MGT 233 Homework #1, Fall 2017

Transcription

1 MGT 233 Homework #1, Fall 2017 Instructions This homework assignment is due at the beginning of class on September 13, 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.

2 Problem #1 Collegecalc.org - How much does it cost to attend a four-year college/university in Nebraska? Out of 26 four-year colleges, the average in-state tuition is nearly $17,000. All price data are reprinted from the U.S. Department of Education s IPEDS Survey and reflect reported costs for the academic year. Below is a partial list of Nebraska colleges and their education costs per year for a full-time resident student. Institution Name Tuition and Fees Creighton University $36,400 Nebraska Wesleyan University 29,800 Midland University 29,400 College of Saint Mary 29,000 Doane University 28,800 Hastings College 27,300 Concordia University-Nebraska 27,100 Union College 22,000 Grace University 20,600 Nebraska Christian College of Hope International University 15,000 Clarkson College 13,900 Nebraska Methodist College of Nursing & Allied Health 13,400 University of Nebraska-Lincoln 8,400 University of Nebraska at Omaha 6,900 Peru State College 6,800 University of Nebraska at Kearney 6,700 Chadron State College 6,200 Wayne State College 5,900 a) Compute and interpret the mean b) Compute the range c) Compute the variance d) Compute the standard deviation e) Compute the coefficient of variation for the scores f) A sample of tuition rates in Nebraska from 2005 provided a sample mean of $10,659 and a sample standard deviation of $9,810. What comparisons can you make between the tuition rates in 2015 and 2005 based on these descriptive statistics?

3 Problem #2 Box Office Mojo - During the second weekend of August, millions of dollars were spent as movie goers viewed the newest films at the theater. The gross weekend results were poor, scoring higher than only three previous weekends throughout the year. This could be due to the lack of movie premiers during the week Annabelle: Creation, The Nut Job 2: Nutty by Nature, and The Glass Castle. The following table provides the 13 films with the highest gross profits for the second weekend of August. Carry answers to 2 decimal places. Movie Title Gross Profits (in Thousands) Annabelle: Creation $35,006 Dunkirk $10,884 The Nut Job 2: Nutty by Nature $8,342 The Dark Tower $7,820 Girls Trip $6,466 The Emoji Movie $6,451 Spider-Man: Homecoming $6,023 Kidnap (2017) $5,097 The Glass Castle $4,679 Atomic Blonde $4,481 War for the Planet of the Apes $3,604 Despicable Me 3 $3,129 Detroit $2,886 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).

4 Problem #3 Google Finance - Nebraska is home to numerous publicly traded companies, some of which are found on the Fortune 500 and 1000 lists. The twelve largest companies in the state represent a wide variety of industries, including the monster conglomerate Berkshire Hathaway, fashion retailer The Buckle Inc., and renowned railroad Union Pacific Corporation. On August 1, 2017, the sample average stock price for twelve of the largest public companies in the state of Nebraska was $66.33/share with a sample standard deviation of $53.18/share. The following five companies were pulled from the list. What are the z-scores for the following stock prices? Company Name Price/Share A. Berkshire Hathaway B $ B. The Buckle Inc. $17.45 C. Cabela s Inc. $56.68 D. Lindsay Corporation $90.89 E. Union Pacific Corporation $101.98

5 Problem #4 Tom Brady had a nearly perfect season for the New England Patriot s in the NFL season, ending it by celebrating his fifth NFL Superbowl Championship. He is now the only quarterback in NFL history with five championship rings. During his last season, including the post-season, Brady averaged 313 passing yards per game with a standard deviation of 80 yards. Using Chebyshev s theorem, determine the probability that Brady recorded passing yards within the given ranges for a single game. a) 113 yards to 513 yards b) 224 yards to 402 yards c) 159 yards to 467 yards

6 Problem #5 If one is looking for a predictable and pleasant climate, he/she would be advised to avoid the state of Nebraska. As evident by the table presented below, the fluctuations in temperature and the irregular patterns of storms, warm fronts, and cold fronts are apparent all year long. The following table presents the highest and lowest recorded temperatures in Kearney, NE according to Weather.com. Recorded Temperatures in Degrees Fahrenheit Month X Highest Y Lowest Jan Feb Mar Apr May June July Aug Sep Oct 95 6 Nov Dec a) Find the mean, variance and standard deviation of the record high temperatures in Kearney. b) Find the mean, variance and standard deviation of the record low temperatures in Kearney. c) Create a Scatter Graph between the record high temperatures (X), and record low temperatures (Y). d) Compute the sample covariance. e) Compute the correlation coefficient. f) Describe the relationship between record high temperatures and record low temperatures.

7 Problem #6 NBA.com - To make it in any professional sport, one must be an amazing athlete. In the NBA, one must be not only possess the technical skills, but also the physical attributes that allow one to be successful. Specifically in the category of rebounds which is a statistic awarded to one who retrieves the basketball after a missed fieldgoal shot or free throw an athlete with height has a significant advantage over others. The following table provides the height in inches for 20 players active in the NBA Season. Also provided is the total number of recorded rebounds for the season, according to NBA.com. Player Height in Inches Rebounds Russell Westbrook James Harden Isaiah Thomas Anthony Davis DeMar DeRozan Damian Lillard DeMarcus Cousins LeBron James Kawhi Leonard Stephen Curry Kyrie Irving Karl-Anthony Towns 84 1,007 Kevin Durant Jimmy Butler Paul George Andrew Wiggins Kemba Walker John Wall Bradley Beal CJ McCollum a) Find the mean, variance and standard deviation for the height of the players. b) Find the mean, variance and standard deviation for the rebounds for the season. c) Create a Scatter Graph between the height of the player (X) and the number of rebounds (Y). d) Compute the sample covariance. e) Compute the correlation coefficient. f) What is the relationship between the height of a NBA player and the number of rebounds he records?

8 Problem #7 Business Insider - Today s data visualization comes from Fortune Magazine, and it compares the world s largest companies by their 2016 revenues to really help put the size and scale of these companies into perspective. As just one example, despite being worth more than the majority of brick and mortar retailers combined, Amazon ranks just #44 in terms of global revenue to barely crack the list. The following table shows 48 of the world s largest companies by revenue, as reported by Fortune Magazine for the previous year. The revenues are recorded in Billions of U.S. Dollars. Revenue in Billions Number of Companies $ $ $ $ $ $ $ a) Create a histogram of the data. b) Create an ogive of the data. c) Find and interpret the mean of the revenue recorded. d) Compute the variance of the revenue earned. (carry to 4 decimal places) e) Compute the standard deviation of the revenue earned. (carry to 4 decimal places)