Advanced Business Statistics
Study Guide Questions
Course Introduction
Advanced Business Statistics explores sophisticated statistical methods and their applications in solving complex business problems. The course covers topics such as multivariate analysis, regression models, time series analysis, hypothesis testing, and statistical quality control. Emphasis is placed on the interpretation of data, utilization of appropriate statistical software, and the integration of statistical findings into business decision-making. Through case studies and real-world business datasets, students will develop analytical skills to support evidence-based strategies and drive organizational success.
Recommended Textbook
Quantitative Methods for Business 11th Edition by David R. Anderson
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Page 2
Chapter 1: Introduction
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Sample Questions
Q1) In a multicriteria decision problem
A)it is impossible to select a single decision alternative.
B)the decision maker must evaluate each alternative with respect to each criterion.
C)successive decisions must be made over time.
D)each of the above is true.
Answer: B
Q2) An author has received an advance against royalties of $10,000.The royalty rate is $1.00 for every book sold in the United States,and $1.35 for every book sold outside the United States.Define variables for this problem and write an expression that could be used to calculate the number of books to be sold to cover the advance.
Answer: Let x<sub>1</sub> = the number of books sold in the U.S. Let x<sub>2</sub> = the number of books sold outside the U.S. 10000 = 1x<sub>1</sub> + 1.35x<sub>2</sub>
Q3) The most successful quantitative analysis will separate the analyst from the managerial team until after the problem is fully structured.
A)True
B)False
Answer: False
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Chapter 2: Introduction to Probability
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Sample Questions
Q1) If P(A)= 0.38,P(B)= 0.83,and P(A \(\cap\) B)= 0.27;then P(A \(\cup\) B)=
A)1.21
B)0.94
C)0.72
D)1.48
Answer: B
Q2) When assigning subjective probabilities,use experience,intuition,and any available data.
A)True
B)False Answer: True
Q3) If A and B are independent events,then P(A\(\cap\)B)= P(A)P(B).
A)True
B)False Answer: True
Q4) P(A|B)= P(A<sup>C</sup>|B)for all events A and B.
A)True
B)False Answer: True
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Chapter 3: Probability Distributions
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Sample Questions
Q1) The probability of a continuous variable having a specific value is 0.
A)True
B)False
Answer: True
Q2) Which of the following are continuous random variables? I.the weight of an elephant II)the time to answer a questionnaire
III)the number of floors in a skyscraper
IV)the square feet of countertop in a kitchen
A)I and II only
B)III and IV only
C)I,II and IV
D)I,II,II,and IV
Answer: C
Q3) Whenever the probability is proportional to the length of the interval,the random variable is uniformly distributed.
A)True
B)False
Answer: True
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Chapter 4: Decision Analysis
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Sample Questions
Q1) For a maximization problem,the conservative approach is often referred to as the A)minimax approach
B)maximin approach
C)maximax approach
D)minimin approach
Q2) Decision alternatives are structured so that several could occur simultaneously.
A)True
B)False
Q3) Square nodes in a decision tree indicate that a decision must be made.
A)True
B)False
Q4) The expected value approach is more appropriate for a one-time decision than a repetitive decision.
A)True
B)False
Q5) For a minimization problem,the optimistic approach is often referred to as the A)minimax approach
B)maximin approach
C)maximax approach
D)minimin approach
6
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Chapter 5: Utility and Game Theory
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Sample Questions
Q1) For a two-person zero-sum game,which one of the following is false?
A)The gain for one player is equal to the loss for the other player.
B)A payoff of 2 for one player has a corresponding payoff of -2 for the other player.
C)The sum of the payoffs in the payoff table is zero.
D)What one player wins,the other player loses.
Q2) The logic of game theory assumes that each player has different information.
A)True B)False
Q3) The outcome with the highest payoff will also have the highest utility.
A)True
B)False
Q4) 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.
Q5) The expected utility is the utility of the expected monetary value.
