Question

A survey of 400 non-fatal accidents showed that 109 involved the use of a cell phone. Construct a 99% confidence interval for the proportion of fatal accidents that involved the use of a cell phone

Answer 1

Answer:

(0.215,0.33)

Step-by-step explanation:

The 99% confidence interval can be calculated as

$p- z_{\frac{\alpha }{2} } \sqrt{\frac{pq}{n} }$

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

$z_{\frac{\alpha }{2} } =z_{\frac{\0.01 }{2} }=z_{0.005}=2.5758$

The 99% confidence interval  is

$0.2725-2.5758 \sqrt{\frac{0.2725(0.7275)}{400} }$

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).