SAT Inference from sample statistics and margin of error Practice Question 2 (Hard) | SAT Owl

Question bank / Inference from sample statistics and margin of error

Math · Problem-Solving and Data AnalysisHard

An energy analyst selected a random sample of $150$ households from the $12{,}000$ households in a city. The mean monthly electricity use for the sample was $870$ kilowatt-hours (kWh), with an associated margin of error of $35$ kWh. Which of the following is the most appropriate conclusion?

A

Most households in the city use between $835$ and $905$ kWh per month.

B

It is plausible that the mean monthly electricity use for all households in the city is between $835$ and $905$ kWh.

C

The mean monthly electricity use for all households in the city is exactly $870$ kWh.

D

Every household in the sample uses between $835$ and $905$ kWh per month.

Show answer and explanation

Answer: B

The margin of error describes how far the sample mean may plausibly be from the population mean. So the interval $870 \pm 35$ , or $835$ to $905$ kWh, is a plausible range for the mean of all $12{,}000$ households. It says nothing about the usage of individual households.

Choice A confuses an interval for the mean with a range that contains most individual values; individual households can vary much more widely than the mean does.

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