Data Analysis for Business Exam
Answer Key
Course Introduction
Data Analysis for Business introduces students to the fundamental concepts and techniques of analyzing data to inform sound business decisions. The course covers key topics such as data collection, cleaning, visualization, and statistical analysis using tools and software commonly employed in business environments. Students will learn to interpret and present data-driven insights, apply quantitative reasoning to real-world business problems, and develop proficiency in using spreadsheets and data analysis platforms. By the end of the course, students will be equipped to transform raw data into actionable intelligence to support strategic decision-making in various business contexts.
Recommended Textbook
Quantitative Methods for Business 11th Edition by David R. Anderson
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Chapter 1: Introduction
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Q1) A physical model that does not have the same physical appearance as the object being modeled is
A)an analog model.
B)an iconic model.
C)a mathematical model.
D)a qualitative model.
Answer: A
Q2) A university schedules summer school courses based on anticipated enrollment.The cost for faculty compensation,laboratories,student services,and allocated overhead for a computer class is $8500.If students pay $420 to enroll in the course,how large would enrollment have to be for the university to break even?
Answer: Enrollment would need to be 21 students.
Q3) The value of any model is that it enables the user to make inferences about the real situation.
A)True
B)False
Answer: True
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Chapter 2: Introduction to Probability
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Q1) A food distributor carries 64 varieties of salad dressing.Appleton Markets stocks 48 of these flavors.Beacon Stores carries 32 of them.The probability that a flavor will be carried by Appleton or Beacon is 15/16.Use a Venn diagram to find the probability a flavor is carried by both Appleton and Beacon.
Answer: The Venn diagram is 11ea83ec_7737_fe17_bb88_c3f66fdf960e_TB2191_00 and P(A\(\cap\) B)= P(A)+ P(B)- P(A\(\cup\) B)= 6/8 + 4/8 - 15/16 = 5/16 = .3125
Q2) P(A\(\cap\)B)\(\ge\) P(A)
A)True
B)False
Answer: False
Q3) Two events that are mutually exclusive cannot be independent.
A)True
B)False
Answer: True
Q4) A package of candy contains 12 brown,5 red,and 8 green candies.You grab three pieces from the package.Give the sample space of colors you could get.Order is not important.
Answer: Order is not implied: S = {BBB,RRR,GGG,BBR,BBG,RRB,RRG,GGB,GGR,BRG}
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Page 4
Chapter 3: Probability Distributions
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Q1) The standard normal distribution is a normal distribution with a mean of 1 and a standard deviation of 1/3.
A)True
B)False
Answer: False
Q2) A manufacturer of computer disks has a historical defective rate of .001.What is the probability that in a batch of 1000 disks,2 would be defective? Answer: 1840
Q3) The expected value of the discrete random variable x is \(\mu\),a weighted average of all possible values of x.
A)True
B)False
Answer: True
Q4) For an exponentially distributed random variable x with a mean of 8,the probability of x < 8 is .5.
A)True
B)False
Answer: False
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Page 5
Chapter 4: Decision Analysis
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Q1) The expected value of an alternative can never be negative.
A)True
B)False
Q2) Dollar Department Stores has just acquired the chain of Wenthrope and Sons
Custom Jewelers.Dollar has received an offer from Harris Diamonds to purchase the Wenthrope store on Grove Street for $120,000.Dollar has determined probability estimates of the store's future profitability,based on economic outcomes,as: P($80,000)= .2,P($100,000)= .3,P($120,000)= .1,and P($140,000)= .4.
a.Should Dollar sell the store on Grove Street?
b.What is the EVPI?
c.Dollar can have an economic forecast performed,costing $10,000,that produces indicators I<sub>1</sub> and I<sub>2</sub>,for which P(I<sub>1</sub><sub>SYMBOL 189 \f "Symbol"</sub>80,000)= .1;P(I<sub>1</sub><sub>SYMBOL 189 \f "Symbol"</sub>100,000)= .2;P(I<sub>1</sub><sub>SYMBOL 189 \f "Symbol"</sub>120,000)= .6;P(I<sub>1</sub><sub>SYMBOL 189 \f "Symbol"</sub>140,000)= .3.Should Dollar purchase the forecast?
