Question

1. 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 test statistic that would be used to examine whether a difference exists in the proportion of in- and out-of-state drivers who received speeding tickets. Take all calculations to four (4) decimal places.

   	Received Ticket	Did Not Receive Ticket
   In State (Group 1)	66	242
   Out of State (Group 2)	124	272

Answer 1

Total number of sample 1 (n1) = 308
Total number of sample 2 (n2) = 396
number of favourable events (X1) = 66
number of favourable events (X2) = 124

We are interested in testing the hypothesis

Since, the test is two-tail test at \alpha = 0.05

Decision Rule: Reject the null hypothesis if the test statistic value is less than the critical value -1.96 or greater than the critical value 1.96.
The statistic value, -2.9309 is less than the critical value -1.96. Hence, reject the null hypothesis.

Test Statistic = -2.9309