Applied Business Statistics
Question Bank
Course Introduction
Applied Business Statistics introduces students to the fundamental concepts and tools used in the collection, analysis, and interpretation of data within a business context. The course covers topics such as descriptive statistics, probability distributions, sampling methods, hypothesis testing, regression analysis, and statistical inference. Emphasizing practical application, students learn to utilize statistical software and real-world business data to inform decision-making, solve problems, and support strategic business objectives. Through case studies and hands-on projects, the course equips students with the quantitative skills necessary to analyze trends, forecast outcomes, and make evidence-based recommendations in various 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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Q1) As part of their application for a loan to buy Lakeside Farm,a property they hope to develop as a bed-and-breakfast operation,the prospective owners have projected: Monthly fixed cost (loan payment, taxes, insurance, maintenance)\(\quad\$ 6000\)
Variable cost per occupied room per night\(\quad\quad\quad\quad\quad\quad\quad\quad\quad\$ 20\)
Revenue per occupied room per night\(\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\$ 75\)
a.Write the expression for total cost per month. Assume 30 days per month.
b.Write the expression for total revenue per month.
c.If there are 12 guest rooms available, can they break even? What percentage of rooms would need to be occupied, on average, to break even?
Answer: a.C(x)= 6000 + 20(30)x (monthly)
b.R(x)= 75(30)x (monthly)
c.Break-even occupancy = 3.64 or 4 occupied rooms per night,so they have enough rooms to break even.This would be a 33% occupancy rate.
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Chapter 2: Introduction to Probability
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Q1) The intersection of A and A<sup>c</sup> is the entire sample space.
A)True
B)False
Answer: False
Q2) If P(A|B)= .4,then
A)P(B|A) = .6
B)P(A)*P(B) = .4
C)P(A) / P(B) = .4
D)None of the alternatives is correct.
Answer: D
Q3) It is estimated that 3% of the athletes competing in a large tournament are users of an illegal drug to enhance performance.The test for this drug is 90% accurate.What is the probability that an athlete who tests positive is actually a user?
Answer: .2177
Q4) If P(A|B)= .4 and P(B)= .6,then P(A \(\cap\) B)= .667.
A)True
B)False
Answer: False
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Chapter 3: Probability Distributions
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Sample Questions
Q1) The binomial distribution is appropriate to use to find the probability of the elapsed time between successes.
A)True
B)False
Answer: False
Q2) Customers at a popular restaurant that refuses reservations arrive according to the Poisson distribution at a rate of 4 parties every 5 minutes.What is the probability that there will be more than 2 minutes between arriving parties?
Answer: .2019
Q3) If one wanted to find the probability of ten customer arrivals in an hour at a service station,one would generally use the Poisson distribution.
A)True
B)False
Answer: True
Q4) The probability of a continuous variable having a specific value is 0.
A)True
B)False
Answer: True
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Chapter 4: Decision Analysis
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Sample Questions
Q1) A decision tree
A)presents all decision alternatives first and follows them with all states of nature.
B)presents all states of nature first and follows them with all decision alternatives.
C)alternates the decision alternatives and states of nature.
D)arranges decision alternatives and states of nature in their natural chronological order.
Q2) If P(high)= .3,P(low)= .7,P(favorable | high)= .9,and P(unfavorable | low)= .6,then P(favorable)=
A).10
B).27
C).30
D).55
Q3) For a maximization problem,the conservative approach is often referred to as the A)minimax approach
B)maximum approach
C)maximax approach
D)minimin approach
Q4) How can a good decision maker "improve" luck?
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Chapter 5: Utility and Game Theory
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Q1) When consequences are measured on a scale that reflects a decision maker's attitude toward profit,loss,and risk,payoffs are replaced by A)utility values.
B)multicriteria measures.
C)sample information.
D)opportunity loss.
Q2) Given two decision makers,one risk neutral and the other a risk avoider,the risk avoider will always give a lower utility value for a given outcome.
A)True
B)False
Q3) Give two examples of situations where you have decided on a course of action that did not have the highest expected monetary value.
Q4) 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 F1F1F1S1 F1F1F102 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.
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Chapter 6: Times Series Analysis and Forecasting
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Sample Questions
Q1) Below you are given information on John's Hair Salon profit for the past 7 years.
\[\begin{array} { c c }
\text { Year } & \text { Profit (In Thousands) } \\
1 & 15.0 \\
2 & 16.2 \\
3 & 17.1 \\
4 & 18.1 \\
5 & 18.8 \\
6 & 19.2 \\
7 & 20.5
\end{array}\]
a. Use regression analysis to obtain an expression for the linear trend projection.
b. Forecast John's Hair Salon profit for the next 5 years.
Q2) All of the following are true about time series methods except
A)They discover a pattern in historical data and project it into the future.
B)They involve the use of expert judgment to develop forecasts.
