Statistical Inference and Hypothesis Testing: Applications in Real-World Scenarios
An applied study on statistical inference and hypothesis testing in practical settings.
Alexander Wilson
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Statistical Inference and Hypothesis Testing: Applications in Real-World Scenarios
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 Virginia
Department of Transportation (VDOT) conducted a comprehensive study of its newly adopted
program and published the results in a2012 study. In one portion of the study, VDOT 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
Fairfax County are given in the first columns in the Minitab file.
a. 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); p, or p1 – p2) and describe it in words.
Since the same intersections are observed before and after the installations of cameras, use paired t-
test for this situation. The parameter of interest is mD (the mean difference from a matched pairs
design
b. Depending on your answer to part (a), construct one or two probability plots and one or
two box-plots to visualize the distribution(s) of your sample data. If you construct two
probability plots and two box-plots, please construct two separate Minitab probability plots
and one Minitab box-plot displaying both boxes on the same graph. Also, properly title and
label your graphs. Copy and paste these graphs into your assignment. Below the graphs,
answer the following questions.
Since the difference between the number of crashes Before and after installations are considered, the
probability plot and the box plots for the differences are constructed and are shown as follows:
All points are close to straight line indicating the parent distribution of differences follows normality.
The box plot:
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 Virginia
Department of Transportation (VDOT) conducted a comprehensive study of its newly adopted
program and published the results in a2012 study. In one portion of the study, VDOT 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
Fairfax County are given in the first columns in the Minitab file.
a. 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); p, or p1 – p2) and describe it in words.
Since the same intersections are observed before and after the installations of cameras, use paired t-
test for this situation. The parameter of interest is mD (the mean difference from a matched pairs
design
b. Depending on your answer to part (a), construct one or two probability plots and one or
two box-plots to visualize the distribution(s) of your sample data. If you construct two
probability plots and two box-plots, please construct two separate Minitab probability plots
and one Minitab box-plot displaying both boxes on the same graph. Also, properly title and
label your graphs. Copy and paste these graphs into your assignment. Below the graphs,
answer the following questions.
Since the difference between the number of crashes Before and after installations are considered, the
probability plot and the box plots for the differences are constructed and are shown as follows:
All points are close to straight line indicating the parent distribution of differences follows normality.
The box plot:
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Subject
Statistics