Q3) EVPI equals the expected regret associated with the minimax decision.
A)True
B)False
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Page 6
Chapter 5: Utility and Game Theory
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Q1) The risk neutral decision maker will have the same indications from the expected value and expected utility approaches.
A)True
B)False
Q2) The expected utility approach
A)does not require probabilities.
B)leads to the same decision as the expected value approach.
C)is most useful when excessively large or small payoffs are possible.
D)requires a decision tree.
Q3) A 3 x 3 two-person zero-sum game that has no optimal pure strategy and no dominated strategies
A)can be solved using a linear programming model.
B)can be solved algebraically.
C)can be solved by identifying the minimax and maximin values.
D)cannot be solved.
Q4) When monetary value is not the sole measure of the true worth of the outcome to the decision maker,monetary value should be replaced by utility.
A)True B)False
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Chapter 6: Forecasting
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Q1) Time series methods base forecasts only on past values of the variables.
A)True
B)False
Q2) Using exponential smoothing,the demand forecast for time period 10 equals the demand forecast for time period 9 plus
A)\(\alpha\) times (the demand forecast for time period 8)
B)\(\alpha\) times (the error in the demand forecast for time period 9)
C)\(\alpha\) times (the observed demand in time period 9)
D)\(\alpha\) times (the demand forecast for time period 9)
Q3) The exponential smoothing forecast for any period is a weighted average of all the previous actual values for the time series.
A)True
B)False
Q4) A hospital records the number of floral deliveries its patients receive each day.For a two week period,the records show 15,27,26,24,18,21,26,19,15,28,25,26,17,23
Use exponential smoothing with a smoothing constant of .4 to forecast the number of deliveries.
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Page 8
Chapter 7: Introduction to Linear Programming
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Q1) It is possible to have exactly two optimal solutions to a linear programming problem.
A)True
B)False
Q2) A constraint that does not affect the feasible region is a
A)non-negativity constraint.
B)redundant constraint.
C)standard constraint.
D)slack constraint.
Q3) The constraint 2x<sub>1</sub> - x<sub>2</sub> = 0 passes through the point (200,100).
A)True
B)False
Q4) All linear programming problems have all of the following properties EXCEPT
A)a linear objective function that is to be maximized or minimized.
B)a set of linear constraints.
C)alternative optimal solutions.
D)variables that are all restricted to nonnegative values.
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Chapter 8: Lp Sensitivity Analysis and Interpretation of Solution
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Q1) In a linear programming problem,the binding constraints for the optimal solution are 5X + 3Y < 30
2X + 5Y < 20
a.Fill in the blanks in the following sentence: As long as the slope of the objective function stays between _______ and _______,the current optimal solution point will remain optimal.
b.Which of these objective functions will lead to the same optimal solution?
1)2X + 1Y 2)7X + 8Y 3)80X + 60Y 4)25X + 35Y
Q2) If the range of feasibility for b<sub>1</sub> is between 16 and 37,then if b<sub>1</sub> = 22 the optimal solution will not change from the original optimal solution.
A)True
B)False
Q3) Relevant costs should be reflected in the objective function,but sunk costs should not.
A)True
B)False
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Page 10
Chapter 9: Linear Programming Applications
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Q1) A company makes two products from steel;one requires 2 tons of steel and the other requires 3 tons.There are 100 tons of steel available daily.A constraint on daily production could be written as: 2x<sub>1</sub> + 3x<sub>2</sub> < 100.
A)True
B)False
Q2) Production constraints frequently take the form: beginning inventory + sales - production = ending inventory
A)True
B)False
Q3) The dual price for a constraint that compares funds used with funds available is .058.This means that
A)the cost of additional funds is 5.8%.
