QCEVault

Interval estimates for proportions — Question 322

Original QCE Vault practice · 4 marks

Q322 · Practice questionTechnology-activeComplex familiar4 marks

QUESTION 322 (4 marks)

A polling team has no prior estimate of the population proportion. It wants a 95%95\% approximate confidence interval with planned margin of error at most 0.030.03. Use z=1.96z=1.96.
a)
Show that p(1−p)≤14p(1-p)\leq\dfrac14 for 0≤p≤10\leq p\leq1.
[2 marks]
b)
Determine a sample size sufficient for any assumed proportion.
[2 marks]
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