Question

In a study of the nicotine patch, 21% of those who used the patch for 2 months reported no smoking incidents in the following year. The 95% confidence interval is (17.4%, 24.8%). Which of the following is an appropriate interpretation of the 95% confidence interval? Group of answer choices

a. There is a 95% probability that the proportion of all nicotine patch users who would report no smoking incidents in the following year is between 17.4% and 24.8%.
b. We can be 95% confident that the proportion of all nicotine patch users who would report no smoking incidents in the following year is between 17.4% and 24.8%.
c. We can be 95% confident that the proportion of the sample who would report no smoking incidents in the following year is between 17.4% and 24.8%.
d. 95% of samples will have between 17.4% and 24.8% who would report no smoking incidents in the following year.

Answer 1

b. We can be 95% confident that the proportion of all nicotine patch users who would report no smoking incidents in the following year is between 17.4% and 24.8%.

Explanation:

The confidence interval is an estimation for the true population parameter, calculated from the information of a sample of this population.

The parameter of the population will be within this interval with a certain degree of confidence.

a. There is a 95% probability that the proportion of all nicotine patch users who would report no smoking incidents in the following year is between 17.4% and 24.8%.

Incorrect. The confidence interval gives only the probability that the true proportion (or population proportion) is within 17.4% and 24.8%, not the proportion of individual samples.

b. We can be 95% confident that the proportion of all nicotine patch users who would report no smoking incidents in the following year is between 17.4% and 24.8%.

Correct.

c. We can be 95% confident that the proportion of the sample who would report no smoking incidents in the following year is between 17.4% and 24.8%.

Incorrect. The confidence interval does not give information about another samples.

d. 95% of samples will have between 17.4% and 24.8% who would report no smoking incidents in the following year.

Incorrect. The confidence interval does not give information about another samples or sampling distributions.