Answer:
0.4740<p<0.5006
Step-by-step explanation:
-Given [tex]n=5409, \ x=2636 , \ CI=0.95[/tex]
#we calculate the proportion of trial quitters;
[tex]\hat p=\frac{2636}{5409}\\\\=0.4873[/tex]
For a confidence level of 95%:
[tex]z_{\alpha/2}=z_{0.025}\\\\=1.96[/tex]
The confidence interval is calculated as follows:
[tex]Interval= \hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\\\\\=0.4873\pm 1.96\times\sqrt{\frac{0.4873(1-0.4873)}{5409}}\\\\\\\\=0.4873\pm0.0133\\\\\\=[0.4740,0.5006][/tex]
Hence, the 95% confidence interval is 0.4740<p<0.5006
