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The mathematics department at a university wants to administer a survey to a sample of students....

The mathematics department at a university wants to administer a survey to a sample of students. Suppose that 20 faculty members volunteered to administer the survey, and those faculty members who volunteered gave the survey to all students in one course of their choice. Would this be considered to be a random and unbiased sample? Why or why not?

Math   Statistics-And-Probability   
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Answer #1

This sample is not random and unbiased. In random sampling, all individuals of the population have equal probability of getting selected. Here, all students are not equally likely to be selected. The 20 professors who volunteered will pick course of their choice and based on that all the students who belong to those courses will get selected with a probability 1 and the rest will be selected with probability 0 (meaning the rest won't be selected).

This is why the sample is not random and unbiased.

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