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Department of Economics & Finance, College of Business, Tennessee State University ECON 3050 (Spring 2020) Examination #1 Online (Data Analysis) Part; Instructor: Dr. Achintya Ray Completed examination and supporting data file must be nicely typed and MUST BE uploaded in the designated folder on Elearn by NO LATER THAN 8:30 pm (US Central Time), Friday, February 28, 2020. You will be asked to perform several hypothesis testing. In each such case, state the precise hypothesis in appropriate form, state the test statistic that you will be using, computed and critical .values, and your conclusion. The conclusion must be stated in a language that should be intelligible to person who may not be quite familiar with advanced statistical tools. Your final submission MUST BE your OWN WORK. Violating the honor code may lead to a failing grade. Your work will be checked for plagiarism. DO NOT VIOLATE THE HONOR CODE. Questions in this examination are based on the accompanying data set named data1.xlsx. 1. 2. 3. 4. 5. 6. 7. 8. Find the mean, median, variance, standard deviation, skewness, maximum, minimum, range, 95% confidence interval for the populationl mean, 99% confidence interval for the population mean, and 90% confidence interval for the population mean for each of the samples. Present your results in a nice table. Test the hypothesis that the variance of the population from which sample 1 is drawn is at least 170. Test the hypothesis that the variance of the population from which sample 2 is drawn is no more than 175. Test the hypothesis that the variance of the population from which sample 3 is drawn is more than 160. Test the hypothesis that the variance of the population from which sample 4 is drawn is no more than 1 Compute the 95% confidence interval of the difference of the population means from which sample 1 and sample 2 were drawn. Compute the 95% confidence interval of the difference of the population means from which sample 3 and sample 4 were drawn. Compute the 95% confidence interval of the difference of the population means from which sample 1 and sample 3 were drawn. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. Test the hypothesis that the variance of the population from which sample 1 was drawn is more than the variance of the population from which sample 2 was drawn. Test the hypothesis that the variance of the population from which sample 3 was drawn is equal to the variance of the population from which sample 4 was drawn. Test the hypothesis that the variance of the population from which sample 1 was drawn is equal to the variance of the population from which sample 3 was drawn. Test the hypothesis that the variance of the population from which sample 2 was drawn is equal to the variance of the population from which sample 4 was drawn. Test the hypothesis that the mean of the population from which sample 1 was drawn is equal to the mean of the population from which sample 2 was drawn. Test the hypothesis that the mean of the population from which sample 1 was drawn is equal to the mean of the population from which sample 3 was drawn. Test the hypothesis that the mean of the population from which sample 1 was drawn is equal to the mean of the population from which sample 4 was drawn. Test the hypothesis that the mean of the population from which sample 2 was drawn is equal to the mean of the population from which sample 3 was drawn. Test the hypothesis that the mean of the population from which sample 2 was drawn is equal to the mean of the population from which sample 4 was drawn. Test the hypothesis that the mean of the population from which sample 3 was drawn is equal to the mean of the population from which sample 4 was drawn. Looking at the answers to the questions above, what can you say about the likelihood that all the samples were essentially drawn from the same population? Carefully expand your argument with statistical reasoning and supporting evidence. ECON 3050 (Quantitative Methods) - Spring 2020 Final Comprehensive Examination Due Date & Time: April 30, 2020, 10:00 PM, CT Dr. Achintya Ray Professor of Economics Department of Economics & Finance College of Business, Tennessee State University, Nashville, TN, USA April 20, 2020 Contents 1 How to submit this assignment? 2 2 What Topics You Need to Cover for This Assignment? 2 3 What Should You Do Before You Work On This Assignment 2 4 Suggested Videos That You Should Watch 4.1 Disclaimers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Microsoft Excel Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Google Sheets Resources: Free and Online . . . . . . . . . . . . . . . . . . . . . . . . 3 3 3 4 5 The Data You Need For the Assignment 5.1 Housing.xlsx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Enplanement.xlsx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4 4 6 PART 1: Suggested Early Submission Date: April 20, 2020. Accounts for 25% of the Final Grade. 