Question

To combat red light running crashes many states have installed red light cameras at dangerous intersections to photograph the license plates of vehicles that run the red light. How effective are photo-red enforcement programs in reducing red-light-running crash incidents at intersections? A state's department of transportation conducted a comprehensive study of its photo-red enforcement program. In one portion of the study, the department provided crash data both before and after installation of red light cameras at several intersections. The data (measured as the number of crashes caused by red-light-running per intersection per year) for 13 intersections in a specific county, are given in the accompanying table. Analyze the data for the department. What do you conclude? Click the icon to view the data table. Lety be the mean number of crashes caused by red light running per intersection per year before cameras were installed, 2 be the mean number of crashes caused by red light running per intersection per year after cameras were installed, and Ma1 "H2 Identify the appropriate null and alternative hypotheses. Ho Hoy Ha Ha Find the test statistic The test statistic is (Round to two decimal places as needed.) State your conclusion Ho at a = 0.05. There is evidence to show that cameras at traffic stops produce a significant caused by red light running per intersection per year. in the mean number of crashes

Answer 1

This is a paired sample t-test

Sample 1 Sample 2 Difference = Sample 1 - Sample 2 3.6 1.36 2.24 0.27 0.27 0.33 0.33 4.56 1.78 2.78 2.59 2.04 0.55 2.29 3.14 -0.85 2.4 2.72 -0.32 0.73 0.26 0.47 3.14 1.57 1.57 3.2 0.43 2.77 0.91 0.29 0.62 1.35 1.07 0.28 7.34 4.9 2.44 Average 2.516 1.505 1.012 St. Dev. 1.969 1.442 1.209 13 13

The following null hypothesis is under test

The following null and alternative hypotheses need to be tested: Ho: up = 0 Ha: pp < 0 This corresponds to a left-tailed test, for which a t-test for two paired samples be used.

The test statistic is

The t-statistic is computed as shown in the following formula: D sp/n 1.012 1.209/13 = 3.018

in two decimal places, the answer is t = 3.02

Based on the information provided, the significance level is a = 0.05, and the degrees of freedom are df = 12. Hence, it is found that the critical value for this left-tailed test is te = -1.782, for a = 0.05 and df = 12. The rejection region for this left-tailed test is R = {t: t < -1.782).

Since it is observed that t = 3.018 > te= -1.782, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p=0.9946, and since p=0.9946 > 0.05, it is concluded that the null hypothesis is not rejected.

Fail to reject H0 at $\alpha =0.05$. There is no evidence to show that cameras at traffic stops produce a significant low in the number of crashes caused by red light running per intersection per year.