In this case study, you will analyze the developments in the number of automobiles entering Canada from the United States via the Fort Erie International Bridge for the years 1990 - 2009. After having gained the basic understanding of the data, you will focus in more detail on years 2000-2001. During the first part of 2000, there were fewer crossings than in the first part of 2001. However, the border crossings between September through December 2001 were less than the same time period in the previous year.
Your main goal in this case study is to determine why there was such a large difference in the number of crossings, particularly in the months of September through December. How were events in the early part of 2000 different from those in the early part of the year 2001? Was the price of gasoline high? Was the exchange rate moving?
The deadline for submission is 9.12.2009 before the start of the lecture. Later submissions will not be accepted.
For this exercise, open the file Border_crossings.wk1 and save it in Excel format. This file contains a number of monthly car border crossings from the U.S. in Fort Erie, Ontario. Using data from the file, calculate the actual and percent monthly change in border crossings (see Table 1). Then calculate the actual and percent monthly change for last four moths in a year by subtracting the monthly values at year t from the monthly values at year t+1 (see Table 2).
Table 1 Month-to-month changes in border crossings, year 2000
|Number of border crossings||Absolute change||Percentage change|
Table 2 Yearly changes in border crossings, example September.
|September||Number of border crossings||Absolute change||Percentage change|
Create a concise report on the developments in border crossings using the calculated data on changes. Employ summary measures you deem important (e.g., frequency tables, medians, etc.). These measures should be recorded transparently in tables and/or figures. Explain, why do you think the chosen summary measures are important.
Assume year-to-year changes in border-crossings in September (as in Table 2) follow a normal distribution with a mean 15000 and standard deviation 2000. Were there any changes that could be described as extreme from statistical perspective? Use your own criteria for ‘extreme’. Assume the statisticians made a mistake and the N(15000;2000) contains wrong information. Calculate the 95-percent confidence interval for the true population mean.
Use the data and verify whether there was a notable difference between the last four months of 2000 and the same period in 2001. In both years, which of these four months shows the biggest drop in border crossings by car?
Now return to the results from Task 3. The price of gasoline may be one possible explanation for the differences noted and verified in Task 3. To find out whether gas prices were higher in this time interval, use file Gas_prices.wk1, which contains gas prices in Canadian dollars for individual months. Could gas prices have influenced the lower number of cars entering Canada from the United States in the last four months of 2000? Choose appropriate measures and/or graphical illustrations to support your argument.
Using a file Exchange rates.csv, investigate whether the exchange rate for American to Canadian currency contributed to the lower number of cars entering Canada in the last four months of 2000.
Here is a brief outline what exactly I would expect in each task:
Think about the problem and try to answer the following questions:
1. What exactly wants me the task to do?
2. What is the information/data I have available?
3. Given this information/data, what tools can I use? Why these and not others? Are there any disadvantages of the tools I am considering?
4. Having though about the tools, what will be my final selection? How would the candidate tools combine together? How should I organize them to get a nice and clear report?
Ad Create a concise report – you should prepare a business-like report that contains key features of given data. There is not a single right answer or format for the answer. You have a wide range of tools you can use that we covered in class – frequency tables, different summary measures, graphical options. You should be able to show you can decide actively what tools to use, organize them in meaningful way and make them understandable to other audience. The report should not consist of a mere collection of means/plots/or whatever, but also of your commentary/explanations. Check for reports prepared e.g. by international institutions or central banks.
The task is I guess clear, this is a pure homework-like exercise.
Maybe a small remark to the sentence in the setup – “Assume the statisticians made a mistake and the N(15000;2000) contains wrong information.” By ‘Wrong information’ I mean either one or both parameters being wrong. It depends on you which option you choose, but note that your solution procedure should be consistent with your option taken.
Again, its up to you what measure you will choose to provide an answer. There might not be a single right measure but many. The key is the selected measure(s) has to be justified. The point is that in your career you will have to make many similar decisions, yet under a much tighter time pressure.
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