Test Bank for Business Analytics, 3rd edition James R. Evans

TEST BANK PAOLO CATASTI Virginia Commonwealth University

B USINESS A NALYTICS THIRD EDITION

James R. Evans University of Cincinnati

The author and publisher of this book have used their best efforts in preparing this book. These efforts include the development, research, and testing of the theories and programs to determine their effectiveness. The author and publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this book. The author and publisher shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing, performance, or use of these programs.

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ISBN-13: 978-0-13-520762-8 ISBN-10: 0-13-520762-2

Business Analytics, 3e (Evans) Test Bank - Table of Contents

Chapter 1: Introduction to Business Analytics

1

Chapter 1: Appendix A1 Basic Excel Skills

16

Chapter 2: Database Analytics

24

Chapter 3: Data Visualization

37

Chapter 4: Descriptive Statistics

50

Chapter 5: Probability Distributions and Data Modeling

92

Chapter 6: Sampling and Estimation

108

Chapter 7: Statistical Inference

127

Chapter 8: Trendlines and Regression Analysis

145

Chapter 9: Forecasting Techniques

163

Chapter 10: Introduction to Data Mining

184

Chapter 11: Spreadsheet Modeling and Analysis

198

Chapter 12: Simulation and Risk Analysis

223

Chapter 13: Linear Optimization

237

Chapter 14: Integer and Nonlinear Optimization Models

260

Chapter 15: Optimization Analytics

295

Chapter 16: Decision Analysis

313

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Business Analytics, 3e (Evans) Chapter 1: Introduction to Business Analytics 1) Descriptive analytics: A) can predict risk and find relationships in data not readily apparent with traditional analyses.

B) helps companies classify their customers into segments to develop specific marketing campaigns.

C) helps detect hidden patterns in large quantities of data to group data into sets to predict behavior.

D) can use mathematical techniques with optimization to make decisions that take into account the uncertainty in the data.

Answer: B Diff: 1 Blooms: Remember Topic: Descriptive, Predictive, and Prescriptive Analytics LO1: Illustrate examples of descriptive, predictive, and prescriptive analytics.

2) A manager at Gampco Inc. wishes to know the company's revenue and profit in its previous quarter. Which of the following business analytics will help the manager?

A) prescriptive analytics B) normative analytics C) descriptive analytics D) predictive analytics Answer: C Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Descriptive, Predictive, and Prescriptive Analytics LO1: Explain the difference between descriptive, predictive, and prescriptive analytics.

3) Predictive analytics: A) summarizes data into meaningful charts and reports that can be standardized or customized.

B) identifies the best alternatives to minimize or maximize an objective.

C) uses data to determine a course of action to be executed in a given situation.

D) detects patterns in historical data and extrapolates them forward in time.

Answer: D Diff: 2 Blooms: Remember Topic: Descriptive, Predictive, and Prescriptive Analytics LO1: Illustrate examples of descriptive, predictive, and prescriptive analytics.

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4) A trader who wants to predict short-term movements in stock prices is likely to use ________ analytics.

A) predictive B) descriptive C) normative D) prescriptive Answer: A Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Descriptive, Predictive, and Prescriptive Analytics LO1: Explain the difference between descriptive, predictive, and prescriptive analytics.

5) Which of the following questions will prescriptive analytics help a company address?

A) How many and what types of complaints did they resolve?

B) What is the best way of shipping goods from their factories to minimize costs?

C) What do they expect to pay for fuel over the next several months?

D) What will happen if demand falls by 10% or if supplier prices go up 5%?

Answer: B Diff: 2 Blooms: Understand AACSB: Analytic Skills Topic: Descriptive, Predictive, and Prescriptive Analytics LO1: Illustrate examples of descriptive, predictive, and prescriptive analytics.

6) The demand for coffee beans over a period of three months has been represented in the form of an L-shaped curve. Which form of model was used here?

A) mathematical model B) visual model C) kinesthetic (tactile) model D) verbal model Answer: B Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Models in Business Analytics LO1: Explain the concept of a model and various ways a model can be characterized.

7) Decision variables: A) cannot be directly controlled by the decision maker.

B) are assumed to be constant.

C) are always uncertain.

D) can be selected at the discretion of the decision maker.

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Answer: D Diff: 2 Blooms: Understand Topic: Models in Business Analytics LO1: Define and list the elements of a decision model.

8) Identify the uncontrollable variable from the following inputs of a decision model.

A) investment returns B) machine capacities C) staffing levels D) intercity distances Answer: A Diff: 1 Blooms: Apply Topic: Models in Business Analytics LO1: Define and list the elements of a decision model.

9) Which of the following inputs of a decision model is an example of data?

A) estimated consumer demand B) inflation rates C) costs D) investment allocations Answer: C Diff: 1 Blooms: Remember Topic: Data for Business Analytics LO1: Define and list the elements of a decision model.

10) Descriptive decision models: A) aim to predict what will happen in the future.

B) describe relationships but do not tell a manager what to do.

C) help analyze the risks associated with various decisions.

D) do not facilitate evaluation of different decisions.

Answer: B Diff: 2 Blooms: Understand Topic: Models in Business Analytics LO1: Explain the concept of a model and various ways a model can be characterized.

