The standard error (SE) is calculated using the formula:
\[ SE = \frac{\sigma}{\sqrt{n}} \]
where \(\sigma\) is the standard deviation and \(n\) is the sample size.
Given:
- Standard deviation (\(\sigma\)) = 17.8
- Sample size (\(n\)) = 23
Now, plug in the values into the formula:
\[ SE = \frac{17.8}{\sqrt{23}} \]
First, calculate \(\sqrt{23}\):
\[ \sqrt{23} \approx 4.7958 \]
Now, calculate the standard error:
\[ SE = \frac{17.8}{4.7958} \approx 3.7091 \]
Rounding to the nearest hundredth, the standard error is:
\[ \boxed{3.71} \]