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To calculate the margin of error, we use the formula:

\[
\text{Margin of Error} = Z_{\alpha/2} \times \text{Standard Error}
\]

Where:
- \( Z_{\alpha/2} \) is the Z-score corresponding to the confidence level.
- The standard error is provided as 3.8.
- For a 95% confidence level, the \( Z_{\alpha/2} \) value is approximately 1.96.

Now, applying the values:

\[
\text{Margin of Error} = 1.96 \times 3.8 = 7.448
\]

Thus, the margin of error is approximately **7.45**.

Would you like more details or have any questions?

Here are some follow-up questions for you:
1. What is the formula for finding the margin of error?
2. How do you find the Z-score for different confidence levels?
3. What does a higher confidence level imply about the margin of error?
4. How does the standard error influence the margin of error?
5. What are the assumptions of using the Z-score for confidence intervals?

**Tip:** Always ensure that the Z-score used corresponds to the exact confidence level specified in the problem.

Find the margin of error given the standard error and the confidence level. Standard error = 3.8, confidence level 95%.

Learn how to calculate the margin of error for a 95% confidence interval, given a standard error of 3.8. This problem covers key statistical concepts including the margin of error formula and the Z-score for a 95% confidence level. Suitable for students in Grades 10-12.

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