A hypothesis test is to be performed. determine the null and alternative hypotheses. the mean credit card debt among households in one state is $8400. a hypothesis test is to be performed to decide whether the mean credit card debt for households in the formerly affluent town of rich-no-more differs from the mean credit card debt for the state.

For this case we want to check if mean credit card debt for households in the formerly affluent town of rich-no-more differs from the mean credit card debt for the state (alternative hypothesis) and the complement rule would represent the null hypothesis.

The system of hypothesis for this case would be:

Null hypothesis:

Alternative hypothesis:

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".  

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".  

Solution to the problem

For this case we want to check if mean credit card debt for households in the formerly affluent town of rich-no-more differs from the mean credit card debt for the state (alternative hypothesis) and the complement rule would represent the null hypothesis.

The system of hypothesis for this case would be:

Null hypothesis:

Alternative hypothesis: