MGT 233 Business Statistics Homework 1 (Fall 2018) Name: Checked by: 1. Number of Employment/County (14 points) 2. Capital Spending (17 points)

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1 MGT 233 Business Statistics Homework 1 (Fall 2018) Name: Checked by: 1. Number of Employment/County (14 points) 2. Capital Spending (17 points) 3. Social Media (6 points) 4. Formula One Racing (6 points) 5. CEO Age vs. Compensation (19 points) 6. Businesses vs. Sales (19 points) 7. High market value companies (6 points) Total (87 possible)

2 MGT 233 Homework #1, Fall 2018 Instructions This homework assignment is due at the beginning of class on September 12, For each problem: Use the proper statistics notation Show the intermediate work Write the equation you are using Give the proper units of measure Write clearly When interpreting an answer do not tell about the procedure, instead write a proper English statement that explains the meaning of the answer with respect to the problem context.

3 Problem #1 - Nebraska continues to be among the states with the lowest unemployment rates, and is logging rates much lower than the rest of the country in Below is a partial list of counties in Nebraska and annual average employment in Employment (jobs) County in 2017 Adams County 15,443 Buffalo County 27,033 Dodge County 17,386 Douglas County 338,886 Hall County 34,937 Lancaster County 168,416 Lincoln County 14,776 Madison County 21,671 Platte County 18,847 Sarpy County 70,371 Scotts Bluff County 16,722 a) Compute the range. b) Compute the variance. c) Compute the standard deviation. d) Compute the coefficient of variation for the scores. e) A sample of counties in Nebraska from 2014 provided a sample mean of 65,559 businesses and a sample standard deviation of 97,135 businesses. What comparisons can you make between the number of businesses/county in 2017 and 2014 based on these descriptive statistics?

4 Problem #2 Wall Street Journal- Samsung Electronics Co. spent more on capital expenditures last year than any other publicly traded company, highlighting in dramatic fashion how technology and telecommunications firms are driving an uptick in manufacturing investment Driving their spending is the proliferation of internet-connected gadgets and the need for skilled manufacture of dozens of micro size components. The advance toward artificial intelligence calls for massive data-server farms that require immense computing power and memory chips. A sample of nine technology companies and their expected capital spending in 2018 are shown below: Company Amount Spend (in billions of $) Alphabet 20 Amazon 21 Apple 16 Facebook 15 IBM 26 Intel 15 Microsoft 13 Oracle 14 Samsung 25 a) Compute and interpret the mean. b) Compute the range. c) Compute the interquartile range. d) Compute the sample variance. e) Compute the sample standard deviation. f) Find the coefficient of variation (carry to 4 decimals).

5 Problem #3 Social Media - The number of worldwide users is expected to reach some 3.1 billion monthly active social media users by The region with the highest penetration rate of social networks in North America, where around 70 percent of the population has at least one social account. As of 2017, 81 percent of the United States population had a social networking profile. The sample average in minutes spent on social media was 30 minutes per day surfing social networks with a sample standard deviation of 7.36 minutes per day. The following five favorite social media were pulled from the list. What are the z-scores for the number of minutes for each of the Social media sites? Social media site Minutes per day YouTube 40 Facebook 35 Snapchat 30 Instagram 32 Pinterest 14

6 Problem #4 Michael Schumacher is a seven-time Formula One World Champion and is widely regarded as one of the greatest F1 drivers of all time. According to the official Formula One website, he is statistically the greatest driver the sport has ever seen. Schumacher suffered a serious head injury while skiing in the French Alps in December, Michael Schumacher was the champion of F1 between 2000 and 2004 with an average of 127 points and a standard deviation of 25 points. Using the Chebyshev theorem, determine the percent of Schumacher s points within the given ranges in a competition. a) 77 to 177 b) 92 to 162 c) 57 to 197

7 Problem #5 Aflcio.org In 2017, CEOs of S&P 500 Index companies received, on average, $13.9 million in total compensation, according to the AFL-CIO s analysis of available data. In contrast, production and nonsupervisory workers earned only $37,632, on average, in 2017 a CEO-to-worker pay ratio of 361 to 1. The following table provides a sample of CEO s in the state of Nebraska and their respective age and total amount of compensation for the 2017 year. Company CEO Age Total Compensation (In $ Thousands) Berkshire Hathaway Warren E. Buffett Buckle Dennis H. Nelson 67 3,029 Green Plains Todd Becker 51 4,505 Lindsay Corporation Richard W. Parod 64 2,546 National Research Corp. Michael D. Hays Nelnet Jeffrey R. Noordhoek 51 1,739 TD Ameritrade Holding Corp. Tim Hockey 54 7,348 Union Pacific Corporation Lance M. Fritz 55 13,794 Valmont Industries Mogens C. Bay 69 4,097 Werner Enterprises Derek J. Leathers 49 2,850 West Corporation Thomas B. Barker 63 2,480 a) Find the mean, variance and standard deviation for the age of the CEO s. b) Find the mean, variance and standard deviation for the total compensation of the CEO s. c) Create a Scatter Graph between the age of the CEO (X) and the total compensation (Y). d) Compute the sample covariance. e) Compute the correlation coefficient. f) What is the relationship between the age of the CEO and the total compensation received?

8 Problem #6 Youreconomy.org The total number of establishments in business during the year 2016 is listed below for a sample of Nebraska counties. In addition, the total number of sales reported in each county is listed for the sample. County # of Businesses Sales (In $ Millions) Adams 2,790 4,400 Buffalo 3,990 7,400 Cass 1,510 1,800 Dakota 1,250 5,100 Dawson 1,980 3,700 Dodge 2,780 4,800 Douglas 45, ,800 Gage 1,880 3,300 Hall 5,090 12,000 Holt 1,250 2,100 Lancaster 22,990 47,700 Lincoln 3,180 5,700 Madison 3,180 7,000 Otoe 1,410 2,900 Platte 2,700 7,300 Sarpy 8,380 19,500 Saunders 1,430 1,700 Scotts Bluff 3,500 6,200 Washington 1,490 3,000 York 1,390 2,700 a) Find the mean, variance and standard deviation for the number of businesses. b) Find the mean, variance and standard deviation for the total amount of sales. c) Create a Scatter Graph between the number of businesses (X) and the amount of sales (Y) per county. d) Compute the sample covariance. e) Compute the correlation coefficient. f) What is the relationship between the number of businesses per county and the amount of sales reported in each county?

9 Problem #7 - Forbes.com - The 16th annual Forbes Global 2000 list in 2018 includes publicly-traded companies from 60 countries. Collectively, the companies on this list account for $39.1 trillion in sales, $3.2 trillion in profit, $189 trillion in assets and $56.8 trillion in market value. The following table represents 50 of the world largest companies by market value, as reported by Forbes Magazine. The market value are recorded in billions of U.S. Dollars. Treat this information as sample data. Market value (in Billions) Number of Companies a) Create a histogram of the data. b) Create an ogive of the data.