Transportation engineers determined that to help ease traffic, they would set up tolls for solo drivers during rush hour times on Route I-66 inside the Capital Beltway (I-495). Carpooling drivers with the proper Ezpass would drive free. The toll program began in December 4, 2017. To test the claim that fewer vehicles would use Route I-66 after the program began, a count of the number of vehicles were collected from two random samples. Both samples were taken on the first Monday of each month for an entire year before and after the toll program was implemented. The data set is called "Number of Vehicles 2" and we will use = 0.05 in this investigation. a) Calculate the difference between the number of vehicles for the first Monday of each month using (go to Data Compute Expression). Please subtract (2018 - 2017). List the difference for each of the pairs in one column in your solutions document. b) Obtain the sample mean of these differences and the sample standard deviation of these differences using StatCrunch. Copy the table that you obtain from StatCrunch into your solutions document and round the values for the sample mean and sample standard deviation to two decimal places. c) Define the population parameter in context in one sentence. d) State the null and alternative hypotheses using correct notation. e) display a frequency histogram overlaid with a Normal curve of the sample differences and display a horizontal boxplot of the sample differences. Title and label each graph appropriately and copy these graphs into your solutions. f) Provide a one-sentence comment about these graphs that allow us to continue conducting inference using the t-distribution in this problem. g) No matter your answer to part (f), calculate the test statistic "by hand" and be sure to show your work (please show work). Use the rounded values you obtained in part (b). Round the test statistic to three decimal places. h) State the degrees of freedom for this test and show how you calculated the degrees of freedom. i) Calculate the p-value using the T-calculator in StatCrunch (Stat Calculators T). Present the T-Calculator image in your solutions document. j) Use StatCrunch Stat T Stats Paired and enter "2018" for Sample 1 and "2017" for Sample 2 to verify your test statistic from part (g) and your p-value in part (i). Copy the output into your solutions document.4 k) State your decision whether you reject or do not reject the null hypothesis and the reason for your decision in one sentence. l) State your conclusion in context of the problem in one or two complete sentences. m) Compare the standard error from the StatCrunch output in part (j) to the standard error obtained in part (h) of Investigation 1. How did the different study designs affect the outcome of each hypothesis test? Answer these in two or three sentences.

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