A voluntary survey anda population percentage
A fictional school has fivehundred students. Eighty voluntarily answer an on line survey about a proposed studyspace, and sixty of those respondents support it. A report says that seventy-five percent of every student supports the proposal because sixty divided by eighty is seventy-five percent. The remaining students didnot respond, and no random sample or follow-up is described. A teacher asks the class to distinguish a correct calculation about respondents from an unsupported generalization to the whole school. The exercise also asks whether the word voluntary proves that the responding group represents every one else. The numbers are supplied assumptions for this school-methods problem; they are not statistics about an actual institution or a regional examination. Students must identify the denominator, selection process and evidence that would be needed before claiming a reliable population estimate.
1. Calculate and interpret the two relevant proportions.
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Among respondents, 60/80=75%support. The known supporters are 60/500=12%of allstudents, but that does not establish thepreferences of nonrespondents. The first rate describes respondents, not every eligible student.
2. Explain these lection issue and one improvement.
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Voluntary response can be systematically related to interest or opinion, so it does not guarantee representativeness. Use an appropriate sampling plan, seek broader participation and report nonresponse and uncertainty rather than presenting the voluntary sample percentage as a certain population result.