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Statistical Inference and Hypothesis Testing: Applications in Real-World Scenarios

An applied study on statistical inference and hypothesis testing in practical settings.

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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; m D (the mean difference from a matched pairs design);m 1 - m 2 (the mean difference from independent samples); p, or p 1 – p 2 ) 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 m D (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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    The box - plot of the difference seem to be approximately normal. i. Are there any major deviations from normality? There are no major deviations from normality as all points are close to straight line in probability plot and the box - plot is approximately symmetric. ii. Are there any outliers present? No, no outliers are observed. iii. Is it appropriate to conduct statistical inference procedures, why or why not? Yes, it is appropriate to conduct the statistical inference procedures as normality assumption is satisfied. c. 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. : 0 H T he installation of the cameras not decreased the mean number of crashes at these particular intersections , 0 d m £ : 1 H T he installation of the cameras decreased the mean number of crashes at these particular intersections , 0 d m > Note: Here d = before – after ii. State the significance level for this problem. The significance level is 0.01. If the P - value is less than the significance level reject the null hypothesis

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    iii. Calculate the test statistic (subtract after – before) The MINITAB output for the paired t - test is as follows: From the output, the test statistic value =3.45 iv. Calculate the P - value and include the probability notation statement. The P - value ( ) ( ) , . . . 13 13 2 0 01 3 45 0 002 From output P t + - = > = v. State whether you reject or do not reject the null hypothesis. Since the P - value is less than the significance level, reject the null hypothesis. vi. State your conclusion in context of the problem(i.e. interpret your results). There is sufficient evidence to support the claim that installation of the cameras decreased the mean number of crashes at these particular intersections d. For the above situation, construct a 96.2% confidence interval for the above data. Interpret the confidence interval as we learned in class. The 96.2% of the confidence interval is shown in the following output. From the output, the 96.2% CI for the mean difference = (0.36, 1.86) . 1 11 d d s x t n a / 2 ± ´ = ±

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