8.41 Systematic random samples. Systematic random samples go through a list of t

Question

8.41 Systematic random samples. Systematic random samples go through a list of the population at fixed intervals from a randomly chosen starting point. For example, a study of dating among college students chose a systematic sample of 200 single male students at a university as follows.18 Start with a list of all 9000 single male students. Because 9000/200 = 45, choose one of the first 45 names on the list at random and then every 45th name after that. For example, if the first name chosen is at position 23, the systematic sample consists of the names at positions, 23, 68, 113, 158, and so on up to 8978.

(a) Use Table B to choose a systematic random sample of 5 addresses from a list of 200. Enter the table at line 120.

(b) Like an SRS, a systematic sample gives all individuals the same chance to be chosen. Explain why this is true, then explain carefully why a systematic sample is none the less not an SRS.

Explanation / Answer

(a) Since 200/5 = 40, we will choose one of the first 40 names at random. Beginning on line 120, the addresses selected are 35, 75, 115, 155, and 195. (Only the first number is chosen from the table.) (b) All addresses are equally likely; each has chance 1/40 of being selected. This is not an SRS because the only possible samples have exactly one address from the first 40, one address from the second 40, and so on. An SRS could contain any 5 of the 200 addresses in the population.

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