To calculate the margin of error (ME) given the standard error (SE) and the confidence level (CL), we use the formula:

$\text{Margin of Error (ME)} = Z \times SE$

Where $Z$ is the critical value corresponding to the confidence level. For a confidence level of 98%, the critical value $Z$ can be found from a standard normal distribution table or calculator.

1. Find the critical value $Z$ for a 98% confidence level:

   • For a 98% confidence level, $\alpha = 1 - 0.98 = 0.02$, and the critical region is split between the two tails.
   • This means each tail has $\alpha/2 = 0.01$.
   • From the Z-table, the critical value for $P(Z \leq z) = 0.99$ (or $1 - 0.01$) is approximately $Z = 2.33$.

2. Substitute the values into the formula: $ME = Z \times SE = 2.33 \times 3.62$

3. Calculate the margin of error: $ME = 8.435$

Thus, the margin of error is:

$\boxed{8.435}$

If you need further clarification or have additional questions, feel free to ask!

Related Questions:

1. What is the significance of the Z-value in margin of error calculations?
2. How does the confidence level affect the margin of error?
3. Can the standard error vary, and how does that influence the margin of error?
4. What is the relationship between sample size and margin of error?
5. How can margin of error be reduced in practical applications?

Tip:

Always ensure that the confidence level and its corresponding Z-value are consistent for accurate margin of error calculations.