From a population of 3,681 people, 300 were chosen at random and surveyed about a new film. Based on the survey, it is estimated that 42% of people in the population greatly enjoyed the film, with an associated margin of error of 2.4%. Based on these results, which of the following is a plausible value for the total number of people in the population who greatly enjoy the film.
The correct answer is (D).
current priority level - the Path to 650+ and higher
A principle reason this question has the current priority level that it has is because this does not seem like a highly likely question to appear. That said, if you end up vibing with this analysis, it would certainly be great to confidently secure this question.
It is very understandable to have thought the correct answer is (B). You may have done 42% of 300(.42 x 300) and arrived at a value of 126. But, this is not our correct answer, because the question is asking about the “population”, not the people who were chosen for the survey.(The idea here is that we are using the results of the survey to extrapolate out to what could be the case for the population as a whole. If this does not vibe, it is not a cause for any concern.)
The likely ideal way to confidently arrive at the correct answer of (D) is to start out by both adding and subtracting 2.4 from 42. Doing so, we arrive at 39.6 and 44.4. Now, we do 39.6% and 44.4% of 3681(the total population).
The values we end up reveal that we want an answer in between 1457.676 and 1634.364.
Here are some things to close out with….