This question involves calculating the standard error of the sample mean ($SE$).

Information provided:

1. Population mean ($\mu$): 40
2. Population standard deviation ($\sigma$): 21
3. Sample size ($n$): 49

Formula for Standard Error:

$SE = \frac{\sigma}{\sqrt{n}}$

Substituting the values:

$SE = \frac{21}{\sqrt{49}} = \frac{21}{7} = 3$

Final Answer:

The standard error of the sample mean is 3 points.

Would you like a more detailed explanation or help with another part of this question?

Here are some related questions to deepen your understanding:

1. How does the standard error change if the sample size is increased to $n = 100$?
2. What is the role of population standard deviation ($\sigma$) in determining the standard error?
3. How would the calculation differ if the sample size was not given but the margin of error was provided instead?
4. Why is it necessary to take the square root of the sample size in the formula for $SE$?
5. What is the difference between standard deviation and standard error?

Tip: A larger sample size decreases the standard error, making the sample mean a more precise estimate of the population mean!