Question

in a program designed to help patients stop smoking, 186 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.
$z = 0.62$
(round to two decimal places as needed)
identify the p - value.
$p - value=square$
(round to three decimal places as needed)

Explanation:

Step1: Determine the nature of the test

Since \(H_1:p
eq0.81\), this is a two - tailed test.

Step2: Calculate the P - value

For a two - tailed \(z\) - test, the \(P\) - value is \(2\times(1 - \Phi(|z|))\), where \(\Phi(z)\) is the cumulative distribution function of the standard normal distribution. Given \(z = 0.62\), we know that \(\Phi(0.62)\) can be found from the standard normal table (or using a calculator with a normalcdf function). \(\Phi(0.62)=0.7324\). Then \(P - value=2\times(1 - 0.7324)\).

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Answer:

\(0.535\)