In a program designed to help patients stop smoking, 198 patients were given sustained care, and 82.8% of them were no longer smoking after one month (based on data from "Sustained Care Intervention and Post-discharge Smoking Cessation Among Hospitalized Adults," by Rigotti et al., Journal of the American Medical Association, Vol. 312, No. 7). Use a 0.01 significance level to test the claim that 80% of patients stop smoking when given sustained care. Does sustained care appear to be effective?

Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.