## 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**:

**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 5.3**:

**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 5.4**: 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.