Better Traffic Flow - exercises 4, 5, and 6

1.The datasetTrafficFlowgives 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. Since this is a matched pairs experiment, the variableDifferencerepresents the time savings from the flexible system (Fixed - Flexible) for each run of the simulation.(You do NOT need to use the actual dataset to answer this problem.)

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 and a brief written description.

b.Answer these questions to establish the process of generating one bootstrap sample:

i.What sample size would you use for your bootstrap sample?____

ii.Would you sample with or without replacement?

iii.What statistic would you record for this one bootstrap sample? Use both a wordand

correct notation:___________________

c.UseStatKeyto construct a bootstrap distribution for the mean time savings, using a few thousand samples.After you have done all parts of this problem, include a screen shot of the graph for this bootstrap distribution with your assignment.

i.How many samples did you use? __________

ii.What is the standard error for this bootsrap distribution? ________

d.Use the standard error of the bootstrap distribution to find a 95% confidence interval for the mean time savings from using the flexible system.

Confidence interval:______________________

e.(Sec. 3.2)Interpret the confidence interval.

f.(Sec. 3.4)Using that same bootstrap distribution, have StatKey use the percentile method to form a 95% confidence interval.

Give the confidence interval here:___________________

g.Does the interval from the 2*SE method come very close to matching the interval from the percentile method?Circle one:YesNo

h.Why do you suppose the interval from the 2*SE method does not come very close to matching the interval from the percentile method?That is, what feature of this bootstrap distribution is most relevant to that?

i.If the interval from the 2*SE method does not closely match the interval from the percentile method, which method is it better to use to form a confidence interval for the population parameter?

Circle one:2*SE methodofPercentile method