Q330 · Practice questionTechnology-activeComplex unfamiliar6 marks
QUESTION 330 (6 marks)
A survey costs $$400$595%0.04z=1.96$.
a)[3 marks]
Determine the minimum response count and minimum budget required.
b)[3 marks]
If the budget is only $$3000$, determine the smallest worst-case planned margin of error, to four decimal places.
WORKED SOLUTION
6 marksPractice marking scheme
ANSWER
a) responses; $$34050.0430$.
Worked solution
a) The largest value of is . Hence , so . The cost is .
b) The budget permits at most responses. A larger sample gives a smaller margin, so use all . The worst-case margin is .
Exact answers unless rounding is specified; equivalent forms accepted.
a) Uses the worst-case variance factor.
a) Finds the minimum integer sample size.
a) Calculates the minimum budget.
b) Finds the maximum affordable sample size.
b) Uses that size in the worst-case margin formula.
b) Calculates the rounded margin.
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