To solve this, we first need to understand the hypotheses for this hypothesis test.

Given:

• We are testing if the sample was taken from a population where the true mean household income is $11,809.
• The null hypothesis ($H_0$) will claim that the population mean is $11,809.
• The alternative hypothesis ($H_1$) reflects what we are trying to prove (whether the population mean differs from $11,809).

The null and alternative hypotheses are generally set up as follows:

• $H_0: \mu = 11,809$ (The population mean household income is $11,809).
• $H_1$: The alternative hypothesis is trying to test if the population mean differs from $11,809.

In this case, because the problem does not mention "greater than" or "less than," it seems like we are performing a two-tailed test. This means we are simply testing whether the mean is different from $11,809, either higher or lower.

Thus, the alternative hypothesis should be:

• $H_1: \mu \neq 11,809$.

Answer: The alternative hypothesis ($H_1$) is: $\mu \neq 11,809$

Do you want further details about how to test this hypothesis or more clarification on two-tailed vs one-tailed tests?

Here are 5 related questions to expand the discussion:

1. How do you calculate the test statistic for this hypothesis test?
2. What does it mean to perform a two-tailed test?
3. How do you interpret the result of a hypothesis test if the null hypothesis is rejected?
4. What are Type I and Type II errors in hypothesis testing?
5. What is the p-value, and how is it used in hypothesis testing?

Tip: Always define your null and alternative hypotheses clearly before conducting any hypothesis test. This helps ensure you're testing the right claim.