5.14 Exercises

Selected answers are available in Sect. D.5.

Exercise 5.1 Suppose we needed to estimate the average number of pages in a book in the USC library (including all campuses), using a sample of 200 books.

  1. Describe how you might select a simple random sample of books.
  2. Describe how you might select a stratified sample of books.
  3. Describe how you might select a cluster sample of books.
  4. Describe how you might select a convenience sample of books.
  5. Describe how you might select a multi-stage sample of books.
  6. Which would be most practical?
Exercise 5.2 Suppose we needed a sample of 80 vehicles parking at USC (Sippy Downs), and we wish to determine the proportion displaying P plates. Determine a useful way to find a suitable representative sample. The map below of the USC Sippy Downs campus may prove helpful (where areas labelled P are car parks).

Exercise 5.3 Suppose we need a sample of 20 residents from apartments in a large residential apartment complex, comprising 20 floors with 30 apartments in each floor. We plan to interview the residents of these apartments.

  1. One approach to obtaining a sample is to randomly select five floors, then randomly select four apartments from each of those five floors, and interview the oldest resident of that apartment. What type of sampling scheme is this?
  2. Another approach is to select one floor at random, and select the first 20 apartments on that floor then interview the oldest resident of that apartment. What type of sampling scheme is this?
  3. Another approach is to wait at the ground-floor elevator, and ask people who emerge to participate in our interview. What type of sampling scheme is this?
  4. Another approach is to select five floors at random, then wait by the elevator and interview residents as they arrive at the elevator. What type of sampling scheme is this?
  5. Which of the above sampling methods are good, and which are poor? Explain your answers.

Exercise 5.4 Suppose a researcher needs a sample of customers who shop at a large, local shopping centre to complete a survey.

  1. The researcher stations themselves outside the supermarket at the shopping centre one morning, and approaches every 10th person who walks past. What is the sampling method?
  2. The researcher waits at the main entrance for 30 minutes at 8am every morning for a week, and approaches every 5th person. What is the sampling method?
  3. The researcher leaves a pile of survey forms at an unattended booth in the shopping centre, and a locked barrell in which to place completed surveys. What is the sampling method?
  4. The researcher goes to the shopping centre every day for two weeks, at a different time and location each day, and approaches someone every 15 minutes. What is the sampling method?
  5. Which would the best sampling method?
  6. Which (if any) of the methods produce a random sample?

Exercise 5.5 A study (Ridgewell, Sipe, and Buchanan 2009) investigated how children in Brisbane travel to state schools. Suppose researchers randomly sampled four schools from a list of Brisbane state schools, and invited every family at each of those four schools to complete a survey.

What type of sampling method is this?