5 7 PART 2: Suggested Early Submission Date: April 25, 2020. Accounts for 25% of the Final Grade. 5 8 PART 3: Suggested Final Submission Date: April 30, 2020. Accounts for 25% of the Final Grade. 6 1 1. How to submit this assignment? 1. Type your answers nicely in a Word document and upload the same in the designated Elearn folder. Any supporting file must be uploaded along with the main submission. All supporting data and calculations must be submitted in an Excel File along with the Word File. You can download a Google Sheet as an Excel File and upload the same in Elearn. 2. If you do not use Word for typing then try to type the answers in a Google Document online using your phone/tablet and download the file as a Word document and then upload that Word document in the designated folder on Elearn. All supporting data and calculations must be submitted in an Excel File along with the Word File. You can download a Google Sheet as an Excel File and upload the same in Elearn. 3. DO NOT VIOLATE the honor code. Your submission MUST BE your OWN WORK. You may earn a failing grade in the assignment if you violate the honor code. 4. No late submission is allowed. Early submission is welcome and strongly encouraged. Make plans to NOT wait until the very last moments to finish and upload your work. You must reserve about 15 − 20 hours to finish the entire work. Actual time may be more or less depending on your level of preparations. 5. No email submission will be accepted. All submissions MUST BE through Elearn. Otherwise, they will not be graded. 2. What Topics You Need to Cover for This Assignment? Watch the videos of ANOVA posted in the Elearn. Read the 10 step ANOVA example. Other topics include: Descriptive Statistics, sampling and confidence interval, t-Test, F-Test, χ2 - Test. χ2 is Pronounced as Chi-Squared, regression analysis, time series and forecasting. All relevant tables are posted in the Elearn. Numerous video resources are referred below to help you master the essential concepts easily. 3. What Should You Do Before You Work On This Assignment 1. Read the whole assignment very very carefully. Make a note of everything that you need to do for this assignment. 2. Read the relevant chapters and the associated lecture slides posted on the Elearn. 3. Consult the additional lecture materials posted on Elearn. 4. Watch the suggested videos mentioned below. 5. The assignment is broken down in many parts. Finish them in order and periodically upload your submissions for different parts by the suggested dates mentioned for the individual parts. 2 4. 4.1. Suggested Videos That You Should Watch Disclaimers The resources are provided so that you can perform your analysis on two largely comparable platforms: Microsoft Excel and Google Sheets. You need to choose between Microsoft Excel or Google Sheets as your preferred analytics platform but it will be entirely fine to learn BOTH. The videos are referred as learning materials. No product, opinion, advertisement, etc. is endorsed. YOU ARE STRONGLY ADVISED TO IGNORE ANY COMMERCIAL MATERIAL THAT IS NOT RELETED TO FORMULAS AND CONCEPTS COVERED IN THE COURSE. Please bring to my attention if you notice any inappropriate material. 4.2. Microsoft Excel Resources 1. For Microsoft Windows: How to Install the Data Analysis ToolPak in Microsoft Excel https://www.youtube.com/watch?v= yNxLFagKgw 2. For Mac: How to Install the Data Analysis ToolPak in Microsoft Excel https://www.youtube.com/watch?v=mtmrAXwLcuU 3. Excel - Simple Linear Regression https://www.youtube.com/watch?v=Cltt47Ah3Q4 4. Multiple Regression in Microsoft Excel https://www.youtube.com/watch?v=cXiZ t2NK1k 5. Using Multiple Regression in Excel for Predictive Analysis https://www.youtube.com/watch?v=HgfHefwK7VQ 6. Excel - Time Series Forecasting - Part 1 of 3 https://www.youtube.com/watch?v=gHdYEZA50KE 7. Excel - Time Series Forecasting - Part 2 of 3 https://www.youtube.com/watch?v=5C012eMSeIU 8. Excel - Time Series Forecasting - Part 3 of 3 https://www.youtube.com/watch?v=kcfiu-f88JQ 9. Creating Pivot Tables in Excel https://www.youtube.com/watch?v=BkmxrvIfDGA 10. Excel - One-Way ANOVA Analysis Toolpack https://www.youtube.com/watch?v=nmHFFFpOVZs 11. F Test in Excel https://www.youtube.com/watch?v=2337cSdINF0 12. Moving Average Time Series Forecasting with Excel https://www.youtube.com/watch?v=mC1ARrtkObc 3 4.3. Google Sheets Resources: Free and Online 1. Installing the XLMiner Analysis ToolPak add-on in Google Sheets https://www.youtube.com/watch?v=JHXsKwcRdRw 2. Multiple Regression with Google Sheets XL Miner https://www.youtube.com/watch?v=YhBU92eyNRo 3. Time Series Forecasting with Google Sheets part (1 of 4) https://www.youtube.com/watch?v=FWNlS7hRQOo 4. Time Series Forecasting with Google Sheets part (2 of 4) https://www.youtube.com/watch?v=lL61SGr1lJk 5. Time Series Forecasting with Google Sheets part (3 of 4) https://www.youtube.com/watch?v=I29vxyfIVtw 6. Time Series Forecasting with Google Sheets part (4 of 4) https://www.youtube.com/watch?v=C68u9nuw50Y 7. Google Sheets: Create Pivot Tables and Charts https://www.youtube.com/watch?v=SzrBbBV adM 8. Two Way ANOVA - with Google Sheets XL-miner https://www.youtube.com/watch?v=uCkycwF2HUU 9. Running a t-Test using Google Sheets https://www.youtube.com/watch?v=YeVF2lnhr7o 10. Using Google Sheets to Calculate Differences in Proportions (Z Test) https://www.youtube.com/watch?v=1uGvuaCw6t8 5. The Data You Need For the Assignment Two data sets will be needed to complete this assignment. Both of these data sets are posted in Elearn. 