Fall Semester, AY 2016-2017 ASSIGNMENT 1 BUSN 401-Quantitative Techniques in Business & Management Student's Name: ID Number: EXERCISE 1. Discuss the differences between statistics as numerical facts and statistics as a discipline or field of study. _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ EXERCISE 2. The U.S. Department of Energy fuel economy information for a variety of motor vehicles. A sample of 10 motor automobiles is shown in Table A (Fuel Economy website, February 22, 2008). TABLE A. FUEL ECONOMY INFORMATION FOR 10 AUTOMOBILES Car Size Cylinder City Highway Fuel s MPG MPG Audi A08 Large 12 13 19 Premium BMW 328Xi Compact 6 17 25 Premium Cadillac CTS Midsize 6 16 25 Regular Chrysler 300 Large 8 13 18 Premium Ford Focus Compact 4 24 33 Regular Hyundai Elantra Midsize 4 25 33 Regular Jeep Grand Midsize 6 17 26 Diesel Cherokee Pontiac G6 Compact 6 15 22 Regular Toyota Camry Midsize 4 21 31 Regular Volkswagen Jetta Compact 5 21 29 Regular Data show the size of the automobile ( compact, midsize or large), the Page 1 of 9-Quantitative Methods in Business & Management number of cylinders in the engine, the city driving miles per gallon, the highway driving miles per gallon, and the recommended fuel(diesel, premium, or regular) A. How many elements are in this data set? B. How many variables are in this data set? C. Which variables are categorical and which variables are quantitative? D. What type of measurement scale is used for each of the variables? EXERCISE 3. Refer to the data from Table A below. TABLE A. FUEL ECONOMY INFORMATION FOR 10 AUTOMOBILES Car Size Cylinder City Highway s MPG MPG Audi A08 Large 12 13 19 BMW 328Xi Compact 6 17 25 Cadillac CTS Midsize 6 16 25 Chrysler 300 Large 8 13 18 Ford Focus Compact 4 24 33 Hyundai Elantra Midsize 4 25 33 Jeep Grand Midsize 6 17 26 Cherokee Pontiac G6 Compact 6 15 22 Toyota Camry Midsize 4 21 31 Volkswagen Jetta Compact 5 21 29 Questions A. What are the average miles per gallon for city driving? B. On average, how much higher is the miles per gallon for highway driving as compared to city driving? C. What percentage of the cars have four-cylinder engines? D. What percentage of the cars use regular fuel? Show Computations here: Page 2 of 9-Quantitative Methods in Business & Management Answers Fuel Premium Premium Regular Premium Regular Regular Diesel Regular Regular Regular EXERCISE 4. Consider the following frequency distribution Class 10-19 20-29 30-39 40-49 50-59 Frequency 10 14 17 7 2 Fill-out Answers here: Class Cumulative Frequency Cumulative Relative Frequency Construct a cumulative frequency distribution and a cumulative relative frequency distribution. Fill-out the columns below. Class Cumulative frequency distribution Show Computations below: Page 3 of 9-Quantitative Methods in Business & Management Cumulative relative frequency distribution Exercise 5. Construct a histogram and an ogive for the data in Exercise 4. EXERCISE 6. Consider the following data: 8.9 6.8 10.2 9.5 11.5 11.5 7.8 11.2 10.0 14.9 12.2 7.5 13.5 10.0 14.1 6.0 10.0 15.8 A. Construct a dot plot. B. Construct a frequency distribution. C. Construct a percent frequency distribution. EXERCISE 7. A physician's office staff studied the waiting times for patients who arrive at the office with a request for emergency service. The following data with waiting times in minutes were collected over a onemonth period. 2 5 10 12 4 4 5 17 11 8 9 8 1 2 2 1 6 8 7 1 3 1 8 3 Use classes of 0-4, 5-9, and so on in the following: A. Show the frequency distribution. B. Show the relative frequency distribution. C. Show the cumulative frequency distribution. D. Show the cumulative relative frequency distribution. E. What proportion of patients needing emergency service wait 9 minutes or less? Exercise 8. Consider a sample with data values of 27, 25, 20,15,30,34, 28 and 25. Provide the five- number summary for the data. Page 4 of 9-Quantitative Methods in Business & Management 12.2 11.5 Exercise 9. Show the five- number summary and the box plot for the following data: `5,15,18,10,8,12,16,10,6. Exercise 10. A data set has a first quartile of 42 and a third quartile of 50. Compute the lower and upper limits for the corresponding box plot. Should a data value of 65 be considered an outlier? Page 5 of 9-Quantitative Methods in Business & Management 1. A large number of manufacturer purchases an identical component from three independent suppliers that differ in unit price and quantity supplied. The relevant data for 2007 and 2009 are given here. Supplier A B C Quantity 150 200 120 Unit Price ($) 2007 5.45 5.60 5.50 2009 6.00 5.95 6.20 1.a. Compute the price relatives for each of the component suppliers separately. Compare the price increases by the suppliers over the two-year period. 