Question 7.47
17. The last stage of the CPS uses a systematic sample. An example will illustrate the idea of a systematic sample. Suppose that we must choose 4 rooms out of the 100 rooms in a dormitory. Because , we can think of the list of 100 rooms as 4 lists of 25 rooms each. Choose 1 of the first 25 rooms at random, using Table 7.1 (page 298). The sample will contain this room and the rooms 25, 50, and 75 places down the list from it. If 13 is chosen, for example, then the systematic random sample consists of the rooms numbered 13, 38, 63, and 88.
- Use Table 7.1 (page 298) to choose a systematic random sample of 5 rooms from a list of 200. Enter the table at line 120.
- Your sample gives every room the same chance to be chosen. Explain why.
- Despite the answer in part (b), this sample is not an SRS. Explain why.
17.
(a) Because , we divide the list into 5 groups of 40. (By the way, if the list has 204 rooms, we divide it into 5 groups of 40 and a final group of 4. A sample contains a room from the final group only when the first room chosen is among the first 4 in the list.) Label the first 40 rooms 01 to 40. Line 120 chooses room 35. The sample consists of rooms 35, 75, 115, 155, and 195.
(b) Each of the first 40 rooms has chance 1 in 40 of being chosen. Each later room is chosen exactly when the corresponding room in the first 40 is chosen. Thus, every room has an equal chance: 1 in 40.
(c) The only possible samples consist of 5 rooms spaced 40 apart in the list. An SRS gives all samples of 5 rooms an equal chance to be chosen.