B)if more funds can be obtained at a rate of 5.5%,some should be.
C)no more funds are needed.
D)the objective was to minimize.
Q4) A decision maker would be wise to not deviate from the optimal solution found by an LP model because it is the best solution.
A)True
B)False
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Chapter 10: Distribution and Network Problems
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Q1) Draw the network for this assignment problem. Min 10x<sub>1A</sub> + 12x<sub>1B</sub> + 15x<sub>1C</sub> + 25x<sub>1D</sub> + 11x<sub>2A</sub> + 14x<sub>2B</sub> + 19x<sub>2C</sub> + 32x<sub>2D</sub> + 18x<sub>3A </sub> + 21x<sub>3B</sub> + 23x<sub>3C</sub> + 29x<sub>3D</sub> + 15x<sub>4A</sub> + 20x<sub>4B</sub> + 26x<sub>4C</sub> + 28x<sub>4D</sub> s.t.x<sub>1A</sub> + x<sub>1B</sub> + x<sub>1C</sub> + x<sub>1D </sub> = 1 x<sub>2A</sub> + x<sub>2B</sub> + x<sub>2C</sub> + x<sub>2D</sub> = 1 x<sub>3A </sub> + x<sub>3B</sub> + x<sub>3C</sub> + x<sub>3D</sub> = 1 x<sub>4A</sub> + x<sub>4B</sub> + x<sub>4C</sub> + x<sub>4D</sub> = 1 x<sub>1A</sub> + x<sub>2A</sub> + x<sub>3A</sub> + x<sub>4A</sub> = 1 x<sub>1B</sub> + x<sub> 2B</sub> + x<sub>3B</sub> + x<sub>4B</sub> = 1 x<sub>1C</sub> + x<sub>2C</sub> + x<sub>3C</sub> + x<sub>4C</sub> = 1 x<sub>1D</sub> + x<sub>2D</sub> + x<sub>3D</sub> + x<sub>4D</sub> = 1
Q2) A transshipment constraint must contain a variable for every arc entering or leaving the node.
A)True
B)False
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Page 12
Chapter 11: Integer Linear Programming
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Q1) If x<sub>1</sub> + x<sub>2</sub> < 500y<sub>1</sub> and y<sub>1</sub> is 0 - 1,then if y<sub>1</sub> is 0,x<sub>1</sub> and x<sub>2</sub> will be 0.
A)True
B)False
Q2) Rounding the solution of an LP Relaxation to the nearest integer values provides A)a feasible but not necessarily optimal integer solution.
B)an integer solution that is optimal.
C)an integer solution that might be neither feasible nor optimal.
D)an infeasible solution.
Q3) If the acceptance of project A is conditional on the acceptance of project B,and vice versa,the appropriate constraint to use is a A)multiple-choice constraint.
B)k out of n alternatives constraint.
C)mutually exclusive constraint.
D)corequisite constraint.
Q4) The classic assignment problem can be modeled as a 0-1 integer program.
A)True
B)False
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Page 13
Chapter 12: Advanced Optimization Application
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Q1) MegaSports,Inc.produces two high-priced metal baseball bats,the Slugger and the Launcher,that are made from special aluminum and steel alloys.The cost to produce a Slugger bat is $100,and the cost to produce a Launcher bat is $120.We can not assume that MegaSports will sell all the bats it can produce.As the selling price of each bat model - Slugger and Launcher - increases,the quantity demanded for each model goes down.
Assume that the demand,S,for Slugger bats is given by S = 640 - 4P<sub>S</sub> and the demand,L,for Launcher bats is given by L = 450 - 3P<sub>L</sub><sub> </sub>where P<sub>S</sub> is the price of a Slugger bat and P<sub>L</sub> is the price of a Launcher bat.The profit contributions are P<sub>S </sub>S - 100S for Slugger bats and P<sub>L </sub>L - 120L for Launcher bats.Develop the total profit contribution function for this problem.
