Respuesta :
Answer:
(0.215,0.33)
Step-by-step explanation:
The 99% confidence interval can be calculated as
[tex]p- z_{\frac{\alpha }{2} } \sqrt{\frac{pq}{n} } <P<p+z_{\frac{\alpha }{2} } \sqrt{\frac{pq}{n} }[/tex]
Where p is the estimated sample proportion that can be calculated as
p=x/n
where x=109 and n=400
p=109/400=0.2725
q=1-p=1-0.273=0.7275
[tex]z_{\frac{\alpha }{2} } =z_{\frac{\0.01 }{2} }=z_{0.005}=2.5758[/tex]
The 99% confidence interval is
[tex]0.2725-2.5758 \sqrt{\frac{0.2725(0.7275)}{400} } <P<0.2725+2.5758 \sqrt{\frac{0.2725(0.7275)}{400} }[/tex]
0.2725-2.5758(0.022262 )< P < 0.2725+2.5758(0.022262)
02725-0.057343 < P < 0.2725+0.057343
0.215157 < P < 0.329843
Rounding the obtained answer to three decimal places
0.215 < P < 0.33
Thus, the 99% confidence interval for the proportion of fatal accidents that involved the use of a cell phone is (0.215,0.33).
We are 99% confident that population the proportion of fatal accidents that involved the use of a cell phone will lie in this interval (0.215,0.33).
