(Source: Yahoo Finance, 1/4/2016) Description Abercrombie & Fitch Co. Aeropostale, Inc. American Eagle Outfitters, Inc Ashley (Laura) Holdings PLC Bebe Stores, Inc. Big Lots Inc. Bon-Ton Stores Inc. Burlington Stores, Inc. Cherokee Inc. Chico's FAS Inc. Christopher & Banks Corporatio Citi Trends, Inc. Costco Wholesale Corporation Danier Leather Inc Destination Maternity Corporat Dillard's Inc. Dollar General Corporation Dollar Tree, Inc. Dollarama Inc DSW Inc. Express Inc. Francesca's Holdings Corporati Fred's, Inc. Genesco Inc. Guess' Inc. J. C. Penney Company, Inc. Kohl's Corp. L Brands, Inc. Macy's, Inc. New York & Company Inc. Nordstrom Inc. Pacific Sunwear of California PriceSmart Inc. Ross Stores Inc. Sears Canada Inc Sears Holdings Corporation Sears Hometown and Outlet Stor Shoe Carnival Inc. Stein Mart Inc. Target Corp. The Buckle, Inc. The Children's Place, Inc. The Gap, Inc. The Men's Wearhouse, Inc. The TJX Companies, Inc. Tilly's, Inc. Tuesday Morning Corporation Urban Outfitters Inc. Wal-Mart Stores Inc. Market Cap ($ millions) 1810 22 3020 320 45 1910 44 3140 150 1450 61 320 71020 6 121 2410 20910 18130 9950 2070 1460 725 611 1260 1580 2040 9040 27730 11000 145 9160 17 2470 21790 719 2190 182 463 307 44730 1480 1100 9930 710 47480 189 284 2670 196280 Return on Equity (% in last year) 1.8 -29.21 17.31 41.56 -21.89 21.07 -23.23 1.02 26.12 -1.04 24.93 7.94 20.22 -12.34 -16.1 17 21.41 9.08 54.63 15.33 18.28 25.81 -2.78 10.75 8.47 -25.2 13.23 5.83 28.31 -16.99 36.67 -4.92 15.99 43.88 -34.23 -16.78 -1.13 8.19 17.2 19.31 35.71 9.99 37.52 -0.49 51.8 7.34 5.07 18.19 18.62 Price to Book (ratio) 1 20 2 20 0 3 20 25 4 2 0 1 7 0 1 1 4 4 16 2 2 6 1 1 2 1 2 15 3 2 7 15 4 9 2 18 0 1 4 3 4 2 4 1 11 1 1 2 2 Net Profit Margin (% in last qtr) 4.8 -7.3 8.1 4.8 -17.8 -0.1 -5.3 1.2 19.1 -1.8 -0.3 0.4 1.8 -13.1 -1.1 3.1 5 1.7 15.1 5.9 4.8 6.7 0.3 4.2 2.4 -4.7 2.7 6.6 2 -2.4 2.4 -1.6 3.2 7.7 -6.7 -7.9 -0.7 3.5 -0.1 3.1 12.8 8.4 6.4 -3.1 7.6 2 -3 6.3 2.8 Statistics Due: March 15th at 9 pm TEST 1 No late papers will be accepted. Prof. Miller SHOW ALL WORK! Directions for this assignment: Answer any 8 out the 9 problems (if you do all 9, I will grade all and count the best 8.) Please show all work, writing explanations of intermediate steps wherever appropriate. Clearly label all graphs, including the scale on the horizontal and vertical axes and the units of measure where appropriate. You may use your notes, your textbook, any other resource book, a graphing calculator or computer software (subject to the statement above about showing intermediate steps) as resources. You may consult with other students in this class, but you cannot simply copy another student's answer and submit it as your own. You may not seek help on these specific questions (or any questions with only minor modifications) from any person who is not in this class. Typing your name below indicates that you followed the rules in completing this assignment (please submit this statement with your solutions): Signed__________________________________________ The data attached is for a sample companies in retail apparel and department stores (Source: Yahoo Finance Industry data for Apparel, Department and Discount stores as of 1/4/16) 1. Make an ungrouped frequency distribution for Price to Book. Use the frequency distribution to find the mean, median, mode and standard deviation for Price to Book. 2. Organize the data for Return on Equity in a grouped frequency distribution using -35 to -25.01 as the class limits of the first class. Make a relative frequency histogram. Describe the shape of the histogram. Predict, from the shape of the histogram, whether the mean is greater than the median or vice-versa. Calculate the mean and the median. Was your prediction correct? 3. Organize the data for Net Profit Margin in classes beginning with the class limits of -20 to -15.1. Draw an ogive for this data. Use your ogive to estimate the median. Then, find the actual median using the original data. Did the ogive provide a good estimate of the median? 4. (a) Determine the proportion of the Market Cap data that lies within 1, 2, and 3 standard deviations of the mean. Determine, using the empirical rule, if the Market Cap data is approximately normally distributed. (b) Determine the proportion of the Price to Book data that lies within 1, 2, and 3 standard deviations of the mean. Determine, using the empirical rule, if the Price to Book data is approximately normally distributed. 5. Find the z-score for Target for Market Cap. Also, find the z-score for Target for Return on Equity. Describe, in a few sentences, the meaning of these z-scores. 6. Please access the article with URL http://articles.mercola.com/sites/articles/archive/2014/02/07/arthroscopicknee-surgery.aspx Referring to the study conducted in Finland, write answers in complete sentences to the following questions: a) b) c) d) e) What is the population? What is the sample? Is the data qualitative, discrete, or continuous? EXPLAIN. Describe the parameter. Give the value if possible. Describe the statistic. Give the value if possible. 7. For each of the following, decide whether the mean, median, or mode would be the most useful measure of central tendency. Explain each answer with at least one complete sentence. (no explanation no points) Calculations are not necessary. a) The following table gives the results of a survey in which 2,400 consumers were asked to indicate which brand of soap they purchased (most recent purchase). Ivory 20.2% Dove 16.2% Softsoap 7.7% Safeguard 7.2% Irish Spring 4.6% Others 44.1% b) A marketing researcher wants to find the income of the people who buy his company's product. He finds the income of ten people who have recently purchased the product. Five earn twenty thousand, three earn thirty thousand, one earns forty thousand, and one customer earns eighty thousand. c) A recent study found that, in the US, the percent of electricity generated by coal is 44.9%, by natural gas is 23.4%, 20.3% by nuclear reactions, 6.9% by hydroelectric, 3.6% by wind and solar power, and 1% is generated using petroleum. 8. There are two brands of light bulbs. Ultralight bulbs that have lives with a mean of 3000 hours with a standard deviation of 200 hours and Electrolyte bulbs whose lives have a mean of 3000 hours with a standard deviation of 250 hours. Under what set of circumstances would a purchasing manager want to purchase Ultralight? Explain thoroughly why. Under what set of circumstances would a purchasing manager want to purchase Electrolight? Explain thoroughly why. 9. Two random samples were taken to determine left foot length of female versus male bears based on measuring their tracks. Numerical summaries of the data are given. Use them to answer the questions. A) Do male bears have longer feet than female bears? Are you sure? B) Give a range of values in which you would expect to find 95% of all bears' feet lengths. Explain why you picked this range. C) What is the shape of the distribution of bears' feet lengths? Explain. EXTRA CREDIT : Consider the following data set with 10 observations: 2, 4, 5, 6, 8, 10, 12, 13, 14, X . Find 3 different values of X for which = . X ~ X