A criminal justice researcher is interested in determining if out-of-state motorists tend to speed more ...

A criminal justice researcher is interested in determining if out-of-state motorists tend to speed more frequently than in-state motorists. After taking a sample of traffic stop data, she recorded whether the vehicle was registered in the state or not and whether or not the driver received a speeding ticket. The data are given in the table below. Calculate the lower bound of a 90% confidence interval for the difference in the proportion of in- and out-of-state drivers who received speeding tickets. Take all calculations to three decimal places.

                            Received Ticket Did Not Receive Ticket

In State                        51                               274

Out of State                111                                289