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HW Problems: 1) For the following data on Year-end Audit times (in days), 17, 20, 25, 27, 19, 19, 20, 32, 26, 23, 24, 23, 27, 38, 21, 23, 22, 28, 33, 18, 27, 20, 23, 27, 31 Prepare a table showing in columns Audit Time Intervals (days), Frequencies, Cumulative Frequencies, Relative Frequencies, Cumulative Relative Frequencies, Percent Frequencies, and Cumulative Percent Frequencies. 2) The following table shows a data set containing information for 5 of the shadow stocks tracked by the American Association of Individual Investors. Shadow stocks are common stocks of smaller companies that are not closely followed by Wall Street analysts. a. How many variables are in the data set? List them. b. List the variables and identify which of the variables are categorical and which are quantitative? c. Find the average values for: Market Cap, Price/Earnings Ratio, and Gross Profit Margin. Company Exchange Ticker Symbol Market Cap ($ millions) Price/Earnings Ratio Gross Profit Margin (%) DeWolfe Companies AMEX DWL 36.4 8.4 36.7 North Coast Energy OTC NCEB 52.5 6.2 59.3 Hansen Natural Corp. OTC HANS 41.1 14.6 44.8 MarineMax, Inc. NYSE HZO 111.5 7.2 23.8 Nanometrics, Inc. OTC NANO 228.6 38.0 53.3 3) A sample of midterm grades for five students showed the results: 72, 65, 82, 90, and 76. Based on the data, which of the following statements are correct, and which should be challenged as being too generalized? Justify your answer. a. The average midterm grade for the sample of five students is 77. b. The average midterm grade for all students who took the exam is 77. c. An estimate of the average midterm grade for all students who took the exam is 77. d. More than half of the students who take this exam will score between 70 and 85. e. If five other students are included in the sample, their grades will be between 65 and 90. 4) In automobile mileage and gasoline-consumption testing, 6 automobiles were road tested for 300 miles in both city and highway driving conditions. The following data were recorded for miles-per-gallon performance. City 16.2 16.7 15.9 14.4 16 16.2 Highway 19.4 20.6 18.3 18.6 18.6 18.7 Use mean, median, and mode to make a statement about the difference in performance for city and highway driving. Which area of Statistics helps you to either validate or disprove such a statement and why? 5) Consider a sample with data values of 12, 17, 10, 16, and 20. Compute mean, median, range, variance, and standard deviation. 6) Consider a sample with data values of 12, 17, 10, 16, and 20. Compute the z-scores for the dataset. 7) The first sheet on QMB3200–Homework#1Data.xlsx is named CommuteTime. It lists the average commute time (in minutes) it takes citizens of 379 metropolitan areas to travel to work and back home each day. a. Using Excels statistical functions such as =AVERAGE(), =SUM() etc., give the mean, median, mode, max, min, variance (sample) and standard deviation (sample) of the average commute times, 10th percentile, 20th percentile, 40th percentile, 50th percentile, 60th percentile, 80th percentile, 1st quartile, 2nd quartile, 3rd quartile. Look at the values of the median and the 2nd quartile and the 50th percentile and comment. b. Find the frequency of commute times between 30-39.99, 40-49.99, 50-59.99, 60-69.99 and 70-79.99. c. Find the relative frequency of the commute times for the above intervals. d. Find the cumulative relative frequency of the commute times for the above intervals. e. Plot a line chart of the relative frequencies obtained in part c above. f. Plot a pie-chart of the relative frequencies. g. Make three statements about the data from the cumulative relative frequency table or the plots. 8) The second sheet on QMB3200–Homework#1Data.xlsx is named BetaEmployees. It gives data about some employees at Beta Corporation. a. For each of the variables, state the type of each of the six variables as either Numeric or Categorical. b. For the Gender variable, find the number of males and females and their proportions. Assume 0 denotes Male and 1 denotes Female. c. Create a frequency table for annual salary by creating frequencies for groups of intervals of 10,000. Create the groups as 0 to 9999, 10,000 to 19,999, 20,000 to 29,999, and so on up to 169,999. d. Create a relative frequency column e. Create a cumulative frequency column f. Create a cumulative relative frequency column g. Plot a chart of the relative frequencies h. Guess if the shape is skewed or not and if so, in what direction. i. Find the skewness of annual salary column and interpret its value. j. Find the kurtosis of annual salary column and interpret its value. k. Make three statements about the data.