SAT question 2bab1399 (Inference From Sample Statistics And Margin Of Error)

Question

A researcher is designing a study to investigate the average number of hours participants in a training course spend on a particular activity per day. The researcher will report an estimated average number of hours participants in the training course spend on this activity per day with an associated margin of error. The researcher is considering using a random sample of either $115$ or $230$ participants from the training course. Which of the following would be the most likely effect of using the larger random sample compared to the smaller random sample?

3

Difficulty:Medium

A

The reported margin of error would be lower.

B

The reported margin of error would be higher.

C

The reported average number of hours would be lower.

D

The reported average number of hours would be higher.

College Board · Accepted Answer

The correct answer is A. Choice A is correct. When using a random sample to report an estimated average, a larger sample size, such as 230 participants instead of 115 participants, generally leads to a smaller margin of error. Therefore, the most likely effect of using the larger random sample compared to the smaller random sample is that the reported margin of error would be lower.

CookSAT · Answer

Note: Margin of error is proportional to 1/sqrt(n), so the larger sample produces a smaller margin of error.

Explanation

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Why the other choices are wrong

SAT Question 2bab1399: 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