Q314 · Practice questionTechnology-activeSimple familiar4 marks
QUESTION 314 (4 marks)
A random sample of café customers includes who prefer reusable cups.
a)[1 mark]
Determine the sample proportion.
b)[2 marks]
Construct a approximate confidence interval for the population proportion. Give the endpoints to three decimal places.
c)[1 mark]
Explain what the confidence level means in this context.
WORKED SOLUTION
4 marksPractice marking scheme
ANSWER
a) . b) . c) About of intervals formed by this procedure from repeated random samples would contain the population proportion.
Worked solution
a) .
b) . The margin is . Add and subtract it from .
c) The confidence level is the long-run coverage of the procedure, not the proportion of customers in the interval.
Exact answers unless rounding is specified; equivalent forms accepted.
a) Determines the sample proportion.
b) Uses the correct critical value and standard error.
b) Gives the interval endpoints.
c) Gives a repeated-sampling interpretation.
Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.
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