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. A researcher completes a hypothesis test with a resulting p-value = 0.076. Choose the best statement to interpret the results.

Answer 1

The proportion of young adults (18-25 years of age) in a certain city in the U.S. are not different from the proportion of the general population of young adults in the U.S.

Explanation:

The hypothesis for the test can be defined as:

H₀: The proportion of young adults (18-25 years of age) in a certain city in the U.S. are not different from the actual proportion, i.e. P = p.

Hₐ: The proportion of young adults (18-25 years of age) in a certain city in the U.S. are different from the actual proportion, i.e. P ≠ p.

The test statistic is defined as:

`z=\frac{\hat p-p}{\sqrt{(p(1-p))/(n)}}`

Assume that the significance level of the test is, α = 0.05.

The decision rule is:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected. And vice-versa.

It is provided that the p-value of the test is, p-value = 0.076.

The p-value = 0.076 > α = 0.05.

Thus, the null hypothesis will not be rejected at 5% level of significance.

Conclusion:

The proportion of young adults (18-25 years of age) in a certain city in the U.S. are not different from the proportion of the general population of young adults in the U.S.