Question

A researcher is wondering whether the smoking habits of young adults (18-25 years of age) in a certain city in the U.S. are different from the proportion of the general population of young adults in the U.S. A recent study stated that the proportion of young adults who reported smoking at least twice a week or more in the last month was 0.16. The researcher collected data from a random sample of 75 adults in the city of interest. State the hypotheses to be tested for this study.

Answer 1

For this case we want to test if in a certain city in the U.S. are different from the proportion of the general population of young adults in the U.S 0.16 (alternative hypothesis) and the best system of hypothesis are:

Null hypothesis:
`p=0.16`

Alternative hypothesis:
`p \\eq 0.16`

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 if in a certain city in the U.S. are different from the proportion of the general population of young adults in the U.S 0.16 (alternative hypothesis) and the best system of hypothesis are:

Null hypothesis:
`p=0.16`

Alternative hypothesis:
`p \\eq 0.16`