Statistical Methods for Management Study Guide Questions
Course Introduction
Statistical Methods for Management introduces students to the fundamental concepts and techniques of statistics as they apply to managerial decision-making. The course covers descriptive statistics, probability distributions, sampling, hypothesis testing, regression analysis, and analysis of variance (ANOVA), emphasizing their practical use in business scenarios. Students will learn how to analyze data, interpret results, and apply statistical reasoning to solve real-world management problems. Through the use of statistical software and case studies, the course equips future managers with the quantitative skills necessary for informed decision-making in diverse business environments.
Recommended Textbook
Quantitative Methods for Business 12th Edition by David R. Anderson
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Chapter 1: Introduction
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Sample Questions
Q1) To find the choice that provides the highest profit and the fewest employees,apply a single-criterion decision process.
A)True
B)False
Answer: False
Q2) Uncontrollable inputs are the decision variables for a model.
A)True
B)False
Answer: False
Q3) As computer service center has the capacity to do 400 jobs per day.The expected level of jobs demanded per day is 250 per day.The fixed cost of renting the computer process is $200 per day.Space rents for $100 per day.The cost of material is $15 per unit of work and $.35 cents of labor per unit.What is the break-even level of work?
Answer: 200 service units
Q4) The first step in the decision making process is to identify the problem. A)True
B)False
Answer: True
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Chapter 2: Introduction to Probability
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Q1) Super Cola sales breakdown as 80% regular soda and 20% diet soda.While 60% of the regular soda is purchased by men,only 30% of the diet soda is purchased by men.If a woman purchases Super Cola,what is the probability that it is a diet soda?
Answer: .30435
Q2) Mini Car Motors offers its luxury car in three colors: gold,silver and blue.The vice president of advertising is interested in the order of popularity of the color choices by customers during the first month of sales.
a.How many sample points are there in this experiment?
b.If the event A = gold is the most popular color, list the outcome(s) in event A.
c.If the event B = blue is the least popular color, list the outcome(s) in A \(\cap\) B.
d.List the outcome(s) in A \(\cap\) B<sup>c</sup>.
Answer: a.6
b.{(G,S,B),(G,B,S)}
c.{(G,S,B)}
d.{(G,B,S)}
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Chapter 3: Probability Distributions
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Sample Questions
Q1) Experiments with repeated independent trials will be described by the binomial distribution if
A)the trials are continuous.
B)each trial result influences the next.
C)the time between trials is constant.
D)each trial has exactly two outcomes whose probabilities do not change.
Answer: D
Q2) The expected value of the discrete random variable x is F1F1F1S1 F1F1F10,a weighted average of all possible values of x.
A)True
B)False
Answer: True
Q3) An exponential distribution,like the Poisson distribution,can be described by a single parameter.
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 optimistic approach is often referred to as the
A)minimax approach
B)maximin approach
C)maximax approach
D)minimin approach
Q2) The difference between the expected value of an optimal strategy based on sample information and the "best" expected value without any sample information is called the
A)information sensitivity
B)expected value of sample information
C)expected value of perfect information
D)efficiency of sample information
Q3) The approach to determine the optimal decision strategy involves
A)a forward (left to right) pass through the decision tree
B)a backward (right to left) pass through the decision tree
C)choosing the outcome of a chance event with the greatest probability
D)choosing the outcome of a chance event with the greatest payoff
Q4) Square nodes in a decision tree indicate that a decision must be made.
A)True
B)False
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Chapter 5: Utility and Game Theory
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Q1) 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.
Q2) For a game with an optimal pure strategy,which of the following statements is false?
A)The maximin equals the minimax.
B)The value of the game cannot be improved by either player changing strategies.
C)A saddle point exists.
D)Dominated strategies cannot exist.
Q3) When the decision maker prefers a guaranteed payoff value that is smaller than the expected value of the lottery,the decision maker is
A)a risk avoider.
B)a risk taker.
C)an optimist.
D)an optimizer.
Q4) Explain the relationship between expected utility,probability,payoff,and utility.
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Chapter 6: Times Series Analysis and Forecasting
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Sample Questions
Q1) Seasonal patterns
A)cannot be predicted.
B)are regular repeated patterns.
C)are multiyear runs of observations above or below the trend line.
D)reflect a shift in the time series over time.
Q2) The average SAT verbal score for students from one high school over the last ten exams is
508,490,502,505,493,506,492,490,503,501
Do the scores support an increasing or a decreasing trend?
Q3) The trend pattern is easy to identify by using
A)a moving average
B)exponential smoothing
C)regression analysis
D)a weighted moving average
Q4) With fewer periods in a moving average,it will take longer to adjust to a new level of data values.
A)True
B)False
Q5) Explain what conditions make quantitative forecasting methods appropriate.