C)They assume that the pattern of the past will continue into the future.
D)Their forecasts are based solely on past values of the variable or past forecast errors.
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Chapter 7: Introduction to Linear Programming
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Sample Questions
Q1) Only binding constraints form the shape (boundaries)of the feasible region.
A)True
B)False
Q2) Muir Manufacturing produces two popular grades of commercial carpeting among its many other products.In the coming production period,Muir needs to decide how many rolls of each grade should be produced in order to maximize profit.Each roll of Grade X carpet uses 50 units of synthetic fiber,requires 25 hours of production time,and needs 20 units of foam backing.Each roll of Grade Y carpet uses 40 units of synthetic fiber,requires 28 hours of production time,and needs 15 units of foam backing. The profit per roll of Grade X carpet is $200 and the profit per roll of Grade Y carpet is $160.In the coming production period,Muir has 3000 units of synthetic fiber available for use.Workers have been scheduled to provide at least 1800 hours of production time (overtime is a possibility).The company has 1500 units of foam backing available for use. Develop and solve a linear programming model for this problem.
Q3) Increasing the right-hand side of a nonbinding constraint will not cause a change in the optimal solution.
A)True
B)False
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Chapter 8: Linear Programming: Sensitivity Analysis and Interpretation of Solution
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Q1) For any constraint,either its slack/surplus value must be zero or its dual price must be zero.
A)True
B)False
Q2) The 100 percent rule can be applied to changes in both objective function coefficients and right-hand sides at the same time. A)True
B)False
Q3) There is a dual price for every decision variable in a model. A)True B)False
Q4) The dual price measures,per unit increase in the right hand side, A)the increase in the value of the optimal solution. B)the decrease in the value of the optimal solution. C)the improvement in the value of the optimal solution. D)the change in the value of the optimal solution.
Q5) How is sensitivity analysis used in linear programming? Given an example of what type of questions that can be answered.
10
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Chapter 9: Linear Programming Applications in Marketing, Finance, and
Operations
Management
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Q1) A marketing research firm must determine how many daytime interviews (D)and evening interviews (E)to conduct.At least 40% of the interviews must be in the evening.A correct modeling of this constraint is: -0.4D + 0.6E > 0.
A)True
B)False
Q2) Double-subscript notation for decision variables should be avoided unless the number of decision variables exceeds nine.
A)True
B)False
Q3) Let A,B,and C be the amounts invested in companies A,B,and C.If no more than 50% of the total investment can be in company B,then
A)B F1F1F1S1 F1F1F10 5
B)A F1F1F1S1 F1F1F10 .5B + C F1F1F1S1 F1F1F10 0
C).5A F1F1F1S1 F1F1F10 B F1F1F1S1 F1F1F10 .5C F1F1F1S1 F1F1F10 0
D)F1F1F1S1 F1F1F10.5A + .5B F1F1F1S1 F1F1F10 .5C F1F1F1S1 F1F1F10 0
Q4) Production constraints frequently take the form: beginning inventory + sales F1F1F1S1 F1F1F10 production = ending inventory
A)True
B)False
Page 11
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Chapter 10: Distribution and Network Models
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Sample Questions
Q1) Consider a shortest route problem in which a bank courier must travel between branches and the main operations center.When represented with a network,
A)the branches are the arcs and the operations center is the node.
B)the branches are the nodes and the operations center is the source.
C)the branches and the operations center are all nodes and the streets are the arcs.
D)the branches are the network and the operations center is the node.
Q2) When a route in a transportation problem is unacceptable,the corresponding variable can be removed from the LP formulation.
A)True
B)False
Q3) The shortest-route problem is a special case of the transshipment problem. A)True
B)False
Q4) How is the assignment linear program different from the transportation model?
Q5) Explain how the general linear programming model of the assignment problem can be modified to handle problems involving a maximization function,unacceptable assignments,and supply not equally demand.
Q6) 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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Q1) In a model,x<sub>1</sub> F1F1F1S1 F1F1F10 0 and integer,x<sub>2</sub> F1F1F1S1 F1F1F10 0,and x<sub>3</sub> = 0,1.Which solution would not be feasible?
A)x<sub>1</sub> = 5, x<sub>2</sub> = 3, x<sub>3</sub> = 0
B)x<sub>1</sub> = 4, x<sub>2</sub> = .389, x<sub>3</sub> = 1
C)x<sub>1</sub> = 2, x<sub>2</sub> = 3, x<sub>3</sub> = .578 D)x<sub>1</sub> = 0, x<sub>2</sub> = 8, x<sub>3</sub> = 0
Q2) If a problem has only less-than-or-equal-to constraints with positive coefficients for the variables,rounding down will always provide a feasible integer solution.
A)True
B)False
Q3) The solution to the LP Relaxation of a minimization problem will always be less than or equal to the value of the integer program minimization problem.
