BA 1605 - Business Decision Analysis - Assignment #1 1 1- For each of the following, indicate whether the data are cross-sectional or time series: A) Company quarterly profits B) Percentage of American adults who work full time C) Historical closing stock prices 2- A full service brokerage firm gathered information on how their clients were investing for retirement. Based on age, clients were categorized according to where the largest percentage of their retirement portfolio was invested. The table below summarized the data. Mutual Funds Stocks Bonds Total A) B) C) D) E) Age 50 or Younger Over Age 50 30 34 37 45 19 23 86 102 Total 64 82 42 188 Identify the variables and tell whether each is categorical or quantitative. What percentage of the clients who invest in mutual funds are over age 50? What percentage of clients over age 50 invest in mutual funds? What percentage of the mutual fund investors are over age 50? Prepare an appropriate chart to display the marginal distribution of age. 3- Below is a histogram of salaries (in $) for a sample of marketing managers. A) Here is the five-number summary of salaries (in $) for a sample of marketing managers. Comment on the shape of the distribution. Min 46,360 Q1 69,693 Median 77,020 Q3 91,750 B) Would you expect the mean salary for this sample of marketing managers to be higher or lower than the median? Explain. C) Which would be a more appropriate measure of central tendency for these data, the mean or median? Explain. D) Calculate the range. E) Calculate the Interquartile range. F) Suppose the marketing manager who was earning $129,420 got a raise and is now earning $140,000. Indicate how this change would affect the following summary statistics (increase, decrease, or stay about the same). a. Mean b. Median c. Range d. IQR e. Standard deviation Max 129,420 BA 1605 - Business Decision Analysis - Assignment #1 4- The table below shows data on total assets ($ million) for a sample of a bank's branches. Prepare a stem and leaf display. Comment on the shape of the distribution. BRANCH 1 2 3 4 5 6 7 8 ASSETS ($ million) 88 80 58 92 81 70 89 84 5- The table below shows closing share prices (on the first trading day of August, 2007) for a small sample of companies. COMPANY 3M Dental Products Tyco Electronics Power Systems Kyocera America Inc. Pfizer Inc. Xerox Company Northrop Grumman Corporation Lockheed Martin Maritime Systems Sony DADC Matsushita Electronic Components Foster Wheeler Environmental Corp. CLOSING SHARE PRICE 08/07 86.95 47.45 94.10 22.39 17.56 75.81 100.17 51.91 17.91 55.67 A) Calculate the mean. B) Calculate the standard deviation. C) Calculate the coefficient of variation. 6- A study was done in which the daily temperature and the number of traffic accidents within the city were recorded. These sample data are shown as follows: Temperature 33 13 24 20 -2 Traffic accidents 7 4 9 10 5 Calculate covariance and coefficient of correlation. 2 BA 1605 - Business Decision Analysis - Assignment #1 7- To determine whether the cash bonuses paid by Johnson Financial Group are related to annual pay, data were gathered for 10 account executives who received such bonuses in 2007. The data, scatterplot and summary statistics are shown below. ANNUAL PAY $ 70,609 $ 58,487 $ 104,561 $ 43,922 $ 82,613 $ 116,250 $ 76,751 $ 68,513 $ 137,000 $ 94,469 CASH BONUS $ 11,225 $ 6,238 $ 14,194 $ 4,188 $ 11,863 $ 13,671 $ 7,758 $ 20,760 $ 55,000 $ 34,368 Estimate the linear regression model (that relates the dependent variable (cash bonus) to the independent variable (annual pay)) by: A) Finding the slope of the regression line. B) Finding the intercept of the regression line. C) Writing the equation of the linear model. D) Finding the value of R2. Interpret its meaning in this context. E) Estimating the cash bonus for an executive at Johnson Financial earning $82,613 a year. 8- A small manufacturing company recently instituted Six Sigma training for its employees. Two methods of training were offered: online and traditional classroom. Management was interested in whether the division in which employees worked affected their choice of method. Below is a table summarizing the data. Traditional Online Total Sales 16 35 51 Quality Operations Total 10 8 34 23 44 102 33 52 136 A) What is the probability that an employee chose online training? B) What is the probability that an employee is in the quality division and chose online training? C) What is the probability that an employee chose online training given that he/she is in the sales division? 3 BA 1605 - Business Decision Analysis - Assignment #1 9- During its grand opening week, Stickler's bicycle shop offers a "wheel of discount savings." After customers select the items they wish to purchase, they spin the wheel to determine the discount they will receive. The wheel is divided into 12 slices. Six slices are red and award a 10% discount, three slices are white and award a 20% discount, and two slices are blue and award a 40% discount. The remaining slice is gold and awards a 100% discount! A) What is the probability that a customer gets at least a 40% discount? B) What is the probability that a customer gets a 10% or 20% discount? C) What is the probability that two customers in a row get a 20% discount? 10- Consider the following to answer the question(s) below: Mutual Funds Stocks Bonds Total Age 50 or Younger 30 45 20 95 Over Age 50 35 45 25 105 Total 65 90 45 200 A) What is the probability that a client is over age 50 and is holding bonds? B) What is the probability that a client is over age 50 and is not holding bonds? C) What is the probability that a client is holding mutual funds given that he/she is age 50 or younger? D) What is the probability that a client only holds bonds? 4