Page 8
Q6) Explain and contrast three measures of forecast accuracy.
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Chapter 7: Introduction to Linear Programming
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Sample Questions
Q1) Does the following linear programming problem exhibit infeasibility,unboundedness,or alternate optimal solutions? Explain.
\[\begin{array} { l l }
\text { Min } & 3 x + 3 y \\
\text { s.t. } & 1 x + 2 y \leq 16 \\ & 1 x + 1 y \leq 10 \\ & 5 x + 3 y \leq 45 \\ & x , y \geq 0
\end{array}\]
Q2) The standard form of a linear programming problem will have the same solution as the original problem.
A)True
B)False
Q3) The constraint 2x<sub>1</sub> F1F1F1S1 F1F1F10 x<sub>2</sub> = 0 passes through the point (200,100).
A)True
B)False
Q4) Explain the concepts of proportionality,additivity,and divisibility.
Q5) Explain what to look for in problems that are infeasible or unbounded.
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Chapter 8: Linear Programming: Sensitivity Analysis and Interpretation of Solution
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Sample Questions
Q1) A section of output from The Management Scientist is shown here. \[\begin{array} { c c c c }
\text { Constraint } & \text { Lower Limit } & \text { Current Value } & \text { Upper Limit } \\
\hline 2 & 240 & 300 & 420 \end{array}\] What will happen if the right-hand-side for constraint 2 increases by 200?
A)Nothing. The values of the decision variables, the dual prices, and the objective function will all remain the same.
B)The value of the objective function will change, but the values of the decision variables and the dual prices will remain the same.
C)The same decision variables will be positive, but their values, the objective function value, and the dual prices will change.
D)The problem will need to be resolved to find the new optimal solution and dual price.
Q2) Explain the two interpretations of dual prices based on the accounting assumptions made in calculating the objective function coefficients.
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Chapter 9: Linear Programming Applications in Marketing, Finance,
and Operations
Management
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Sample Questions
Q1) FarmFresh Foods manufactures a snack mix called TrailTime by blending three ingredients: a dried fruit mixture,a nut mixture,and a cereal mixture.Information about the three ingredients (per ounce)is shown below. \[\begin{array} { l r c c c }
\text { Ingredient } & \text { Cost } & \text { Volume } & \text { Fat Grams } & \text { Calories } \\
\hline \text { Dried Fruit } & .35 & 1 / 4 \mathrm { cup } & 0 & 150 \\
\text { Nut Mix } & .50 & 3 / 8 \mathrm { cup } & 10 & 400 \\
\text { Cereal Mix } & .20 & 1 \mathrm { cup } & 1 & 50
\end{array}\] The company needs to develop a linear programming model whose solution would tell them how many ounces of each mix to put into the TrailTime blend.TrailTime is packaged in boxes that will hold between three and four cups.The blend should contain no more than 1000 calories and no more than 25 grams of fat.Dried fruit must be at least 20% of the volume of the mixture,and nuts must be no more than 15% of the weight of the mixture.Develop a model that meets these restrictions and minimizes the cost of the blend.
Q2) Discuss the need for the use of judgment or other subjective methods in mathematical modeling.
Q3) Describe some common feature of multiperiod financial planning models.
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Chapter 10: Distribution and Network Models
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Sample Questions
Q1) In a transportation problem with total supply equal to total demand,if there are four origins and seven destinations,and there is a unique optimal solution,the optimal solution will utilize 11 shipping routes.
A)True
B)False
Q2) If a transportation problem has four origins and five destinations,the LP formulation of the problem will have nine constraints.
A)True
B)False
Q3) The assignment problem is a special case of the transportation problem in which all supply and demand values equal one.
A)True
B)False
Q4) The parts of a network that represent the origins are
A)the capacities
B)the flows
C)the nodes
D)the arcs
Q5) Is it a coincidence to obtain integer solutions to network problems? Explain.
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Chapter 11: Integer Linear Programming
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Sample Questions
Q1) Let x<sub>1</sub> and x<sub>2</sub> be 0 - 1 variables whose values indicate whether projects 1 and 2 are not done or are done.Which answer below indicates that project 2 can be done only if project 1 is done?
A)x<sub>1</sub> + x<sub>2</sub> = 1
B)x<sub>1</sub> + x<sub>2</sub> = 2
C)x<sub>1</sub> F1F1F1S1 F1F1F10 x<sub>2</sub> F1F1F1S1 F1F1F10 0
D)x<sub>1</sub> F1F1F1S1 F1F1F10 x<sub>2</sub> F1F1F1S1 F1F1F10 0
Q2) 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.
Q3) The 0-1 variables in the fixed cost models correspond to
A)a process for which a fixed cost occurs.