5.1. Housing.xlsx This data set contains the following data for 150 homes sold recently in a large city. Price: In US Dollars Beds: Number of bedrooms in the house Baths: Number of bathrooms Garage: Number of cars that can be parked in a covered space (like a grage) Sqft-House: Finished Sq-ft for the house Sqft-Land: Sq-ft of the land on which the house sits Kitchen: If the kitchen is updated: 0 means not updated & 1 means updated Roof: Number of years of useful life left for the roof Age: Age of the house 5.2. Enplanement.xlsx Enplanements for U.S. Air Carrier International, Scheduled Passenger Flights, Thousands, Monthly, Seasonally Adjusted. This is a monthly data starting on January 2000 and ending December, 2019. 4 6. PART 1: Suggested Early Submission Date: April 20, 2020. Accounts for 25% of the Final Grade. By using the Housing.xlsx data, answer the following questions. 1. Test the following hypotheses and also state the alternate hypothesis in each case. Write a sentence or two summarizing your conclusion after you have completed each hypothesis testing. Hypothesis 1 Average price per sq-ft of houses with ≤ 3 bedrooms is more than the average price per sq-ft of other houses. (Use the sq-ft of the house only) Hypothesis 2 Average price per sq-ft of houses with updated kirchen is more than the average price per sq-ft of other houses. Hypothesis 3 Average price per sq-ft of houses with ≥ 15, 000 sq-ft of land is more than the average price per sq-ft of other houses. Hypothesis 4 Average price per sq-ft of houses with ≥ 10 years of usable roof life left is more than the average price per sq-ft of other houses. Hypothesis 5 Average price per sq-ft of houses with ≤ 10 years old houses is more than the average price per sq-ft of other houses. Hypothesis 6 Variance of the price per sq-ft of houses with ≤ 10 years old houses is more than the variance of the price per sq-ft of other houses. Hypothesis 7 Average price per sq-ft of 3, 4, or, 5 bedroom houses are basiacally equal to each other. (Hint: Think ANOVA) 2. Run the following regressions and present the results nicely. Also interpret the results carefully: Price per sq-ft of the house = β0 + β1 (Sqf t − House) +  (1) Price per sq-ft of the house = β0 + β1 (Sqf t − Land) +  (2) Price per sq-ft of the house = β0 + β1 (Roof ) +  (3) Price per sq-ft of the house = β0 + β1 (Age) +  (4) Price per sq-ft of the house = β0 + β1 (Beds) +  (5) Price per sq-ft of the house = β0 + β1 (Baths) +  (6) Price per sq-ft of the house = β0 + β1 (Kitchen) +  (7) 3. Write a short essay summarizing your results in the above regressions. Make your presentation in a simple enough format that may be understood by an average home buyer. 7. PART 2: Suggested Early Submission Date: April 25, 2020. Accounts for 25% of the Final Grade. By using the Housing.xlsx data, answer the following questions. 5 1. Run the following regressions and present the results nicely. Also interpret the results carefully: Price = β0 + β1 (Sqf t − House) + β2 (Sqf t − Land) +  (8) Price = β0 + β1 (Sqf t − House) + β2 (Sqf t − Land) + β3 (Beds) + β4 (Baths) +  (9) Price = β0 + β1 (Sqf t − House) + β2 (Beds) + β3 (Baths) + β4 (Age) +  (10) Price = β0 + β1 (Sqf t − House) + β2 (Sqf t − Land) + β3 (Beds) + β4 (Baths) + β5 (Kitchen) +  (11) Price = β0 + β1 (Sqf t − House) + β2 (Garage) + β3 (Beds) + β4 (Baths) + β5 (Kitchen) +  (12) Price = β0 +β1 (Sqf t−House)+β2 (Garage)+β3 (Beds)+β4 (Baths)+β5 (Kitchen)+β6 (Age)+ (13) 2. Find out the predicted values of the houses for each of the models above. How do the actual values differ from the predicted values? 3. Based on the regressions that you have estimated above, what do you think will be a good model to esimate the price of a house that you may be considering? You are allowed to run other regression models and find out if there is another model that performs better than the models above. 