Question

An insurance company checks police records on 360 automobile accidents selected at random and notes that seniors were driving in 54 of them. Create a 95% confidence interval for the proportion of auto accidents in the U.S. that involve senior drivers. Check conditions, show all calculations using the exact critical value, and write a proper statement of the confidence interval.

Answer 1

The conditions are:

n*p = 360*0.15 = 54 10

n*(1 - p) = 360*(1 - 0.15) = 306   10

The conditions are met.

p = 54/360 = 0.15

n = 360

z = 1.96

The 95% confidence interval will be:

= p ± z*(√p(1-p)/n)

= 0.15 ± 1.96*(√0.15(1-0.15)/360)

= (0.1131, 0.1869)