Use the following information to answer questions (10)- (12). 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 the same as 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.
-Check that the conditions hold so that the sampling distribution of the z-statistic will approximately follow the standard normal distribution. Are the conditions satisfied? If not, choose the condition that is not satisfied.
A)Yes, all the conditions are satisfied.
B)No, the researcher did not collect a random sample.
C)No, the researcher did not collect a large enough sample.
D)No, the population of interest is not large enough to assume independence.

Question

Quizplus · Accepted Answer

The conditions for the sampling distribution of the z-statistic to approximately follow the standard normal distribution include having a random sample, a large enough sample size (usually n*p and n*(1-p) both greater than 10), and a population at least 10 times larger than the sample. The question states that a random sample of 75 adults was collected, which satisfies the randomness condition. Assuming the proportion of 0.16 applies, 75*0.16 = 12 and 75*0.84 = 63, both of which are greater than 10, satisfying the large enough sample size condition. Since the population is the young adults in a U.S. city and by extension the general population of young adults in the U.S., it is reasonable to assume it is more than 750 (10 times the sample size), satisfying the large population condition.

Use the Following Information to Answer Questions (10)- (12)