Question #f04d40b2 - SAT Suite Question Bank

ID: f04d40b2

Modded SAT Question Bank by Abdullah Mallik

From a population of $50,000$ people, $1,000$ were chosen at random and surveyed about a proposed piece of legislation. Based on the survey, it is estimated that $35 percent sign$ of people in the population support the legislation, with an associated margin of error of $3 percent sign$ . Based on these results, which of the following is a plausible value for the total number of people in the population who support the proposed legislation?

$350$
$650$
$16,750$
$31,750$

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Correct Answer: C

Rationale

Choice C is correct. It’s given that an estimated $35 percent sign$ of people in the population support the legislation, with an associated margin of error of $3 percent sign$ . Subtracting and adding the margin of error from the estimate gives an interval of plausible values for the true percentage of people in the population who support the legislation. Therefore, it’s plausible that between $32 percent sign$ and $38 percent sign$ of people in this population support the legislation. The corresponding numbers of people represented by these percentages in the population can be calculated by multiplying the total population, $50,000$ , by $0.32$ and by $0.38$ , which gives $50,000 left parenthesis 0.32 right parenthesis equals 16,000$ and $50,000 left parenthesis 0.38 right parenthesis equals 19,000$ , respectively. It follows that any value in the interval $16,000$ to $19,000$ is a plausible value for the total number of people in the population who support the proposed legislation. Of the choices given, only $16,750$ is in this interval.

Choice A is incorrect. This is the number of people in the sample, rather than in the population, who support the legislation.

Choice B is incorrect. This is the number of people in the sample who do not support the legislation.

Choice D is incorrect. This is a plausible value for the total number of people in the population who do not support the proposed legislation.

Question Difficulty: Medium