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Inference from sample statistics and margin of error — SAT practice questions

Inference from sample statistics and margin of error on SAT Math covers using a sample mean or proportion plus a margin of error to describe a plausible range for a population parameter, and comparing how sample size affects that range. Students must choose a valid conclusion about the population, not about every individual, and recognize that a larger random sample, such as eight hundred workers versus eighty, yields a smaller margin of error at the same confidence level. Questions typically ask which conclusion is most appropriate; answer choices are competing claims, and traps include treating the estimate as exact or claiming every member of the population lies in the interval.

  • Section: Math 44 questions on the paper
  • 102 practice questions in the app

Sample questions

Question 1

Two research teams each estimate the mean commute time for workers in the same large metro area. Team A uses a random sample of 80 workers; Team B uses a random sample of 800 workers from the same population. Both teams use the same survey method and the same confidence level. Which of the following is most likely true?

  1. ATeam A’s estimate will have a smaller associated margin of error than Team B’s estimate.
  2. BTeam B’s estimate will have a smaller associated margin of error than Team A’s estimate.
  3. CThe two estimates will have the same associated margin of error because they concern the same population.
  4. DNeither estimate can have an associated margin of error because commute times are continuous.
Show answer

Answer: B — Team B’s estimate will have a smaller associated margin of error than Team A’s estimate.

For random samples from the same population under comparable methods, a larger sample size generally produces a smaller margin of error. Team B’s sample is ten times as large, so its MoE is expected to be smaller; sharing a population does not make the MoEs equal.

Question 2

Based on a random sample, researchers estimate that the proportion of adults in a county who volunteer at least once a month is 0.28, with an associated margin of error of 0.05. Based on this estimate and margin of error, which of the following is the most appropriate conclusion about the proportion of adults in the county who volunteer at least once a month?

  1. AIt is plausible that the proportion is between 0.23 and 0.33.
  2. BIt is plausible that the proportion is less than 0.23.
  3. CThe proportion is exactly 0.28.
  4. DIt is plausible that the proportion is greater than 0.33.
Show answer

Answer: A — It is plausible that the proportion is between 0.23 and 0.33.

The interval 0.28±0.050.28 \pm 0.05 is 0.23 to 0.33, so it is plausible that the population proportion lies in that interval. Values below 0.23 or above 0.33 are not supported by the estimate and margin of error, and claiming the proportion equals 0.28 exactly overstates what the estimate and margin of error support.

Question 3

Based on a random sample of tomatoes from a farm, a researcher estimates that the mean weight of tomatoes on the farm is 148 grams, with an associated margin of error of 6 grams. Which of the following is the most appropriate conclusion about the mean weight of tomatoes on the farm?

  1. AIt is plausible that the mean weight is between 142 and 154 grams.
  2. BThe mean weight is exactly 148 grams.
  3. CIt is plausible that the mean weight is less than 142 grams.
  4. DEvery tomato on the farm weighs between 142 and 154 grams.
Show answer

Answer: A — It is plausible that the mean weight is between 142 and 154 grams.

The estimate plus or minus the margin of error gives the interval 148−6=142148 - 6 = 142 to 148+6=154148 + 6 = 154. The most appropriate conclusion is that the population mean plausibly lies in that interval; exact equality, values outside the interval, or claims about every individual tomato are not supported.

Practice 102 Inference from sample statistics and margin of error questions in the app

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