SAT question da978ee6 (Inference From Sample Statistics And Margin Of Error)

Question

A researcher surveyed a random sample of $1, 020$ people from a certain city to estimate the percentage of people who support a recently announced proposal. From the survey, the researcher estimated that $86%$ of people from the city support this proposal, with an associated margin of error of $2.13%$ . The researcher repeated the survey with a random sample of people from the city that was double the original sample size. Assuming the margins of error were calculated in the same way, which of the following is true about the margin of error associated with the estimate from the larger sample?

21

Difficulty:Hard

A

The margin of error is between $2.13%$ and $3.13%$ .

B

The margin of error is between $4.13%$ and $5.13%$ .

C

The margin of error is greater than $5.13%$ .

D

The margin of error is less than $2.13%$ .

College Board · Accepted Answer

The correct answer is D. Choice D is correct. It's given that from the initial survey, the margin of error associated with the estimate was 2.13 % . A larger sample size generally leads to a smaller margin of error. Therefore, assuming the margins of error were calculated in the same way, the margin of error associated with the estimate from the larger sample is less than 2.13 % .

CookSAT · Answer

Note: Doubling the sample size reduces the margin of error by the square root of the sample-size scale factor, making it less than 2.13%.

Explanation

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Why the other choices are wrong

SAT Question da978ee6: Inference From Sample Statistics And Margin Of Error answer and explanation with Desmos solution

Explanation

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Why the other choices are wrong