A researcher obtains an alphabetical list of the 2560 students at a college. She

Question

A researcher obtains an alphabetical list of the 2560 students at a college. She uses a random number generator to obtain 50 numbers between 1 and 2560. She chooses the 50 students corresponding to those numbers. Does this sampling plan result in a random sample? Simple random sample? Explain.



a. Yes; no. The sample is random because all students have the same chance of being selected. It is not a simple random sample because some samples are not possible, such as a sample containing the first 50 students on the list.

b. Yes; yes. The sample is random because all students have the same chance of being selected. It is a simple random sample because all samples of 50 students have the same chance of being selected.

c. No; yes. The sample is not random because not all students have the same chance of being selected. It is a simple random sample because all samples of 50 students have the same chance of being selected.

d. No; no. The sample is not random because not all students have the same chance of being selected. It is not a simple random sample because some samples are not possible, such as a sample containing the the first 50 students on the list.

Explanation / Answer

a) Yes, the sample is random sample. but not the simple random sample. Because the samples are generated using a random number generator. and not all the samples of same size is not being selected. Hence (a) is the correct answer. Yes; no. The sample is random because all students have the same chance of being selected. It is not a simple random sample because some samples are not possible, such as a sample containing the first 50 students on the list.

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