Exercise 2.144 on page 102 introduces the dataset Traffic Flow, which gives delay time in seconds for 24 simulation runs in Dresden, Germany, comparing the current timed traffic light system on each run to a proposed flexible traffic light system in which lights communicate traffic flow information to neighboring lights. On average, public transportation was delayed 105 seconds under the timed system and 44 seconds under the flexible system. Since this is a matched pairs experiment, we are interested in the difference in times between the two methods for each of the 24 simulations. For the n = 24 differences D, we saw in Exercise 2.144 that x̅_D = 61 seconds with s_D = 15.19 seconds. We wish to estimate the average time savings for public transportation on this stretch of road if the city of Dresden moves to the new system.
(a) What parameter are we estimating? Give correct notation.
(b) Suppose that we write the 24 differences on 24 slips of paper. Describe how to physically use the paper slips to create a bootstrap sample.
(c) What statistic do we record for this one bootstrap sample?

(d) If we create a bootstrap distribution using many of these bootstrap statistics, what shape do we expect it to have and where do we expect it to be centered?
(e) How can we use the values in the bootstrap distribution to find the standard error?
(f) The standard error is 3.1 for one set of 10,000 bootstrap samples. Find and interpret a 95% confidence interval for the average time savings.

Exercise 2.144

Have you ever driven along a street where it seems that every traffic light is red when you get there? Some engineers in Dresden, Germany, are looking at ways to improve traffic flow by enabling traffic lights to communicate information about traffic flow with nearby traffic lights. The data in TrafficFlow show results of one experiment that simulated buses moving along a street and recorded the delay time (in seconds) for both a fixed time and a flexible system of lights. The simulation was repeated under both conditions for a total of 24 trials.