Question

A survey of 400 non-fatal accidents showed that 181 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

Solution :

Given that,

n = 400

x = 181

Point estimate = sample proportion = = x / n = 181/400=0.453

1 -   = 1-0.453 =0.547

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576 ( Using z table )

  Margin of error = E = Z / 2    * (((( * (1 - )) / n)

= 2.576* (((0.453*0.547) / 400)

E = 0.064

A 99% confidence interval is,

- E < p < + E

0.453-0.064 < p < 0.453+0.064

0.389< p < 0.517