Q2) The goal of portfolio models is to create a portfolio that provides the best balance between risk and return.
A)True B)False
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Page 14
Chapter 13: Project Scheduling: Pertcpm
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Q1) Slack equals
A)LF - EF.
B)EF - LF.
C)EF - LS.
D)LF - ES.
Q2) When activity times are uncertain,an activity's most likely time is the same as its expected time.
A)True
B)False
Q3) The latest finish time for an activity is the largest of the latest start times for all activities that immediately follow the activity.
A)True
B)False
Q4) Activities with zero slack
A)can be delayed.
B)must be completed first.
C)lie on a critical path.
D)have no predecessors.
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Page 15
Chapter 14: Inventory Models
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Q1) The EOQ model
A)determines only how frequently to order.
B)considers total cost.
C)minimizes both ordering and holding costs.
D)All of the alternatives are correct.
Q2) A weekly sports magazine publishes a special edition for the World Series.The sales forecast is for the number of copies to be normally distributed with mean 800,000 copies and standard deviation 60,000 copies.It costs $.35 to print a copy,and the newsstand price is $1.95.Unsold copies will be scrapped.How many copies should be printed?
Q3) The maximum inventory with backorders is
A)Q
B)Q - S
C)S
D)(Q - S)/ 2
Q4) The Fitness Shop is considering ordering a special model exercise machine.Each unit will cost the shop $410 and it will sell for $750.Any units not sold at the regular price will be sold at the year-end model clearance for $340.Assume that demand follows a normal probability distribution with \(\mu\) = 20 and \(\sigma\) = 6.What is the recommended order quantity?
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Chapter 15: Waiting Line Models
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Q1) The insurance department at Shear's has two agents,each working at a mean speed of 8 customers per hour.Customers arrive at the insurance desk at a mean rate of one every six minutes and form a single queue.
Management feels that some customers are going to find the wait at the desk too long and take their business to Word's,Shear's competitor. In order to reduce the time required by an agent to serve a customer Shear's is contemplating installing one of two minicomputer systems: System A which leases for $18 per day and will increase an agent's efficiency by 25%;or,System B which leases for $23 per day and will increase an agent's efficiency by 50%.Agents work 8-hour days. If Shear's estimates its cost of having a customer in the system at $3 per hour,determine if Shear's should install a new minicomputer system,and if so,which one.
Q2) Use of the Poisson probability distribution assumes that arrivals are not random. A)True B)False
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Chapter 16: Simulation
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Q1) A table of uniformly distributed random numbers should be read
A)from left to right.
B)from top to bottom.
C)diagonally,starting from the top left corner and moving to the bottom right.
D)in any consistent sequence.
Q2) Verification is the process of ensuring that the simulation model provides an accurate representation of the real system.
A)True
B)False
Q3) The word "uniform" in the term "uniform random numbers" means
A)all the numbers have the same number of digits.
B)if one number is,say,10 units above the mean,the next number will be 10 units below the mean.
C)all the numbers are odd or all are even.
D)each number has an equal probability of being drawn.
Q4) Computer-generated random numbers are normally distributed over the interval from 0 to 1.
A)True
B)False
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Chapter 17: Markov Processes
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Q1) In Markov analysis,we are concerned with the probability that the A)state is part of a system.
B)system is in a particular state at a given time.
C)time has reached a steady state.
D)transition will occur.
Q2) All Markov chain transition matrices have the same number of rows as columns.
A)True
B)False
Q3) The probability of reaching an absorbing state is given by the A)R matrix.
B)NR matrix.
C)Q matrix.
D)(I - Q)<sup>-1</sup> matrix
Q4) Analysis of a Markov process
A)describes future behavior of the system.
B)optimizes the system.
C)leads to higher order decision making.
D)All of the alternatives are true.
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