A)True
B)False
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Chapter 6: Forecasting
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Sample Questions
Q1) Use a four period moving average to forecast attendance at baseball games.Historical records show 5346,7812,6513,5783,5982,6519,6283,5577,6712,7345
Q2) The number of pizzas ordered on Friday evenings between 5:30 and 6:30 at a pizza delivery location for the last 10 weeks is shown below.Use exponential smoothing with smoothing constants of .2 and .8 to forecast a value for week 11.Compare your forecasts using MSE.Which smoothing constant would you prefer?
58,46,55,39,42,63,54,55,61,52
Q3) If data for a time series analysis is collected on an annual basis only,which component may be ignored?
A)trend
B)seasonal
C)cyclical
D)irregular
Q4) To make period-to-period comparisons more meaningful and identify trend,the time series should be deseasonalized.
A)True
B)False
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Page 8
Chapter 7: Introduction to Linear Programming
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Sample Questions
Q1) Consider the following linear programming problem
Max 8X + 7Y
s.t.15X + 5Y < 75
10X + 6Y < 60
X + Y < 8
X,Y \(\ge\) 0
a.Use a graph to show each constraint and the feasible region.
b.Identify the optimal solution point on your graph.What are the values of X and Y at the optimal solution?
c.What is the optimal value of the objective function?
Q2) Find the complete optimal solution to this linear programming problem.
Max 2X + 3Y<sub> </sub>
s.t.4X + 9Y < 72
10X + 11Y < 110
17X + 9Y < 153
X<sub> </sub>,Y > 0
Q3) An optimal solution to a linear programming problem can be found at an extreme point of the feasible region for the problem.
A)True
B)False
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Chapter 8: Lp Sensitivity Analysis and Interpretation of Solution
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Sample Questions
Q1) The reduced cost for a positive decision variable is 0.
A)True
B)False
Q2) The optimal solution of the linear programming problem is at the intersection of constraints 1 and 2.
Max 2x<sub>1</sub> + x<sub>2</sub> s.t.4x<sub>1</sub> + 1x<sub>2</sub> < 400
4x<sub>1</sub> + 3x<sub>2</sub> < 600 1x<sub>1</sub> + 2x<sub>2</sub> \(\le\) 300 x<sub>1</sub> ,x<sub>2</sub> > 0
a.Over what range can the coefficient of x<sub>1</sub> vary before the current solution is no longer optimal?
b.Over what range can the coefficient of x<sub>2</sub> vary before the current solution is no longer optimal?
c.Compute the dual prices for the three constraints.
Q3) There is a dual price for every decision variable in a model.
A)True B)False
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Chapter 9: Linear Programming Applications
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Sample Questions
Q1) 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
Q2) Revenue management methodology was originally developed for the banking industry.
A)True
B)False
Q3) Double-subscript notation for decision variables should be avoided unless the number of decision variables exceeds nine.
A)True
B)False
Q4) Compared to the problems in the textbook,real-world problems generally require more variables and constraints.
A)True
B)False
Q5) Portfolio selection problems should acknowledge both risk and return.
A)True
B)False
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Chapter 10: Distribution and Network Problems
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Sample Questions
Q1) A dummy origin in a transportation problem is used when supply exceeds demand.
A)True
B)False
Q2) We assume in the maximal flow problem that
A)the flow out of a node is equal to the flow into the node.
B)the source and sink nodes are at opposite ends of the network.
C)the number of arcs entering a node is equal to the number of arcs exiting the node.
D)None of the alternatives is correct.
Q3) A transshipment constraint must contain a variable for every arc entering or leaving the node.
A)True
B)False
Q4) A transportation problem with 3 sources and 4 destinations will have 7 decision variables.
A)True B)False
Q5) The shortest-route problem is a special case of the transshipment problem.
A)True B)False
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Chapter 11: Integer Linear Programming
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Sample Questions
Q1) In an all-integer linear program,
A)all objective function coefficients must be integer.
B)all right-hand side values must be integer.
C)all variables must be integer.
D)all objective function coefficients and right-hand side values must be integer.
Q2) 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.
Q3) The constraint x<sub>1</sub> - x<sub>2</sub> = 0 implies that if project 1 is selected,project 2 cannot be.
A)True
B)False
Q4) Slack and surplus variables are not useful in integer linear programs.
