A local high school has 300 students in each grade. In order to conduct a survey

Question

A local high school has 300 students in each grade. In order to conduct a survey of the 1200 students on their study habits researchers need a sample of 80 students. Rather than choose a simple random sample of 80 of the 1200 students, the researchers decide to choose a simple random sample of 20 students from each grade and combine these four simple random samples to form their sample. Which of the following statements about the resulting sample of 80 students is true? A. This sample is not a simple random sample because each student is not equally likely to be selected for the sample. B. This sample is not a simple random sample because each possible group of 80 students is not equally likely to be selected as the sample. C. Both (A) and (B) are true statements. D. This sample is a simple random sample.

Explanation / Answer

Answer : This is an example of 'Statified random sampling'. Because we divide population in three groups then select same via simple random sampling.

Hence given sample is not simple random sample because each student is not equally likely to be selected for the sample.

Similarly This is not simple random random sample because each possible group of 80 student is not equally likely to be selected as a sample.

Hence both A and B sstatment is true

Hence option C is correct.

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