Question

In a trial of 144 patients who received 10-mg doses of a drug daily, 36 reported a headache as a side effect. Use the information above to answer the following questions (a) Verify that the requirements for constructing a confidence interval about p are satisfied. Are the requirements for constructing a confidence interval about p satisfied? Yes No (b) Construct a 99% confidence interval for the population proportion of drug users who will report a headache as a side effect. (Use ascending order. Round to three decimal places as needed.)

ch 14, q 4

Hi! the second example shows the entire qestion to the first problem, please answer the first question with those steps. :-)

Answer 1

Q.1) Given that, n = 144 and x = 36

sample proportion $(\hat p)$ = x/n = 36/144 = 0.25

A 99% confidence level has significance level $(\alpha)$ = 0.01 and critical value is, $Z_{\alpha/2} = 2.575$

99% confidence interval for population proportion ( p ) is,

$\hat p \pm Z_{\alpha/2} * \sqrt { \frac {\hat p *(1-\hat p)}{n}}$

$0.25 \pm 2.575* \sqrt { \frac {0.25 *(1-0.25)}{ 144}}$

$0.25 \pm 0.093$

$0.25 - 0.093 < p < 0.25 &plus; 0.093$

$0.157 < p < 0.343$

Therefore, the 99% confidence intetval for the population proportion of drug users who will report a headaches as a side effect is, ( 0.157, 0.343 )

Interpretation: we are 99% confident that the interval actually does contain the true value of p.