B)the number of products produced.
C)the number of units produced.
D)the actual value of the fixed cost.
Q4) Explain how integer and 0-1 variables can be used in a constraint to enable production.
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Chapter 12: Advanced Optimization Applications
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Sample Questions
Q1) 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
Q2) In portfolio models,risk is minimized by diversification.
A)True
B)False
Q3) Explain how the local minimum,local maximum,local optimum,global minimum,global maximum,and global optimum relate to one another in nonlinear optimization problems.
Q4) Modern revenue management systems maximize revenue potential for an organization by helping to manage
A)pricing strategies.
B)reservation policies.
C)short-term supply decisions.
D)All of the alternatives are correct.
Q5) List several industries in which revenue management has been applied and list several different types of decisions being made with the aid of the methodology.
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Chapter 13: Project Scheduling: Pertcpm
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Sample Questions
Q1) Activities with zero slack
A)can be delayed.
B)must be completed first.
C)lie on a critical path.
D)have no predecessors.
Q2) Activities require time to complete while events do not.
A)True
B)False
Q3) Name at least three managerial situations where answers are provided by project management solutions.
Q4) Slack equals
A)LF F1F1F1S1 F1F1F10 EF.
B)EF F1F1F1S1 F1F1F10 LF.
C)EF F1F1F1S1 F1F1F10 LS.
D)LF F1F1F1S1 F1F1F10 ES.
Q5) PERT and CPM are applicable only when there is no dependence among activities.
A)True B)False
Q6) Explain how and why all successor activities must be considered when finding the latest finish time.
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Chapter 14: Inventory Models
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Sample Questions
Q1) 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 F1F1F1S1 F1F1F10 annual backordering cost.
Q2) To be considered as inventory,goods must be finished and waiting for delivery.
A)True B)False
Q3) Chez Paul Restaurant orders special Styrofoam "doggy bags" for its customers once a month and lead time is one week.Weekly demand for doggy bags is approximately normally distributed with an average of 120 bags and a standard deviation of 25.Chez Paul wants at most a 3% chance of running out of doggy bags during the replenishment period.If he has 150 bags in stock when he places an order,how many additional bags should he order? What is the safety stock in this case?
Q4) As lead time for an item increases,the cycle time increases.
A)True B)False
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Chapter 15: Waiting Line Models
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Sample Questions
Q1) Which of the following can not be found by the queuing formulas presented in the textbook?
A)the probability that no units are in the system.
B)the average number of units in the system.
C)the maximum time a unit spends in the system.
D)the average time a unit spends in the system.
Q2) Use of the Poisson probability distribution assumes that arrivals are not random.
A)True
B)False
Q3) Diagram the servers and arrivals in the single- and multiple-channel models.Designate the line and the system.
Q4) The equations provided in the textbook for computing operating characteristics apply to a waiting line operating
A)at start-up
B)at steady-state
C)under optimal conditions
D)in transition
Q5) How can a system be changed to improve the service rate?
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Chapter 16: Simulation
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Q1) Simulation is an excellent technique to use when a situation is too complicated to use standard analytical procedures.
A)True
B)False
Q2) One disadvantage of simulation is that it is limited in the variety of probability distributions that can be used in modeling a system.
A)True
B)False
Q3) Simulation is an optimization technique.
A)True
B)False
Q4) The process of generating probabilistic inputs and computing the value of the output is called A)simulation.
B)verification.
C)validation.
D)implementation.
Q5) Why would one want to use a general purpose programming language rather than a spreadsheet to develop a simulation?
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Chapter 17: Markov Processes
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Q1) At steady state
A)F1F1F1S1 F1F1F10<sub>1</sub>(n + 1) > F1F1F1S1 F1F1F10<sub>1</sub>(n)
B)F1F1F1S1 F1F1F10<sub>1</sub> = F1F1F1S1 F1F1F10<sub>2</sub>
C)F1F1F1S1 F1F1F10<sub>1</sub> + F1F1F1S1 F1F1F10<sub>2</sub> F1F1F1S1 F1F1F10 1
D)F1F1F1S1 F1F1F10<sub>1</sub>(n + 1) = F1F1F1S1 F1F1F10<sub>1</sub>
Q2) The sum of the probabilities in a transition matrix equals the number of rows in the matrix.
A)True
B)False
Q3) The probability that the system is in state 2 in the 5th period is F1F1F1S1 F1F1F10<sub>5</sub>(2).
A)True
B)False
Q4) A transition probability describes
A)the probability of a success in repeated, independent trials.
B)the probability a system in a particular state now will be in a specific state next period.
C)the probability of reaching an absorbing state.
D)None of the alternatives is correct.
Q5) Explain the concept of memorylessness.
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