From a population of 50,000 people, 1,000 were chosen at random and surveyed about a proposed piece of legislation. Based

Question

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 % of people in the population support the legislation, with an associated margin of error of 3 % . 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?

Accepted Answer

Choice C is correct. It&rsquo;s given that an estimated 35 % of people in the population support the legislation, with an associated margin of error of 3 % . 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&rsquo;s plausible that between 32 % and 38 % 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 0.32 = 16,000 and 50,000 0.38 = 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.

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