year 8 maths

9J
Surveying and sampling
583
12 Whenever a survey is conducted, even if the people being asked are randomly selected, bias can be
introduced by the fact that some people will not answer the questions or return the surveys.
a Assume 1000 surveys are mailed out to a random sample of people asking the question
‘Do you think Australia should be a republic?’ and 200 replies are received: 150 say ‘yes’ and
50 say ‘no’.
i On the basis of the 200 people who returned the survey, what percentage are in favour of a
republic?
ii If all 800 people who did not respond would have said ‘yes’, what percentage are in favour
of a republic?
iii If all 800 people who did not respond would have said ‘no’, what percentage are in favour
of a republic?
iv If the 1000 people receiving the survey are representative of the Australian population, what
conclusion can be drawn about the popularity of a republic?
b A survey is being conducted to decide how many people feel they are busy. Describe how bias
is introduced by the people who agree to participate in the survey.
c Give an example of another survey question that would cause a bias to be introduced simply on
the basis of the people who participate.
d Sometimes surveys ask the same question in different ways over a number of pages. Although
this additional length makes it less likely that people will return the survey, why might the
questioner wish to ask the same question in different ways?
13 A popular phrase is “Lies, damned lies, and statistics”. Why is it important that someone making
or conducting a survey behaves ethically?
ENRICHMENT
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14
Media bias
14 Search a newspaper, magazine or website and find an example of a survey or poll that has been
conducted.
a Decide the following, with justifications.
i Can you tell if they chose a large enough sample for the survey?
ii Can you tell whether the sample chosen was representative or biased?
iii Would this newspaper, magazine or website have an incentive to choose or publish biased
results?
iv How much are you relying on the publisher to behave ethically in choosing and displaying a
representative sample?
b Design a perfect survey to get the information that has been reported, and describe how you
would choose the survey recipients.
c Conduct the survey on a small random sample that is representative of the wider population,
and compare your results with those reported.
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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