8. PART 3: Suggested Final Submission Date: April 30, 2020. Accounts for 25% of the Final Grade. By using the Enplanement.xlsx data, answer the following questions. Let us assume that Yt denotes the number of passengers who enplaned in month t. By that logic, if Yt represents the data for December, 2018, then Yt−1 represents the data for November, 2018, Yt−2 represents the data for October, 2018, etc. In the data t represents time that starts at t = 0 or, the beginning of the data. 1. Present the data in a nice graph and generally describe the changes over time. 2. Derive the 3-month, 6-month, 9-month, and 12-month moving averages of the data and present those series nicely on a graph. Generally describe the changes of the moving averages over time. (Hint: Watch the moving average video avilable at https://tinyurl.com/w5f6e8e and calculate the MAD, MSE, and MAPE to answer this question. It will be pretty straightforward once you watch the video.) 3. Watch the 3-part time series forecasting videos referenced above before you answer this question. Perform the following regressions and explain the resuts in a way that makes good sense. Yt = β0 + β1 (t) +  (14) Yt = β0 + β1 (Yt−1 ) +  (15) Yt = β0 + β1 (Yt−1 ) + β2 (t) +  (16) Yt = β0 + β1 (Yt−1 ) + β2 (Yt−2 ) +  (17) Yt = β0 + β1 (Yt−1 ) + β2 (Yt−2 ) + β3 (t) +  (18) Yt = β0 + β1 (Yt−1 ) + β2 (Yt−2 ) + β3 (Yt−3 ) +  (19) Yt = β0 + β1 (Yt−1 ) + β2 (Yt−2 ) + β3 (Yt−3 ) + β4 (t) +  (20) Yt = β0 + β1 (Yt−1 ) + β2 (Yt−2 ) + β3 (Yt−3 ) + β4 (Yt−4 ) + β5 (t) +  (21) 6 4. Which of the above forecasting models estimated above works best for the data that we have? (Hint: First calculate the predicted values from each of the equations. Watch the moving average video avilable at https://tinyurl.com/w5f6e8e and calculate the MAD, MSE, and MAPE (for the difference between the actual and predicted values) to answer this question. It will be pretty straightforward once you watch the video.) 7 ECON 3110 (Quantitative Methods) - Spring 2020 Assignment Due: Monday, March 30, 2020, 10:00 AM, CT This Assignment is worth 10% of the Final Grade Dr. Achintya Ray Department of Economics & Finance College of Business, Tennessee State University, Nashville, TN, USA March 23, 2020 1. How to submit this assignment? 1. Type your answers nicely in a Word document and upload the same in the designated Elearn folder. Any supporting file must be uploaded along with the main submission. 2. If you do not have a computer or, do not want to use Word for typing then try to type the answers in a Google Document online using your phone/tablet and download the file as a Word document and then upload that Word document in the designated folder on Elearn. 3. If you cannot do any of the above then nicely write your answers on regular clean papers. Use a dark ink pen for nice contrast. Then use your phone’s camera to take pictures of the answer sheets and make a single PDF file for submission. Upload the PDF into the designated Elearn folder. Check out these guides on how to use your phone’s camera to make PDF files: How to use iOS 11’s Notes app as a document scanner: https://www.cnet.com/news/how-to-use-ios-11s-notes-app-as-a-document-scanner/ How to Scan Documents to PDF with Your Android Phones Camera https://www.howtogeek.com/166610/who-needs-a-scanner-scan-a-document-to-pdf-with-your-androidphone/ 4. DO NOT VIOLATE the honor code. Your submission MUST BE your OWN WORK. You may earn a failing grade in the assignment if you violate the honor code. 5. No late submission is allowed. Early submission is welcome and strongly encouraged. Make plans to NOT wait until the very last moments to finish and upload your work. You must reserve about 3 − 4 hours to finish the entire work. Actual time may be more or less depending on your level of preparations. 6. No email submission will be accepted. All submissions MUST BE through Elearn. Otherwise, they will not be graded. 1 2. What Topics You Need to Cover for This Assignment? Watch the videos of ANOVA posted in the Elearn. Read the 10 step ANOVA example. Other topics include: Descriptive Statistics, sampling and confidence interval, t-Test, F-Test, χ2 - Test. χ2 is Pronounced as Chi-Squared. All relevant tables are posted in the Elearn. 3. The Data You Need For the Assignment A restaurant chain has 4 locations around a city. Management wants to know if customers are spending roughly the same amount of time during the peak hours per table. Analyst collected data for 5 random tables at each loaction. That data is presented in the table below. For example, 47 means that a randomly selected table was occupied for 47 minutes to serve one group of patrons. Restarant Time Spent Per Table (During Peak Hours) Data 4. Location A Location B Location C Location D 52 59 81 63 73 75 55 95 46 85 67 77 47 74 56 58 38 82 77 91 Answer the Following Questions 1. Find the average time spent per table in each location. Also find the variance, standard deviation, and 95% confidence interval of the mean for each location. 2. Construct the 95% confidence interval of the differences of means between a) Location A & Location ...
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