Question

The current population of Australia is estimated to be approximately 25,440,000 and the population of the Brisbane metropolitan area is estimated to be approximately 2,400,000. A national polling organisation wishes to select a stratified random sample of 1,500 subjects from various cities and regions in Australia for one of its surveys. Assuming that each city or region is sampled in proportional to its population, how many subjects should be recruited from the Brisbane metropolitan area?

Round your answer to the nearest multiple of 5 persons. (Note: For the purposes of this question, you may ignore any issues relating to ages of potential survey subjects.)

Answer 1

Current population of Australia (n) = 25,440,000

Population of Brisbane Metropolitan Area (n​​​​​​1​​​) = 2,400,000

Proportion of Total population in Brisbane Metropolitan Area = p​​​​​​1 = n​​​​​​1 / n = 2400000/25440000 = 0.0943

Total sample size (m) = 1500

Number of subjects that should be recruited from Brisbane Metropolitan Area = m x p​​​​​​1 = 1500 x 0.0943 = 141.45

When rounded to nearest 5 number multiple it becomes 140.

So 140 people should be sampled from Brisbane Metropolitan Area.