To determine which method would not produce a representative sample of the favorite sport of students at the local high school, we can analyze each option:
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Ask every tenth student from a list of names in the student directory: This method is likely to produce a representative sample, assuming the list is comprehensive and includes a diverse range of students.
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Ask every ten students wearing football jerseys each day for a week: This method is likely biased, as it only includes students who wear football jerseys, potentially over-representing those who prefer football while excluding students who may prefer other sports and do not wear jerseys.
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Ask every tenth student who arrives at school on Wednesday: This method could be representative, depending on the overall student population and any specific biases related to the day students arrive. However, if there are specific patterns or events on Wednesdays, it may lead to underrepresentation of some groups.
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Ask five students from each classroom chosen by picking numbers: This method has the potential to be representative, as it includes a sample from multiple classrooms, which can capture a wider range of opinions within the school.
Based on this analysis, the option that would not produce a representative sample is:
Ask every ten students wearing football jerseys each day for a week.