A)True
B)False
Q4) Why are 0 - 1 variables sometimes called logical variables?
Q5) The classic assignment problem can be modeled as a 0-1 integer program.
A)True
B)False
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Chapter 12: Advanced Optimization Applications
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Q1) Native Customs sells two popular styles of hand-sewn footwear: a sandal and a moccasin.The cost to make a pair of sandals is $18,and the cost to make a pair of moccasins is $24.The demand for these two items is sensitive to the price,and historical data indicate that the monthly demands are given by S = 400 F1F1F1S1 F1F1F10 10P<sub>1</sub> and M = 450 F1F1F1S1 F1F1F10 15P<sub>2 </sub>,where S = demand for sandals (in pairs),M = demand for moccasins (in pairs),P<sub>1</sub> = price for a pair of sandals,and P<sub>2</sub> = price for a pair of moccasins.To remain competitive,Native Customs must limit the price (per pair)to no more than $60 and $75 for its sandals and moccasins,respectively.Formulate this nonlinear programming problem to find the optimal production quantities and prices for sandals and moccasins that maximize total monthly profit.
Q2) Write a summary of the DEA approach and explain how you would interpret the solution.
Q3) Because most nonlinear optimization codes will terminate with a local optimum,the solution returned by the codes will be the best solution.
A)True
B)False
Q4) Explain the differences between the LP formulations for a conservative portfolio and moderate-risk portfolio.
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Chapter 13: Project Scheduling: Pertcpm
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Q1) Critical activities are those that can be delayed without delaying the entire project.
A)True
B)False
Q2) In deciding which activities to crash,one must
A)crash all critical activities.
B)crash largest-duration activities.
C)crash lowest-cost activities.
D)crash activities on the critical path(s) only.
Q3) 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.
Q4) The earliest finish time for the final activity is the project duration.
A)True
B)False
Q5) Why should projects be monitored after the critical path is found?
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Chapter 14: Inventory Models
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Q1) 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 F1F1F1S1 F1F1F10 = 20 and F1F1F1S1 F1F1F10 = 6.What is the recommended order quantity?
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) Bank Drugs sells Jami Michelle lipstick.The Jami Michelle Company offers a 6% discount on orders of at least 500 tubes,a 10% discount on orders of at least 1,000 tubes,a 12% discount on orders of at least 1,800 tubes and a 15% discount on orders at least 2,500 tubes.
Bank sells an average of 40 tubes of Jami Michelle lipstick weekly.The normal price paid by Bank drugs is $1 per tube.If it costs Bank $30 to place an order,and Bank's annual holding cost rate is 27%,determine the optimal order policy for Bank Drugs.
Q4) Derive and explain the total cost expression for the EOQ model.
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Chapter 15: Waiting Line Models
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Q1) 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 server.
D)the mean number of arrivals per time period.
Q2) The assumption of exponentially distributed service times indicates that
A)37% of the service times are less than the mean service time.
B)50% of the service times are less than the mean service time.
C)63% of the service times are less than the mean service time.
D)service time increase at an exponential rate as the waiting line grows.
Q3) Little's flow equations
A)require Poisson and exponential assumptions.
B)are applicable to any waiting line model.
C)require independent calculation of W, L, W<sub>q</sub>, and L<sub>q</sub>.
D)All of the alternatives are correct.
Q4) If some maximum number of customers is allowed in a queuing system at one time,the system has a finite calling population.
A)True
B)False
Q5) How can a system be changed to improve the service rate?
Page 17
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Chapter 16: Simulation
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Q1) If customer 2 has a service time of 1.6,and if customer 3 has an interarrival time of 1.1 and a service time of 2.3,when will customer 3's service be completed?
A)5.0
B)3.9
C)3.4
D)There is not enough information to answer.
Q2) Each simulation run provides only a sample of how the real system will operate.
A)True
B)False
Q3) A static simulation model is used in situations where the state of the system affects how the system changes or evolves over time.
A)True
B)False
Q4) Computer-generated random numbers are not technically random.
A)True
B)False
Q5) How can historical information be used to create discrete probability distributions?
Q6) How are both analysts and managers involved in the validation process?
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Chapter 17: Markov Processes
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Q1) 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.
Q2) A state,i,is an absorbing state if,when i = j,p<sub>ij</sub> = 1.
A)True B)False
Q3) The probability of going from state 1 in period 2 to state 4 in period 3 is
A)p<sub>12</sub>
B)p<sub>23</sub>
C)p<sub>14</sub>
D)p<sub>43</sub>
Q4) State j is an absorbing state if p<sub>ij</sub> = 1.
A)True B)False
Q5) Give two examples of how Markov analysis can aid decision making.
Q6) What assumptions are necessary for a Markov process to have stationary transition probabilities?
Page 19
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