A researcher is wondering whether the smoking habits of young adults (18-25 year

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.

Select one:

a. The p-value is above a standard cutoff value of = 0.05 and therefore there is insufficient evidence to support that the city of interest has a different proportion of smokers than the general public.

b. The p-value is above a standard cutoff value of = 0.05 and therefore there is sufficient evidence to support that the city of interest has a different proportion of smokers than the general public.

c. The p-value for a two-sided test is divided by 2 resulting in a value less than a standard cutoff value of = 0.05 supporting the hypothesis that the city of interest has a different proportion of smokers than the general public.

d. The standard cutoff value of = 0.05 is multiplied by two for a two-sided test and the resulting value of 0.10 is greater than the p-value. Therefore there is no evidence to support that the city of interest has a different proportion of smokers than the general public.

Explanation / Answer

Since the hypothesis test was for a 2 tailed test, the p-value obtained is for a 2 tailed test, which was conducted at = 0.05.

The decision rule is if p-value is < , Reject H0, else Fail to Reject H0, and conclude that there is insufficient evidence for Ha, the alternate Hypothesis.

Therefore Option a. is the correct answer. The p-value is above a standard cutoff value of = 0.05 and therefore there is insufficient evidence to support that the city of interest has a different proportion of smokers than the general public.

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