Question

in a poll, 450 people are surveyed about their preferred political candidate. 12% of respondents say they support candidate A. what is the margin of error rounded to the nearest tenth

Answer 1

To calculate the margin of error for a survey, you can use the formula for the margin of error (ME) in a proportion based on a confidence level, commonly using a 95% confidence level:

\[
ME = z \times \sqrt{\frac{p(1-p)}{n}}
\]

Where:
- \( z \) is the z-score corresponding to the desired confidence level (for 95%, \( z \approx 1.96 \))
- \( p \) is the sample proportion (in this case, 0.12 for candidate A)
- \( n \) is the sample size (in this case, 450)

Let's calculate it step by step.

1. **Calculate \( p(1-p) \)**:
\[
p(1-p) = 0.12 \times (1 - 0.12) = 0.12 \times 0.88 = 0.1056
\]

2. **Calculate the standard error (SE)**:
\[
SE = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.1056}{450}} \approx \sqrt{0.0002358} \approx 0.0154
\]

3. **Calculate the margin of error (ME)**:
\[
ME = 1.96 \times SE \approx 1.96 \times 0.0154 \approx 0.0302
\]

4. **Round the margin of error**:
\[
ME \approx 0.0302 \approx 0.03
\]

To express this as a percentage:
\[
ME \times 100 \approx 3.0\%
\]

Therefore, the margin of error, rounded to the nearest tenth, is approximately **3.0%**.