A)True
B)False
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13
Chapter 12: Advanced Optimization Application
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Q1) The function f (X,Y)= X <sup>2</sup> + Y <sup>2</sup> has a single global minimum and is relatively easy to minimize.
A)True
B)False
Q2) A nonlinear optimization problem is any optimization problem in which at least one term in the objective function or a constraint is nonlinear.
A)True
B)False
Q3) The overall goal of portfolio models is to create a portfolio that provides the best balance between
A)short-term and long-term investments.
B)gains and losses.
C)risk and return.
D)liquidity and stability.
Q4) A key trade-off in most portfolio optimization models must be made between risk and return.
A)True
B)False
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Page 14
Chapter 13: Project Scheduling: Pertcpm
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Sample Questions
Q1) Activities K,M and S immediately follow activity H,and their latest start times are 14,18,and 11.The latest finish time for activity H
A)is 11.
B)is 14.
C)is 18.
D)cannot be determined.
Q2) Slack equals
A)LF - EF.
B)EF - LF.
C)EF - LS.
D)LF - ES.
Q3) PERT and CPM are applicable only when there is no dependence among activities.
A)True
B)False
Q4) When activity times are uncertain,
A)assume they are normally distributed.
B)calculate the expected time,using (a + 4m + b)/6.
C)use the most likely time.
D)calculate the expected time,using (a + m + b)/3.
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Chapter 14: Inventory Models
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Sample Questions
Q1) The cost of overestimating demand is usually harder to determine than the cost of underestimating demand.
A)True
B)False
Q2) The terms "inventory on hand" and "inventory position" have the same meaning.
A)True
B)False
Q3) For the inventory model with planned shortages,the optimal order quantity results in
A)annual holding cost = annual ordering cost.
B)annual holding cost = annual backordering cost.
C)annual ordering cost = annual holding cost + annual backordering cost.
D)annual ordering cost = annual holding cost - annual backordering cost.
Q4) The objective of the EOQ with quantity discounts model is to
A)determine the minimum order quantity required for the maximum discount.
B)balance annual ordering and holding costs.
C)minimize annual purchase cost.
D)minimize the sum of annual carrying,holding,and purchase costs.
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Chapter 15: Waiting Line Models
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Sample Questions
Q1) For a single-server queuing system,the average number of customers in the waiting line is one less than the average number in the system.
A)True
B)False
Q2) When a waiting system is in steady-state operation,the number of units in the system is not changing.
A)True
B)False
Q3) Operating characteristics formulas for the single-channel queue do NOT require A)\(\lambda\) >\(\mu\).
B)Poisson distribution of arrivals.
C)an exponential distribution of service times.
D)an FCFS queue discipline.
Q4) The arrival rate in queuing formulas is expressed as
A)the mean time between arrivals.
B)the minimum number of arrivals per time period.
C)the mean number of arrivals per channel.
D)the mean number of arrivals per time period.
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Chapter 16: Simulation
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Q1) A simulation model used in situations where the state of the system at one point in time does not affect the state of the system at future points in time is called a
A)dynamic simulation model.
B)static simulation model.
C)steady-state simulation model.
D)discrete-event simulation model.
Q2) In a Monte Carlo simulation,each simulation trial is dependent upon the result of a previous trial.
A)True
B)False
Q3) Using simulation to perform risk analysis is like playing out many what-if scenarios by randomly generating values for the probabilistic inputs.
A)True
B)False
Q4) The degree of risk is associated with the probability or magnitude of loss.
A)True
B)False
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Chapter 17: Markov Processes
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Q1) If an absorbing state exists,then the probability that a unit will ultimately move into the absorbing state is given by the steady state probability.
A)True
B)False
Q2) Markov processes use historical probabilities.
A)True
B)False
Q3) A state i is a transient state if there exists a state j that is reachable from i,but the state i is not reachable from state j.
A)True
B)False
Q4) When absorbing states are present,each row of the transition matrix corresponding to an absorbing state will have a single 1 and all other probabilities will be 0.
A)True
B)False
Q5) All entries in a matrix of transition probabilities sum to 1.
A)True
B)False
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