To calculate the margin of error for a proportion in a survey, we can use the following formula for a confidence level of approximately 95%:
\[ \text{Margin of Error (ME)} = z \times \sqrt{\frac{p(1-p)}{n}} \]
Where:
- \( z \) is the z-score for the desired confidence level (approximately 1.96 for 95% confidence),
- \( p \) is the proportion of respondents supporting the candidate (in decimal form),
- \( n \) is the total number of respondents.
In this case:
- \( n = 1325 \)
- \( p = 0.38 \)
Now, plugging these values into the formula:
- Calculate \( p(1-p) \):
\[ p(1-p) = 0.38 \times (1 - 0.38) = 0.38 \times 0.62 = 0.2356 \]
- Calculate the standard error (SE):
\[ \text{SE} = \sqrt{\frac{0.2356}{1325}} \approx \sqrt{0.0001776} \approx 0.01333 \]
- Now, calculate the margin of error:
\[ \text{ME} = 1.96 \times 0.01333 \approx 0.0261 \]
- Convert the margin of error to a percentage:
\[ \text{ME} \approx 0.0261 \times 100 \approx 2.61% \]
Finally, rounded to the nearest tenth of a percent, the margin of error is approximately:
\[ \boxed{2.6%} \]