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 for this poll, rounded to the nearest tenth of a percent?

(1 point)
The margin of error is
%
.
Remaining Attempts

Answer 1

To calculate the margin of error for a poll, you can use the formula:

\[
\text{Margin of Error} = z \times \sqrt{\frac{p(1-p)}{n}}
\]

where:
- \( z \) is the z-score that corresponds to the desired confidence level (for a 95% confidence level, \( z \) is approximately 1.96),
- \( p \) is the proportion of respondents who support the candidate (in this case, 0.12),
- \( n \) is the total number of respondents (450).

First, we calculate \( p(1-p) \):

\[
p(1-p) = 0.12(1 - 0.12) = 0.12 \times 0.88 = 0.1056
\]

Next, we calculate \( \frac{p(1-p)}{n} \):

\[
\frac{p(1-p)}{n} = \frac{0.1056}{450} \approx 0.00023467
\]

Now, we take the square root:

\[
\sqrt{\frac{p(1-p)}{n}} \approx \sqrt{0.00023467} \approx 0.01533
\]

Now we multiply by the z-score (1.96):

\[
\text{Margin of Error} \approx 1.96 \times 0.01533 \approx 0.0301
\]

To express this as a percentage, we multiply by 100:

\[
\text{Margin of Error} \approx 0.0301 \times 100 \approx 3.01\%
\]

Rounding to the nearest tenth of a percent, the margin of error is:

\[
\text{Margin of Error} \approx 3.0\%
\]

So, the margin of error for this poll is **3.0%**.