The records for automotive accidents for a given year in a s

The records for automotive accidents for a given year in a specific road section were classified for the amount of money in damages caused (under $2,000 or $2,000 or more), and if there were physical injuries to passengers involved. The results summarize as follows:

                                                      Under $2,000                                  $2,000 or more
# of accidents                                       34                                                     45
# of accidents with injured pass.          13                                                      25

a. Make an estimate of the true proportion of accidents in which people result injured when the damages are $2,000 or more, and find the margin of error for said estimate.

b. Obtain an estimate of the difference between the proportion of accidents in which people result injured when the damages are under $2,000 and those in which the damages are $2,000 or more.

Solution

a) estimate of the true proportion of accidents in which people result injured when the damages are $2,000 or more is

no. of accidents with injured passengers with damages are $2,000 or more/total no. of accidents with damages are $2,000 or more=25/45 [answer]

b) estimate of the true proportion of accidents in which people result injured when the damages are under $2,000 is
no. of accidents with injured passengers with damages are under $2,000/total no. of accidents with damages are under $2,000=13/34 [answer]

so estimate of the difference is 13/34-25/45=-0.1732 [answer]