Homework Sourse1To combat redlightrunning crashes many states are installin
1.)To combat red-light-running crashes, many states are installing red light cameras at dangerous intersections. These cameras photograph the license plates of vehicles that run red lights and automatically issue tickets. How effective are these photo enforcement programs? The Michigan Department of Transportation (MDOT) conducted a comprehensive study of its newly adopted program and published the results in a 2012 study. In one portion of the study, MDOT provided crash data both before and after installation of the 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 Ann Arbor County are below.
What is (are) the parameter(s) we are conducting inference on? Choose one of the following symbols [m; mD (the mean difference from a matched pairs design); m1 - m2 (the mean difference from independent samples)] and describe it in words.
Construct and properly interpret a 95% confidence interval on the parameter of interest.
At the 0.01 significance level, test the claim that the installation of the cameras decreased the mean number of crashes at these particular intersections.
i.State the null and alternative hypotheses.
ii.State the significance level for this problem.
iii.Calculate the test statistic (subtract after – before)
iv.Calculate the P-value and include the probability notation statement.
v.State whether you reject or do not reject the null hypothesis.
vi.State your conclusion in context of the problem (i.e. interpret your results).
| Intersection | Before Camera | After Camera |
| 1 | 3.6 | 1.87 |
| 2 | 0.27 | 0 |
| 3 | 0.29 | 0 |
| 4 | 4.55 | 1.79 |
| 5 | 3.09 | 2.04 |
| 6 | 2.29 | 3.14 |
| 7 | 2.4 | 2.72 |
| 8 | 1.09 | 0.24 |
| 9 | 3.15 | 1.57 |
| 10 | 3.21 | 0.43 |
| 11 | 1.88 | 0.28 |
| 12 | 1.35 | 1.09 |
| 13 | 7.35 | 4.92 |
Solution
This is a paired test one tailed at 0.01 significance level
H0: mu1 =mu2
Ha: mu1>mu2
Right tailed test.
Mean difference = -1.11
S2 = SSdf = 16.16(13-1) = 1.35
S2M = S2N = 1.3513 = 0.10
SM = S2M = 0.10 = 0.32
T-value Calculation
t = (M - )SM = (-1.11 - 0)0.32 = -3.45
t is -3.449050. The value of p is 0.002407. The result is significant at p 0.01.
Conclusion: Reject null hypothesis.
After camera no of crashes reduced significantly.
