COURSE OBJECTIVES

Upon successful completion of this course, the student will be able to: 1. Summarize methods for organizing, displaying, and interpreting data 2. Discuss counting methods and finding probabilities 3. Outline the functions of different probability distributions 4. Examine normal and exponential continuous probability distributions 5. Evaluate sampling distributions and populations

BACKGROUND INFORMATION

Climate change is a complex and highly charged issue. Evidence for change includes sea level rise, warming oceans, shrinking ice sheets, declining arctic sea ice, glacial retreat, extreme temperature events, ocean acidification, and global temperature rise.

Regarding the latter issue, major global surface temperature reconstructions show that Earth has warmed since 1880. Most of this warming has occurred since the 1970s, with the 20 warmest years having occurred since 1981 and with all 10 of the warmest years occurring in the past 12 years. Although the 2000s witnessed a solar output decline resulting in an unusually deep solar minimum in 2007-2009, surface temperatures continue to increase.

For this project, you will use weather data from Weather Underground, a weather data site created by a student/professor team at the University of Michigan, to examine whether there is evidence of temperature rise in Fresno, California over the last century.

PROJECT INSTRUCTIONS

Your project will consist of two parts: a series of calculations and a summary of your findings. After completing the calculations listed below, you will answer the questions given and describe your conclusions in a paper of a suggested length of 4-6 pages. Your paper must be formatted according to APA style guidelines.

Part I: Calculating Temperature Change

In this portion of the project, you will use the data given in the table below to compute and interpret descriptive statistics and make inferences. Review the table, then begin your calculations and think about the questions posed. Once you have finished, you will write about your findings and answer the questions in Part II.

Final Project Statistics

Average Annual Temperature in Fresno, CA

First Decade 20th Century

Average Temp (°F)

Last Decade 20th Century

Average Temp (°F)

First Decade 21st Century

Average Temp (°F)

Second Decade 21st Century

Average Temp (°F) 1900 62.3 1990 63.2 2000 64.2 2010 64.1 1901 63.0 1991 63.8 2001 65.1 2011 64.0 1902 61.8 1992 65.1 2002 64.5 2012 67.0 1903 61.8 1993 63.7 2003 65.4 2013 67.0 1904 63.2 1994 63.3 2004 64.7 1905 62.5 1995 64.5 2005 65.1 1906 62.7 1996 65.2 2006 64.5 1907 61.2 1997 64.8 2007 64.6 1908 61.3 1998 62.3 2008 65.1 1909 61.2 1999 63.3 2009 65.0

Source: Weather Underground (www.wunderground.com)

1. Compute the mean, median, mode, range, and standard deviation for each of the three full decades of data for Fresno, CA provided in the table above. Be sure to show the steps you took to calculate each.

2. Compute the mean and standard deviation for the years 2010 through 2013. Again, show the steps you took to calculate each.

3. Based on your analysis of the descriptive statistics you prepared, answer the following:

a. Do you believe there is evidence to suggest that there has been a gradual warming trend over the last 100 years? Please be sure to explain your answer with details from your descriptive statistics.

b. Compare the 100-year warming trend over the first and last decades of the twentieth century to the 20-year trend from the last decade of the twentieth century (19901999) to the following decade (2000-2009).

Is there evidence that the warming trend is speeding up? Again, please be sure to explain your answer with details from the data.

Final Project Statistics

4. Regardless of the conclusion you reached in question 3, what type of analysis do you believe would be required to conclude there was actually a climate effect driving a temperature change? Why? Are there any additional explanatory variables that could impact the data? [Hint: think about the number of locations (such as cities) you might require data from and the period of time you would want to observe these locations.]

5. For three of the given decades, we have a complete set of data (there are no missing years), so our data are considered actual results. However, the data for the second decade of the twenty-first century is incomplete with only four years in the sample.

You will now use this sample to test a hypothesis that the mean (μ) of the second decade (2010-2019) will be warmer than that of the first decade (2000-2009). Specifically, you will test the hypothesis that μ > 66 °F.

Test the hypothesis at the 95% confidence level (.05 level of significance) and explain your conclusion. Does your conclusion change if you increase the confidence level to 99%?

Part II: Presenting Your Information

In this portion of the project, you will draw conclusions from the data and present your results in the form of a short research paper (suggested length 4-6 pages). Remember to format your paper according to APA style guidelines.

1. To begin, write an introduction that outlines the hypothesis you hope to prove and how you will perform the test. The introduction should provide enough information for the reader to understand what statistical test you will be using. You should also explain the proper sequence of steps involved in performing the test.

2. Present the results of questions 1 and 2 from Part I in tabular form by completing the table below and inserting it in your report. You can download a Word document version of the table from the Project page of your course. Also include on a separate page the steps you took to calculate each figure in the table.

Final Project Statistics

First Decade 20th Century

Last Decade 20th Century

First Decade 21st Century

Second Decade 21st Century Mean Standard Dev Median Mode Range

3. Answer the questions posed in Part I, question 3 based on the descriptive statistics you prepared, then provide your answer to Part I, question 4. Be sure to explain your answers.

4. On a separate page (or pages), answer question 5 from Part I and draw your conclusions regarding the tests you have performed. Be sure to show all of the steps in your hypothesis test by addressing the points below:

a. State the research question or claim and translate it into a hypothesis statement (clearly specify the null and alternative hypothesis as the claim); be sure to carefully determine whether your test is one-sided or two-sided and state the hypotheses accordingly [hint: keep in mind that the hypothesis you want to test is stated as the alternative].

b. Use the level of significance (confidence level) to determine the critical values and calculate the size of the rejection region (the region rejecting Hₒ). Include the steps you took to calculate this figure.

c. Compute the test statistic and its corresponding p-value (probability). Again, include the steps you took to calculate this figure.

d. State your conclusion (Reject or Fail to Reject) based on the computed statistic. Does the data support or refute your claim?

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