In a survey of 250 voters prior to an election 40 indicated

In a survey of 250 voters prior to an election, 40% indicated that they would vote for the incumbent
candidate.
a) [4] Estimate with a 90% confidence interval the population proportion of voters who support the
incumbent.
b) [4] Using the sample estimate of p from the above study, how large a sample is necessary to
estimate the proportion of voters who favour the incumbent to within 0.04 with 90%
confidence?
c) [4] Repeat (b) assuming that no previous study has been conducted.

Solution

Sample size = 250

Sample proportion for voting incumbent candidate = 40%

Margin of error = -5.1, 5.1

Confidence interval for 90%

= (34.9, 45.1)

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b) Margin of error =0.04

Margin of error = std error/rt n where n is the sample size.

i.e. Sample size >3206570

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c) If 40% is not given then we take p =0.5 or 50%

Margin of error =0.04

means sample size <= 3350000