1.b. Compute the unweighted aggregate price index for the component part in 2009. 1.c. Compute a 2009 weighted aggregate price index for the component part. What is the interpretation of this index for the manufacturing firm? 2) R & B Beverages, Inc. provides a complete line of beer, wine, and soft drink products for distribution through retail outlets in Central Iowa. Unit price data for 2006 and 2009 and quantities sold in cases for 2006 follow. Item Beer Wine Softdrink 2006 Quantity (cases) 35,000 5,000 60,000 2006 2009 17.50 100.00 8.00 20.15 118.00 8.80 Page 6 of 9-Quantitative Methods in Business & Management Compute a weighted aggregate index for R & B Beverages, Inc. sales in 2009, with 2006 as the base period. 3) Under the last-in-first out (LIFO) inventory valuation method, a prize index for inventory must be established for tax purposes. The quantity weights are based on year-ending inventory levels. Use the beginning-ofthe-year price unit as the base-period price and develop a weighted aggregate index for the total inventory value at the end of the year. What type of weighted aggregate price index must be developed for the LIFO inventory valuation? Product Ending Inventory A B C D 500 50 100 40 Unit Price($) Beginning .15 1.60 4.50 12.00 Ending .19 1.80 4.20 13.20 4) Data on quantities of three items sold in 1995 and 2009 are given here along with the sales prices of the items in 1995. Compute a weighted aggregate quantity index for 2009. Item 1995 A 350 Quantity sold 2009 300 Page 7 of 9-Quantitative Methods in Business & Management Price /Unit 1995 (s) 18.00 B C 220 730 400 850 4.90 15.00 5) A trucking firm handles four commodities for a particular distributor . Total shipments for the commodities in 1994 and 2009 , as well as the 1994 prices, are reported in the following table. Shipments Commodity A B C D 1994 120 86 35 60 2009 95 75 50 70 Price/shipme nt 1994 $ 1200 $ 1800 $ 2000 $ 1500 Develop a weighted aggregate quantity index with a 1994 base. Comment on the growth or decline in quantities over the 1994-2009 period. 6) Consider the following time series data. Week Value 1 18 2 13 3 16 4 5 11 17 6 14 Page 8 of 9-Quantitative Methods in Business & Management Using the nave method (most recent value) as the forecast for the next week. Compute the following measures of forecast accuracy: 6.a. Mean absolute error 6.b. Mean squared error 6.c. Mean absolute percentage error 6.d. What is the forecast for week 7? 7) Refer to the time series data in exercise 6. Using the average of all the historical data as a forecast for the next period, compute the following measures of forecast accuracy: 7a. Mean absolute error 7b. Mean squared error 7c. Mean absolute percentage error 7d. What is the forecast for week 7? 8) Consider the following time series data. Week Value 1 18 2 13 3 16 4 11 5 17 6 14 8a. Construct a time series plot. What type of pattern exists in the data? 8b. Develop the three-week moving average forecasts for this time series. Compute MSE and a forecast for week 7. 8c. Use = .2 to compute the exponential smoothing forecasts for the time series. Compute MSE and a forecast for week 7. 8d. Compare the three -week moving average approach with the exponential smoothing approach using = .2. Which appears to provide more accurate forecasts based on MSE? Explain. 8e. Use a smoothing constant of = .4 to compute the exponential smoothing forecasts. Does a smoothing constant of .2 or .4 appear to provide more accurate forecasts based on MSE? EXPLAIN. Page 9 of 9-Quantitative Methods in Business & Management