How large a sample must a pollster take in order to estimate with 95% confidence and to within 3 percentage points, the proportion of voters who are in favor of a certain measure

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01-04-2022
Mathematics

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How large a sample must a pollster take in order to estimate with 95% confidence and to within 3 percentage points, the proportion of voters who are in favor of a certain measure

Sagot :

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jimthompson5910 jimthompson5910 · Answer 1 · 2022-04-01T22:44:54-04:00

Answer: 1068

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Work Shown:

[tex]n = \hat{p}*(1-\hat{p})\left(\frac{z}{E}\right)^2\\\\n \approx 0.5*(1-0.5)\left(\frac{1.96}{0.03}\right)^2\\\\n \approx 1067.111\\\\n \approx \boldsymbol{1068}\\\\[/tex]

Notes:

At 95% confidence, the z critical value is roughly z = 1.96 which is determined using a Z table.
E = 0.03 to represent the 3% error.
We're not told the value of [tex]\hat{p}[/tex], so we assume the most conservative estimate of 0.5
Always round up to the nearest integer. The value 1067.111 is closer to 1067, but we round up to 1068 to clear the hurdle needed.

Sagot :

Answer: 1068

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