watch nature shows.
  3. This means it's plausible that between 32% - 3.41%, or 28.59%, and 32% + 3.41%, or 35.41%, of all adults who own televisions use their televisions to watch nature shows.
  4. Therefore, choice B is the most plausible conclusion: it is plausible that between 28.59% and 35.41% of all adults who own televisions use their televisions to watch nature shows.
Why the other choices miss
Choice A is incorrect and may result from conceptual errors. Choice C is incorrect. To make a plausible conclusion about all adults who own televisions, the sample must be selected at random from all adults who own televisions, not just those who use their televisions to watch nature shows. Choice D is incorrect. Since the sample was selected at random from all adults who own televisions, a plausible conclusion can be made about all adults who own televisions.
Question 3 of 3Medium
A park ranger asked a random sample of visitors how far they hiked during their visit. Based on the responses, the estimated mean was found to be 4.5 miles, with an associated margin of error of 0.5 miles. Which of the following is the best conclusion from these data?
  1. It is likely that all visitors hiked between 4 and 5 miles.
  2. It is likely that most visitors hiked exactly 4.5 miles.
  3. It is not possible that any visitor hiked less than 3 miles.
  4. It is plausible that the mean distance hiked for all visitors is between 4 and 5 miles.
Show answer and solution
Correct answerD. It is plausible that the mean distance hiked for all visitors is between 4 and 5 miles.

Solution walkthrough

  1. The given estimated mean has an associated margin of error because from sample data, the population mean can't be determined precisely.
  2. Rather, from the sample mean, an interval can be determined within which it's plausible that the population’s mean is likely to lie.
  3. Since the estimated mean is 4.5 miles with an associated margin of error of 0.5 miles, it follows that between miles and miles, or between 4 and 5 miles, is plausibly the mean distance hiked for all visitors.
Why the other choices miss
Choices A, B, and C are incorrect. Based on the estimated mean, no determination can be made about the number of miles hiked for all visitors to the park.

Avoid these traps

Common mistakes on this skill

Generalizing from a biased sample

A large sample can still be misleading if the selection method systematically excludes part of the population.

Treating margin of error as a percent multiplier

When margin of error is stated in percentage points, add and subtract it directly from the estimate.

Assuming a sample result is exact

A sample estimates a population value; the margin of error communicates the expected uncertainty.

Study plan

How to practice this skill in Dolphin

  1. Identify the population the study wants to describe.
  2. Check whether the sample was selected in a representative way.
  3. Use the sample proportion to estimate a population value when asked.
  4. Add and subtract the margin of error to form the supported interval.
Practice sampling and margin of error in Dolphin SAT

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FAQ

Questions about SAT Sampling and Margin of Error Practice

What is margin of error on the SAT?

It describes how far a sample estimate may reasonably be from the true population value.

Does a larger sample always remove bias?

No. A larger sample usually reduces random sampling error, but it does not repair a biased selection method.

Can a sample be used to estimate a whole population?

Yes, when the sample is selected randomly and represents the population the study intends to describe.