To generate a random sample to survey the favorite snacks of students in the school, the best method among the given options is:
Obtain an alphabetized list of all the students in the school and select every seventh student.
This method is an example of systematic sampling, which can produce a more representative sample than selecting a specific group (like only boys) or choosing based on a trait (like height). It still ensures a level of randomness if the list is well mixed.
The other methods listed have limitations:
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Line up the students by height and choose the first 20 students: This introduces bias based on height, as it only includes students of certain heights.
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Use the school roster and randomly choose 50 boys: This option is not truly random since it excludes girls, which can lead to an unrepresentative sample of the whole school.
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Place all the names of the students in Mrs. Walsh's math class in a hat and randomly select 10 students: This is a random sample but is limited to only Mrs. Walsh's math class, not the entire school, which can also lead to bias.
Therefore, systematic sampling from an alphabetized list would provide a more inclusive and random sample.