In a program designed to help patients stop smoking, 177 patients were given sustained care, and 82.5% of them were no longer smoking after one month. Use a 0.01 significance level to test the claim that 78% of patients stop smoking when given sustained care. Use the P-value method. Use the normal distribution as an approximation to the binomial distribution.

a. Let p denote the population proportion of patients who would no longer be smoking after one month when given sustained care. Identify the null and alternative hypotheses.

Ho:p ? ?

H1:p ? ?

(Type integers or decimals. Do not round.)

b. Identify the test statistic.

z = ?

(Round to two decimal places as needed)

c. P-value =

(Round to three decimal places as needed)

d. State the conclusion about the null hypothesis, as well as the final conclusion that addresses the origin claim.

? the null hypothesis. There is ? sufficient evidence to ? the claim that 0.78% of patients stop smoking when given sustained care.