Question

A report on the U.S. economy indicates that​ 28% of Americans have experienced difficulty in making mortgage payments. A news organization randomly sampled 400 Americans from 10 cities judged to be especially economically depressed and found that 136 reported such difficulty. Does this indicate that the problem is more severe among these​ cities? What are the correct null and alternative hypotheses for testing such a​ claim?

Answer 1

For this case we want to test that the true proportion of americans have experienced difficulty in making mortgage payments is higher than 0.28 (alternative hypothesis) and the sytem of hypotheis are:

NUll hypothesis:
`p \leq 0.28`

Alternative hypotheis:
`p >0.28`

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 test that the true proportion of americans have experienced difficulty in making mortgage payments is higher than 0.28 (alternative hypothesis) and the sytem of hypotheis are:

NUll hypothesis:
`p \leq 0.28`

Alternative hypotheis:
`p >0.28`