In a program designed to help patients stop​ smoking, 177 patients were given sustained​ care, and ​81.9% of them were no longer smoking after one month. Use a 0.01 significance level to test the claim that ​80% of patients stop smoking when given sustained care. Identify the test statistic for this hypothesis test.

The test statistic for this hypothesis test is

The​ P-value for this hypothesis test is

Identify the conclusion for this hypothesis test