Q219 · Practice questionTechnology-freeComplex unfamiliar6 marks
QUESTION 219 (6 marks)
A random sample of voters gives who support a proposal. Use for an approximate confidence interval for the population proportion.
a)[1 mark]
Find the sample proportion.
b)[3 marks]
Construct the approximate confidence interval.
c)[2 marks]
Interpret the interval and state one condition required for the approximation.
WORKED SOLUTION
6 marksPractice marking scheme
ANSWER
Interpretation: the method gives a plausible range of about to for the population support proportion (under repeated-sampling confidence interpretation). A required condition is an approximately random/independent sample with np-hat and (-hat) sufficiently large.
Worked solution
Part (a): -hat.
Part (b): . . approximately.
Part (c): Interpretation: the method gives a plausible range of about to for the population support proportion (under repeated-sampling confidence interpretation). A required condition is an approximately random/independent sample with np-hat and (-hat) sufficiently large.
Part (a): completes the requested reasoning and obtains a correct result.
Part (b): completes the requested reasoning and obtains a correct result.
Part (c): completes the requested reasoning and obtains a correct result.
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