SAT Inference from sample statistics and margin of error Practice Question 11 (Medium) | SAT Owl

Question bank / Inference from sample statistics and margin of error

Math · Problem-Solving and Data AnalysisMedium

A researcher used a random sample of trees in a forest to estimate the mean height of all trees in the forest. The researcher reported that plausible values for the mean height are from $42$ feet to $50$ feet. Which of the following gives the sample mean and the margin of error for this estimate?

A

Sample mean $46$ feet, margin of error $4$ feet

B

Sample mean $46$ feet, margin of error $8$ feet

C

Sample mean $42$ feet, margin of error $8$ feet

D

Sample mean $50$ feet, margin of error $4$ feet

Show answer and explanation

Answer: A

An interval of plausible values is centered at the sample mean and extends one margin of error in each direction. The center of $42$ to $50$ is $\frac{42 + 50}{2} = 46$ . The margin of error is the distance from the center to either end: $50 - 46 = 4$ feet.

Choice B uses the full width of the interval, $8$ , as the margin of error, but the margin is only half the width.

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