To calculate the standard error of the mean ($SE_{\bar{x}}$), we use the formula:

$SE_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$

Where:

• $\sigma = 31,000$ (the standard deviation),
• $n = 42$ (the sample size).

Let's compute this.

$SE_{\bar{x}} = \frac{31,000}{\sqrt{42}}$The standard error of the mean for a sample of 42 households is approximately 4,783.

Would you like any further details or clarifications?

Here are five related questions:

1. How does sample size affect the standard error of the mean?
2. What does the standard error of the mean represent in the context of sampling?
3. How would the result change if the sample size increased to 100 households?
4. Why is the normal distribution assumption important in this problem?
5. How is the standard error different from the standard deviation?

Tip: A larger sample size generally reduces the standard error, providing a more precise estimate of the population mean.