## D.5 Answers: Sampling

Answers to exercises in Sect. 5.14.

Answer to Exercise 5.1: A tricky thing here is that some books are not physically in the library, as they have been borrowed.

1. Simple random sample: A list of all the books held by the USC library is needed. This may be possible for a librarian (it may not be, and would be really huge), it certainly is not possible for a student or non-library stafff member. In principle though, number each book, and randomly select a sample from that list. 2. Stratified: Use locations (Sippy Downs; Fraser Coast; Caboolture; Gympie; Southbank; SCHI) as strata, and then a random sample of all the book in each locations. 3. Cluster: Consider each set of shelves as a cluster, and randomly select some shelves, and determine the number of pages in each book on the selected shelves. 4. Multistage: Consider taking a random of campuses, then a random sample of the sets of shelves in the selected libraries, then selecting a random shelf from each one, then a small number of random book from each shelf. 5. Convenience: Finding books in the libraries within reach and easily accessible and on the shelves, 6. Multistage perhaps.
Answer to Exercise 5.2: Use a multi-stage sample: Select a carpark at random, then a row of cars at random, then cars at random.
Answer to Exercise 5.3: 1. Multi-stage. 2. It’s a bit like stratified… but not quite. 3. Convenience. 4. The last is poor. The second is bit odd but is probably OK. The first might be the best.
Answer to Exercise 5.4: 1. Convenience, but by approaching every 10th person they are trying to make it a little more representative… but they can do a lot better. 2. Convenience, but by approaching every 5th person and going every day for a week they are trying to make it a little more representative… but they can do a lot better. 3. Self-selecting. 4. Convenience. At least the researcher is trying to get a more representative sample, by going every day for two weeks, and at different times and locations each week, and approaching someone every 15 minutes. 5. The fourth is the best, but it is still far from ‘random.’ 6. None.
Answer to Exercise 5.5: A bit like cluster sampling (randomly taking a small sample from many groups, and taking everyone (or everything) in those selected groups)… but not every person in the selected schools would respond (they would decide if they responded). A combination of cluster and voluntary response sampling.