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Problem-Solving and Data Analysis / Inference from sample statistics and margin of error Difficulty: Easy

There are $55$ students in Spanish club. A sample of the Spanish club students was selected at random and asked whether they intend to enroll in a new study program. Of those surveyed, $20 percent sign$ responded that they intend to enroll in the study program. Based on this survey, which of the following is the best estimate of the total number of Spanish club students who intend to enroll in the study program?

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Explanation

Choice A is correct. It’s given that $20 percent sign$ of the students surveyed responded that they intend to enroll in the study program. Therefore, the proportion of students in Spanish club who intend to enroll in the study program, based on the survey, is $0.20$ . Since there are $55$ total students in Spanish club, the best estimate for the total number of these students who intend to enroll in the study program is $55 left parenthesis 0.20 right parenthesis$ , or $11$ .

Choice B is incorrect. This is the best estimate for the percentage, rather than the total number, of students in Spanish club who intend to enroll in the study program.

Choice C is incorrect. This is the best estimate for the total number of Spanish club students who do not intend to enroll in the study program.

Choice D is incorrect. This is the total number of students in Spanish club.