SAT question 1e562f24 (Inference From Sample Statistics And Margin Of Error)

Question

To estimate the proportion of a population that has a certain characteristic, a random sample was selected from the population. Based on the sample, it is estimated that the proportion of the population that has the characteristic is $0.49$ , with an associated margin of error of $0.04$ . Based on this estimate and margin of error, which of the following is the most appropriate conclusion about the proportion of the population that has the characteristic?

2

Difficulty:Easy

A

It is plausible that the proportion is between $0.45$ and $0.53$ .

B

It is plausible that the proportion is less than $0.45$ .

C

The proportion is exactly $0.49$ .

D

It is plausible that the proportion is greater than $0.53$ .

College Board · Accepted Answer

The correct answer is A. Choice A is correct. It's given that the estimate for the proportion of the population that has the characteristic is 0.49 with an associated margin of error of 0.04 . Subtracting the margin of error from the estimate and adding the margin of error to the estimate gives an interval of plausible values for the true proportion of the population that has the characteristic. Therefore, it's plausible that the proportion of the population that has this characteristic is between 0.45 and 0.53 .

Explanation

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Why the other choices are wrong

SAT Question 1e562f24: Inference From Sample Statistics And Margin Of Error answer and explanation with Desmos solution

Explanation

Enter in Desmos:

Why the other choices are wrong