I have provided the pdf with the description for the project
MATH 1700 PROJECT INSTRUCTIONS You will be working on your first full statistical report, making use of the material you learned in class. This project will guide you through some questions and you’ll be using these questions in your report. DUE DATE: THURSDAY, DECEMBER 5, 2019 §1. Overview and Dataset Public universities are required to disclose their salary data, as public university em- ployees are considered state employees. This data can be found online at the following website: http://content.greenbaypressgazette.com/greenbay/database/2019/ UW1718sal-actual/#!/gross18.desc.1/ from theGreen Bay PressGazette. You have been given a subset of this data. You will be examining four departments (Mathematics, Physics, Psychology, and Visual Arts) at two UW campuses: Milwaukee and Madison. The titles we’re focusing on are various levels of professor (adjunct, associate, full, as- sistant, and emeritus) as well as the administrative title Chancellor for each of the two universities. The names of the employees have been removed. In the Excel spreadsheet, the columns are labeled with the title, campus, gross pay, base pay, overtime pay, overload pay, other pay, and department. The dataset consists of 430 employees. We are reprising the role of the Green Bay Press Gazette’s journalists and looking to analyze this data for a story on college faculty and administrative compensation. §2. Report instructions You will be required to turn in a report, typed in your word processor or typesetting language of choice. The report structure will follow the section template that will be given below when questions are given. Maintain this order. Other font/styling choices are yours to make. Handwritten reports will not be accepted. Please ensure the work is neat and easy to read. All charts should be clearly labeled with titles and axes. Show your summary statistics clearly. §3. Grading The grade will be out of 100 points, and broken down as follows: Section Points Exploratory Analysis 45 Statistical Analysis 35 Conclusion 20 Points will be removed for conclusions without justification, or numbers given with- out context. (e.g. if a confidence interval is being given, give the distribution you used, Date: 14 Nov 2019. 1 http://content.greenbaypressgazette.com/greenbay/database/2019/UW1718sal-actual/#!/gross18.desc.1/ http://content.greenbaypressgazette.com/greenbay/database/2019/UW1718sal-actual/#!/gross18.desc.1/ Math 1700 Project Instructions the confidence level, and what the confidence interval actually means). You should imag- ine you’re handing this to a boss at your place of employment, and that it will be read widely across your company or division. §4. The Report In this section, the questions to be answered will be laid out. Please write in complete sentences. This is a report, not an exam. 4.1. Exploratory Analysis. Here, you will explore the data in different ways, and its distributions. (a) Choose an appropriate graphical method to display the gross pay by university and by department. E.G. show me the distribution of gross pay for the UW Milwaukee physics department, and a separate one for the UW Madison physics department, etc. Comment on these graphs, including any potential issues with this graphical method of analysis. (b) Give numerical summaries of the gross pay by department and university, by title and university, by title and department and university. Comment on any seemingly significant differences you see. (c) Create a histogram of the UW Milwaukee full professor salaries (across all depart- ments), and another of the UW Madison full professor salaries. Comment on these distributions. Are they symmetric? Skewed? Visually comment on differences in mean salaries between the two universities. (d) Create a table that counts the number of professor levels for the mathematics depart- ments in each of the two universities. e.g. How many UW Milwaukee mathematics professors are associate professors, etc? (e) Create a bar chart of professor levels in the mathematics departments of the two universities. Note observations. 4.2. Statistical Analysis. In this section, we’re going to answer some statistical ques- tions. (a) We would like to estimate the mean full professor salary for the entire UW Mil- waukee campus. Since we only have 4 departments listed, we don’t know the true mean. Construct a 95% confidence interval for the mean full professor salary using the normal distribution and the t− distribution. Are these two confidence intervals close? (b) Repeat the same exercise for the titles Assistant Professor, Associate Professor for UW Milwaukee. (c) Repeat (a) and (b) for the UW Madison campus. (d) Repeat (a) and (b) for the Psychology departments of both campuses. (e) Repeat (a) and (b) for the Physics departments of both campuses. (f) Are the gross pays significantly different at the full professor level between the two campuses? Justify this. (g) What about the other professor levels? (h) Is there evidence to suggest the mean pay between the mathematics and physics de- partments within theUWMilwaukee campus are significantly different? What about physics and psychology atUWMilwaukee? All of this should be justified clearly with a statistical test. (i) Now we’ll investigate the chancellor salaries. Is there a significant difference in the mean salaries of chancellor (all levels) between the two universities? Justify this. 2 Math 1700 Project Instructions ( j) Compare the admin salaries to the faculty salaries within each university. What con- clusions can you draw? Would you need more information to make a better compar- ison? Explain. (k) Is there evidence to suggest the physical science faculty salaries (math and physics) are significantly different than the other departments across the entire UW system? Do you have enough information to answer this question fully? 4.3. Conclusions. Here, you’ll address some particular arguments that are likely to be put forth with your report and this data. Address each statement or argument clearly, using your previous analyses to back up your conclusions. (a) Suppose someone wants to make the claim that UW Milwaukee doesn’t value its professors as highly as UW Madison does. How does your report support or refute that claim? (b) Suppose a taxpayer watchdog group thinks the chancellor (all levels) salaries are con- sidered bloated and far above the typical faculty pay. How would you address this claim? (c) Suppose a politician thinks the art departments across theUW system is underfunded compared to the other departments, and wants to use your report to back up this claim. Is this appropriate? How would you advise the politician to interpret this data and these results? (d) Suppose the mathematics faculty at UW Milwaukee would like to argue for more promotions. They argue that the numbers of lower level faculty (assistant and asso- ciate professors) are too high compared to UWMadison, and that UWMadison has more full professors who are better paid. Does your data support this claim? (e) What are some cautions you would give your newspaper editor regarding the use of this data, and the conclusions that may be drawn? (f) What are some other questions youwould like to explore in future analyses regarding this data? Would you recommend using a larger dataset to answer these questions? 3 Overview and Dataset Report instructions Grading The Report Exploratory Analysis Statistical Analysis Conclusions