Question

in a program designed to help patients stop smoking, 190 patients were given sustained care, and 82.8% of them were no longer smoking after one month. use a 0.05 significance level to test the claim that 81% of patients stop smoking when given sustained care. use the p - value method. use the normal distribution as an approximation to the binomial distribution
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.
$h_0:p$
$h_1:p$
(type integers or decimals. do not round.)

Explanation:

Step1: Identify the claim

The claim is that \(81\%\) of patients stop smoking when given sustained care. So, \(p = 0.81\).

Step2: Set up the null hypothesis

The null hypothesis \(H_{0}\) is a statement of equality. So, \(H_{0}:p = 0.81\).

Step3: Set up the alternative hypothesis

Since there is no indication of a one - sided (left - tailed or right - tailed) claim other than testing the proportion, and typically in such cases (if not specified otherwise) we assume a two - tailed test. But if we consider the general hypothesis testing for a proportion claim, the alternative hypothesis \(H_{1}\) is \(H_{1}:p
eq0.81\)

Answer:

\(H_{0}:p = 0.81\)
\(H_{1}:p
eq0.81\)