Historical Trends and Patterns in Temperatures around the World

Historical Trends and Patterns in Temperatures around the World
The file contains Annual Average Temperature records for two cities: New York, USA and Sydney, Australia. The Annual Average Temperature value for any year is a result of averaging daily high temperature readings from every day of that year observed in a specific location (Central Park for New York City and Observatory Hill for Sydney.)
We would like to use statistical methods to determine whether the data shows any significant patterns or trends in temperature over time.
In the SPSS data file, three variables are recorded: the Year (“year”), the Annual Average Temperature for New York City (“NYCtemp”) and the Annual Average Temperature for Sydney (“Sydtemp”.)The data are sorted by year in ascending order. (In the Excel file, NYC and Sydney data are placed into two separate worksheets. ) New York data goes back to 1869, while Sydney has records from 1859 to present. For your convenience, Sydney temperatures have been converted from Celsius to Fahrenheit.
Original sources of data (for reference only, TempRecs.sav is the only data file you need to use for the project) New York City: http://www.erh.noaa.gov/okx/climate/records/monthannualtemp.html Sydney:http://www.bom.gov.au/jsp/ncc/cdio/weatherData/av?p_nccObsCode=36&p_display_type=dataFile&p_startYear=&p_c=&p_stn_num=066062

Exercise 1
• Use a computer package to produce a scatter plot (or time series plot) of the temperatures for New York City using the “year” as the x-axis.
• Provide a paragraph describing what you see and whether any trend or pattern appears in your graph.
• Produce a similar plot for Sydney.
• In a paragraph, describe what you see for that city and describe any differences you observe between Sydney and New York City.
Exercise 2
• Use a statistical package to find the summary measurements: min, max, mean, median, standard deviation for New York City, using all of the historical temperature values provided.
• Draw a Box Plot for the data set. Identify the hottest year and the coldest year.
• Repeat this exercise for the historical temperature values in Sydney.
• Write a paragraph describing how the two cities differ in temperature. Hint: Base you answer on any notable differences you observe in the two Box Plots.

Exercise 3
• Use a statistical package to obtain a relative frequency (percent) histogram of the annual temperatures in New York City. Describe the “shape” of distribution.
• Repeat the process for Sydney, using the same class limits you had for New York City.
• In a paragraph, describe any similarities and differences you observe between the shapes of the two distributions and interpret the meaning of these differences.

Exercise 4-A
Limit your attention to the most “recent” temperature data, (which we define as years 1990-2013), for New York City. Answer the following questions:
• For how many years during the recent period, did the annual temperature rise above the historical mean calculated for the entire period? Does this represent a reasonable, relatively large or relatively small percentage of the recent years?
• Of the 25 warmest years in recorded history, what percentage occurs during the recent period? Do you think the recent period has more or less than its fair share of warmer years? (Hint: It may help to re-sort the data according to temperature).
• Is the mean temperature for the recent period higher or lower than that of the entire period? Calculate the z-score for the recent mean based on the mean and standard deviation for the entire period. What does the value of the z-score tell you about the difference between the two means?
• Extra Credit: Draw a Box Plot for the recent years and place it next to the Box Plot obtained from the data corresponding to the years prior to 1990. Are there any noteworthy differences between the two?
Exercise 4-B Repeat the process for the data associated with Sydney
Exercise 5-A
• Use a statistical package to find the value of the linear correlation coefficient between “year” and “NYCtemp”
• Is the correlation significant? Explain the reason for your answer
• If the correlation is significant, what does it imply about the trend in temperatures?
• Use technology( SPSS or Excel) to find the equation for the least squares regression (LSR) line
• Interpret the meaning of the slope of the LSR line.
• Based on the equation of LSR line, what is the “best predicted” value for the NYC Annual Average Temperature for 2013? How accurate is the prediction?
• Can we use this LSR line equation to predict the Annual Average Temperatures for the future? Explain.
• Write a paragraph to summarize your findings: Is there statistically significant evidence of any pattern or trend in temperature over the observation period in NYC?
Exercise 5-B Repeat the process for Sydney.

Exercise 6
For depositing in the assessment area of the ePortfolio. Please read the instructions carefully!)
Write a short (1-page) essay which includes the following:?• Using information from the internet and/or other reliable sources, define the terms “Global Warming” and “Global Climate Change”. Please cite your sources.?• Provide a couple of reasons that people believe Global Warming is occurring. What are some opinions to the contrary??• Based upon your analysis of the historical temperature data for New York City and Sydney, tell if you believe it is reasonable to conclude that Global Warming is occurring.
With your essay, include one graph or chart that you have created in this project that would best support your argument.