Systematic random samples. Systematic random samples are often used to choose a sample of apartments in a large building or dwelling units in a block at the last stage of a multistage sample. An example will illustrate the idea of a systematic sample. Suppose that we must choose four addresses out of 100. Because 100/4 5 25, we can think of the list as four lists of 25 addresses.

Choose one of the first 25 at random, using Table B. The sample contains this address and the addresses 25, 50, and 75 places down the list from it. If 13 is chosen, for example, then the systematic random sample consists of the addresses numbered 13, 38, 63, and 88.

(a) A study of dating among college students wanted a sample of 200 of the 9000 single male students on campus. The sample consisted of every 45th name from Ashley Oaks Bay Pointe Beau Jardin Bluffs Brandon Place Briarwood Brownstone Burberry Cambridge Chauncey Village Country Squire Country View Country Villa Crestview Del-Lynn Fairington Fairway Knolls Fowler Franklin Park Georgetown Greenacres a list of the 9000 students. Explain why the survey chooses every 45th name.

(b) Use software or Table B at line 135 to choose the starting point for this systematic sample.
3.37 Systematic random samples versus simple random samples. The previous exercise introduces systematic random samples. Explain carefully why a systematic random sample does give every case the same chance to be chosen but is not a simple random sample.