One program to help people stop smoking cigarettes uses the method of posthypnotic suggestion to remind subjects to avoid smoking. A random sample of 18 subjects agreed to test the program. All subjects counted the number of cigarettes they usually smoke a day; then they counted the number of cigarettes smoked the day after hypnosis. (It usually takes several weeks for a subject to stop smoking completely, and the method does not work for everyone.) The results follow.

Using a 1% level of significance, test the claim that the number of cigarettes smoked per day was less after hypnosis.
(a) What is the level of significance? State the null and alternate hypotheses.
(b) Compute the sample test statistic. What is the sampling distribution?
(c) Find the P-value of the sample test statistic.
(d) Conclude the test.
(e) Interpret the conclusion in the context of the application.

Cigarettes Smoked per Day Cigarettes Smoked per Day After Before Before HypnosisSubject After Hypnosis 28 15 Hypnosis Hypnosis Subject 19 32 42 26 37 19 38 23 24 10 28 35 14 20 25 40 18 15 12 20 30 19 12 13 20 31 19 15 16 17 18 16 4 19 17