Background: To prevent crashes caused by running red lights, many states are installing cameras at dangerous intersections. These cameras are used to take photographs of the license plates of vehicles that run a red light. The Virginia Department of Transportation (VDOT) obtained data on the number of crashes per year caused by running a red light at 13 intersections in Fairfax County, Virginia. Source: Virginia Transportation Research Council, "Research Report: The Impact of Red Light Cameras (Photo-Red Enforcement) on Crashes in Virginia", June 2007 Directions: Perform an appropriate significance test to determine whether or not the reduction in the number of crashes was statistically significant. 1. Click on the Data button below to display the data. Copy the data into a statistical software package and click the Data button a second time to hide it. Data Before 3.5 0.47 0.39 4.55 2.6 2.39 RED LIGHT PHOTO ENFORCED After 1.46 0.1 0 1.69 2.04 3.14 2.5 2.62 0.83 0.14 3.25 1.57 3.41 0.53 0.78 0.18 1.45 1.09 7.55 4.92 2. Use the statistical software package to compute a numerical summary of the weight differences (difference - Before - After). 3. Perform the significance test. a. State the null and alternative hypothesis. Note: is defined as (average number of crashes before the cameras were installed) - (average number of crashes after the cameras were installed). Ho: Pd=0 H₂: Hd>0 Ho: p=0 Ha: Hd0 ⒸH₂: d=0 Ha: 4 <0 0 Ho: H₂: d=0 b. Compute the test statistic. Round your answer to 4 decimal places. c. Compute the p-value. Round your answer to 4 decimal places. d. Interpret the results of the test. The p-value provides little evidence against the null hypothesis. The reduction in the number of crashes caused by running red lights is not statistically significant. ●The p-value provides strong evidence against the null hypothesis. The reduction in the number of crashes caused by running red lights is statistically significant.
Background: To prevent crashes caused by running red lights, many states are installing cameras at dangerous intersections. These cameras are used to take photographs of the license plates of vehicles that run a red light. The Virginia Department of Transportation (VDOT) obtained data on the number of crashes per year caused by running a red light at 13 intersections in Fairfax County, Virginia. Source: Virginia Transportation Research Council, "Research Report: The Impact of Red Light Cameras (Photo-Red Enforcement) on Crashes in Virginia", June 2007 Directions: Perform an appropriate significance test to determine whether or not the reduction in the number of crashes was statistically significant. 1. Click on the Data button below to display the data. Copy the data into a statistical software package and click the Data button a second time to hide it. Data Before 3.5 0.47 0.39 4.55 2.6 2.39 RED LIGHT PHOTO ENFORCED After 1.46 0.1 0 1.69 2.04 3.14 2.5 2.62 0.83 0.14 3.25 1.57 3.41 0.53 0.78 0.18 1.45 1.09 7.55 4.92 2. Use the statistical software package to compute a numerical summary of the weight differences (difference - Before - After). 3. Perform the significance test. a. State the null and alternative hypothesis. Note: is defined as (average number of crashes before the cameras were installed) - (average number of crashes after the cameras were installed). Ho: Pd=0 H₂: Hd>0 Ho: p=0 Ha: Hd0 ⒸH₂: d=0 Ha: 4 <0 0 Ho: H₂: d=0 b. Compute the test statistic. Round your answer to 4 decimal places. c. Compute the p-value. Round your answer to 4 decimal places. d. Interpret the results of the test. The p-value provides little evidence against the null hypothesis. The reduction in the number of crashes caused by running red lights is not statistically significant. ●The p-value provides strong evidence against the null hypothesis. The reduction in the number of crashes caused by running red lights is statistically significant.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Background: To prevent crashes caused by running red lights, many states are installing cameras at
dangerous intersections. These cameras are used to take photographs of the license plates of vehicles that
run a red light. The Virginia Department of Transportation (VDOT) obtained data on the number of crashes
per year caused by running a red light at 13 intersections in Fairfax County, Virginia.
Source: Virginia Transportation Research Council, "Research Report: The Impact of Red Light Cameras
(Photo-Red Enforcement) on Crashes in Virginia", June 2007
Directions: Perform an appropriate significance test to determine whether or not the reduction in the
number of crashes was statistically significant.
RED
LIGHT
PHOTO
ENFORCED
1. Click on the Data button below to display the data. Copy the data into a statistical software package
and click the Data button a second time to hide it.
Data
Before After
3.5
1.46
0.47
0.1
0.39
0
4.55 1.69
2.6 2.04
2.39
3.14
2.5
2.62
0.83
0.14
3.25
1.57
3.41
0.53
0.78 0.18
1.45
7.55
1.09
4.92
2. Use the statistical software package to compute a numerical summary of the weight differences
(difference Before After).
3. Perform the significance test.
a. State the null and alternative hypothesis. Note: d is defined as (average number of crashes
before the cameras were installed) - (average number of crashes after the cameras were
installed).
ⒸHo: Hd = 0
Ha: Hd > 0
Ho: Hd = 0
Ha: Hd #0
Ho: d=0
Ha: d < 0
Ο Ho: μα / 0
Ha Hd=0
b. Compute the test statistic. Round your answer to 4 decimal places.
c. Compute the p-value. Round your answer to 4 decimal places.
d. Interpret the results of the test.
O The p-value provides little evidence against the null hypothesis. The reduction in the
number of crashes caused by running red lights is not statistically significant.
The p-value provides strong evidence against the null hypothesis. The reduction in the
number of crashes caused by running red lights is statistically significant.
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