Question

In a clinical trial of a certain​ drug, 17 subjects experience headaches among the 221 subjects treated with the drug. Construct a ​95% ​(Wald) confidence interval estimate for the proportion of treated subjects who experience​ headaches.

a. Find the best point estimate of the population proportion.
b. Identify the value of the margin of error E.
c. Construct the confidence interval.
d. write a statement that correctly interprets the confidence interval.

Answer 1

Solution :

Given :

n = 221

x = 17

a). $p=\frac{17}{221}$

       = 0.076

b). At the 95 confidence interval

   Value of z = 1.96

  Margin of error

    $=1.96 \times \sqrt{\frac{p(1-p)}{n}}$

    $=1.96 \times \sqrt{\frac{0.076(1-0.076)}{221}}$

   $=1.96 \times \sqrt{\frac{0.076\times 0.924 }{221}}$

   = 1.96 x 0.017

   = 0.03332

c). confidence interval

   = ( 0.076-0.033,  0.076+0.033)

   = ( 0.043, 0.109 )

d). The confidence interval does not contain null value, so it is significant.