Question

Mrs. Marshall wants to select a random sample of six of the 36 students in her class to present their book reports, which are due today. She will number her students from 1 to 36 on her class list and roll a six-sided die. She will pick the student corresponding to the number she rolls and every sixth student on the list after that number. For example, if she rolls a 3, she will pick students 3, 9, 15, 21, 27, and 33. Is the resulting sample a simple random sample?

(A) Yes, because every student has an equal chance of being selected.

(B) Yes, because every group of six students has an equal chance of being selected.

(C) Yes, because the sample was selected randomly using a die.

(D) No, because every student does not have an equal chance of being selected.

(E) No, because every group of six students does not have an equal chance of being selected.

Why is it not simple random sampling?

Answer 1

This is not a simple random sampling.

Suppose the teacher gets the number i, where i=1,2,..6, when she rolls the die, then she will choose the student numbered i, i+6 and so on.Clearly when she will make the second selection i.e when she will select the i+6 th student, there is no chance of selecting students numbered 1 to 6 and 13 to 36 which means that in the 2nd selection a student belonging to the 2nd group will be selected.

Similerly in the ith selection a student belonging to the ith group will be selected where i=1,2,..6,there is no chance of being selected of a student who does not belong to the said group.Therefore the probability of selecting students among all the 36 students in her class in each draw is not the same.Every group of six students does not have equal chance of being selected.

Therefore this is not simple random sampling. option E is correct.

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