Question

In a poll, 1,325 people are surveyed about their preferred political candidate. 38% of respondents said they support candidate A.

What is the margin of error for this poll, rounded to the nearest tenth of a percent?

(1 point)
The margin of error is %

Answer 1

To calculate the margin of error for a poll, you can use the formula for the margin of error (ME) at a 95% confidence level, which is given by:

\[
ME = \frac{Z \cdot \sqrt{p(1-p)}}{\sqrt{n}}
\]

where:
- \( Z \) is the Z-score (approximately 1.96 for a 95% confidence level),
- \( p \) is the proportion of respondents supporting candidate A (0.38 in this case),
- \( n \) is the total number of respondents (1,325).

Now we can plug in the values:

1. Calculate \( p(1-p) \):
\[
p(1-p) = 0.38 \times (1 - 0.38) = 0.38 \times 0.62 = 0.2356
\]

2. Take the square root:
\[
\sqrt{p(1-p)} = \sqrt{0.2356} \approx 0.4853
\]

3. Calculate the margin of error:
\[
ME = \frac{1.96 \cdot 0.4853}{\sqrt{1325}}
\]

4. Calculate \( \sqrt{1325} \):
\[
\sqrt{1325} \approx 36.4
\]

5. Now plug it back into the ME formula:
\[
ME = \frac{1.96 \cdot 0.4853}{36.4} \approx \frac{0.9511}{36.4} \approx 0.0261
\]

6. Convert to percentage:
\[
ME \approx 0.0261 \times 100 \approx 2.61\%
\]

Finally, rounding to the nearest tenth of a percent:
\[
\text{Margin of error} \approx 2.6\%
\]

Thus, the margin of error for this poll is **2.6%**.