QuestionAugust 5, 2025

What is the margin of error for a poll with a sample size of 1000 people?Round your answer to the nearest hundredth of a percent. square %

What is the margin of error for a poll with a sample size of 1000 people?Round your answer to the nearest hundredth of a percent. square %
What is the margin of error for a poll with a sample size of 1000 people?Round your answer to the nearest
hundredth of a percent.
square %

Solution
4.2(224 votes)

Answer

3.10\% Explanation 1. Identify the Formula for Margin of Error The margin of error (ME) is calculated using the formula: **ME = \frac{z \cdot \sigma}{\sqrt{n}}**, where z is the z-score for the desired confidence level, \sigma is the standard deviation, and n is the sample size. For a 95% confidence level, z \approx 1.96. 2. Assume Standard Deviation for Proportion For polls, assume maximum variability with \sigma = 0.5 (since proportion p = 0.5 gives maximum variability). 3. Calculate Margin of Error Substitute z = 1.96, \sigma = 0.5, and n = 1000 into the formula: ME = \frac{1.96 \times 0.5}{\sqrt{1000}} = \frac{0.98}{31.62} \approx 0.03097. 4. Convert to Percentage Convert the margin of error to percentage: 0.03097 \times 100 \approx 3.10\%.

Explanation

1. Identify the Formula for Margin of Error<br /> The margin of error (ME) is calculated using the formula: **$ME = \frac{z \cdot \sigma}{\sqrt{n}}$**, where $z$ is the z-score for the desired confidence level, $\sigma$ is the standard deviation, and $n$ is the sample size. For a 95% confidence level, $z \approx 1.96$.<br />2. Assume Standard Deviation for Proportion<br /> For polls, assume maximum variability with $\sigma = 0.5$ (since proportion $p = 0.5$ gives maximum variability).<br />3. Calculate Margin of Error<br /> Substitute $z = 1.96$, $\sigma = 0.5$, and $n = 1000$ into the formula: <br /> $ME = \frac{1.96 \times 0.5}{\sqrt{1000}} = \frac{0.98}{31.62} \approx 0.03097$.<br />4. Convert to Percentage<br /> Convert the margin of error to percentage: $0.03097 \times 100 \approx 3.10\%$.
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