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.