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Problem-Solving and Data AnalysisHardRecovering the margin of error from an interval

Problem-Solving and Data Analysis practice question

Using data from a random sample, a biologist reported that a plausible interval for the mean mass, in grams, of a species of beetle is 42.8 to 47.6.

What is the margin of error for this estimate, in grams?

Answer: 2.4

The interval runs from the estimate minus the margin of error to the estimate plus the margin of error, so the margin of error is HALF the interval's width. The width is 47.6 - 42.8 = 4.8, so the margin of error is 4.8 / 2 = 2.4 grams. (Check: the sample mean sits at the centre, (42.8 + 47.6) / 2 = 45.2, and 45.2 - 2.4 = 42.8.)

Common wrong answers

If you answered 4.8
That's the full width of the interval. The margin of error reaches out in BOTH directions from the estimate, so it's half the width: 4.8 / 2 = 2.4.
If you answered 45.2
That's the sample mean — the centre of the interval — rather than how far the interval extends from it. Subtract the centre from an endpoint: 47.6 - 45.2 = 2.4.
If you answered 90.4
That's the two endpoints added together. Take their difference and halve it instead: (47.6 - 42.8) / 2 = 2.4.

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