Question

In an online poll, 350 students were asked if they prefer to learn a language using a computer program or by learning from a tutor. 39% of respondents said they preferred learning from a computer program.

What is the margin of error for this poll?

(1 point)
Responses

18.7%
18.7%

39%
39%

5.3%
5.3%

61%

Answer 1

To calculate the margin of error for the given poll, we can use the formula for the margin of error in a proportion, which is:

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

Where:
- \( ME \) is the margin of error,
- \( z \) is the z-score corresponding to the desired confidence level (for a 95% confidence level, \( z \approx 1.96 \)),
- \( p \) is the proportion of respondents who selected a particular answer (0.39 in this case),
- \( n \) is the total number of respondents (350).

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

\[
p = 0.39 \quad \text{and} \quad 1 - p = 1 - 0.39 = 0.61
\]

\[
p(1-p) = 0.39 \times 0.61 = 0.2379
\]

Next, we calculate the standard error (SE):

\[
SE = \sqrt{\frac{0.2379}{350}} \approx \sqrt{0.000678} \approx 0.026
\]

Now, we compute the margin of error:

\[
ME = 1.96 \times 0.026 \approx 0.0511
\]

To express this as a percentage:

\[
ME \approx 0.0511 \times 100 \approx 5.11\%
\]

Considering rounding, the closest answer in the provided options to the calculated margin of error (5.11%) is **5.3%**.

Thus, the final answer is:

**5.3%**