Question

in a program designed to help patients stop smoking, 100 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
$h_0:p = 0.81$
$h_1:p
eq 0.81$
(type integers or decimals. do not round)
identify the test statistic.
$z = 0.82$
(round to two decimal places as needed)
identify the p - value.
$p - value = 0.535$
(round to three decimal places as needed)
state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.
\\( \
abla \\) the null hypothesis. there \\( \
abla \\) sufficient evidence to \\( \
abla \\) the claim that 81% of patients stop smoking when given sustained care

Explanation:

Step1: Determine the decision rule

Since the significance level \(\alpha = 0.05\), and for a two - tailed test (because \(H_1:p
eq0.81\)), we compare the P - value with \(\alpha\).

Step2: Compare P - value and \(\alpha\)

The P - value \(P = 0.535\) and \(\alpha=0.05\). Since \(P> \alpha\) (i.e., \(0.535>0.05\))

Step3: Make a decision about the null hypothesis

When \(P> \alpha\), we fail to reject the null hypothesis \(H_0\).

Step4: State the final conclusion

Since we fail to reject \(H_0\), there is not sufficient evidence to reject the claim that \(81\%\) of patients stop smoking when given sustained care.

Answer:

Fail to reject the null hypothesis. There is not sufficient evidence to reject the claim that \(81\%\) of patients stop smoking when given sustained care.