SAT Inference from sample statistics and margin of error Practice Question 9 (Medium)

Question bank / Inference from sample statistics and margin of error

Math · Problem-Solving and Data AnalysisMedium

A random sample of $120$ employees at a large company was used to estimate the mean commute time for all employees. The sample mean was $34$ minutes, with an associated margin of error of $3$ minutes. Which of the following is NOT a plausible value for the mean commute time of all employees at the company?

$31.5$ minutes

$33$ minutes

$36.5$ minutes

$38$ minutes

Show answer and explanation

Answer: D

The plausible values for the population mean are within $3$ minutes of $34$ , from $31$ to $37$ minutes. The values $31.5$ , $33$ , and $36.5$ are in this interval, but $38$ is not.

Choice A is tempting because it is below the sample mean, but it is still within the $31$ to $37$ minute interval.

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