11) Prescriptive decision models help: A) make predictions of how demand is influenced by price.

B) make trade-offs between greater rewards and risks of potential losses.

C) decision makers identify the best solution to decision problems.

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D) describe relationships and influence of various elements in the model.

Answer: C Diff: 1 Blooms: Remember Topic: Models in Business Analytics LO1: Define the terms optimization, objective function, and optimal solution.

12) The manager at Soul Walk Inc., a shoe manufacturing company, wants to set a new price (P) for a shoe model to maximize total profit. The demand (D) as a function of price is represented as: D = 1,500 - 2.5P The total cost (C) as a function of demand is represented as: C = 3,200 + 3.5D Which of the following is a model for total profit as a function of price?

A) (1,508.75× price) - (2.5 × price2) - 8,450 B) (3.5 × price2) + 3,200 - (1925.50 × price) C) (1,250 × price) + (5 × price2) - 8,320 D) [4521 + (4.5 × price)] × price - 9684.25 Answer: A Diff: 3 Blooms: Apply Topic: Models in Business Analytics LO1: Define the terms optimization, objective function, and optimal solution.

13) Which decision model incorporates the process of optimization?

A) predictive B) prescriptive C) descriptive D) normative Answer: B Diff: 1 Blooms: Remember Topic: Models in Business Analytics LO1: Define the terms optimization, objective function, and optimal solution.

14) Which of the following is the first phase in problem solving?

A) defining the problem B) analyzing the problem C) recognizing the problem D) structuring the problem Answer: C Diff: 1 Blooms: Remember

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Topic: Problem Solving and Decision Making LO1: List and explain the steps in the problem-solving process.

15) Middle managers in operations: A) develop staffing plans.

B) determine product mix.

C) develop advertising plans.

D) make pricing decisions.

Answer: A Diff: 1 Blooms: Remember Topic: Problem Solving and Decision Making LO1: List and explain the steps in the problem-solving process.

16) The product mix is determined by the: A) accounting staff.

B) middle managers.

C) finance managers.

D) top managers.

Answer: D Diff: 1 Blooms: Remember Topic: Problem Solving and Decision Making LO1: List and explain the steps in the problem-solving process.

17) During which phase in problem solving is a formal model often developed?

A) analyzing the problem B) structuring the problem C) defining the problem D) implementing the solution Answer: B Diff: 1 Blooms: Remember Topic: Problem Solving and Decision Making LO1: List and explain the steps in the problem-solving process.

18) Which of the following is true about problem solving?

A) Recognizing problems involves stating goals and objectives.

B) Analyzing the problem involves characterizing the possible decisions.

C) Decision making involves translating the results of the model in the organization.

D) Structuring the problem involves identifying constraints.

Answer: D

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Diff: 2 Blooms: Understand Topic: Problem Solving and Decision Making LO1: List and explain the steps in the problem-solving process.

The manager at Goody Woods Inc., a manufacturer of wooden utensil sets, has observed that when the company sells its sets at $240, 1,540 units are sold, and when the price is raised to $320, demand falls to 1,220 units. Use this information to answer the following two questions.

19) Develop a linear model relating the demand for Goody Woods' units to the price.

Answer: Economic theory tells us that demand for a product is negatively related to its price.

The linear model to predict demand as a function of price is: D = a - bP where D is the quantity demanded, P is the unit price, a is a constant that estimates the demand when the price is zero, and b is the slope of the demand function.

Substituting the values given in the data: 1,540 = a - (b × 240) 1,220 = a - (b × 320) By solving the two equations, values of a and b can be found. a = 2,500, which indicates the demand for wood units when price is zero, b = 4, which is the slope of the demand function.

Substituting values of a and b in the linear demand prediction model: D = 2,500 - 4P Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Predictive Spreadsheet Models.

LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

20) Develop a prescriptive model that will help Goody Woods identify the price that maximizes the total revenue.

Answer: Having found out the model for demand as a function of price, sales (S) can be expressed as: S = 2,500 - 4P Revenue (R) = Sales x Price = (2,500 - 4P) × P = 2,500P - 4P2 Thus, Goody Woods Inc. can identify the price that maximizes the total revenue using: R = 2,500P - 4P2 Diff: 3

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Blooms: Apply AACSB: Analytic Skills Topic: Models in Business Analytics LO1: Define the terms optimization, objective function, and optimal solution.

21) Decision support systems evolved from efforts to improve military operations prior to and during World War II. Answer: FALSE Diff: 1 Blooms: Remember Topic: Evolution of Business Analytics LO1: Summarize the evolution of business analytics and explain the concepts of business intelligence, operations research and management science, and decision support systems.

22) A deterministic model is one in which all model input information is either known or assumed to be known with certainty.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Models in Business Analytics LO1: Explain the difference between a deterministic and stochastic decision model.

23) The complexity of a problem increases when the problem belongs to an individual rather than a group.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Problem Solving and Decision Making LO1: List and explain the steps in the problem-solving process.

24) A goal of Korel & Marke, a dot-com company, is to gain strategic advantage over its rival firms. How can Korel & Marke use analytics and exploit social media to accomplish this goal?

Answer: Analytics is helping businesses learn from social media and exploit social media data for strategic advantage. Using analytics, Korel & Marke can integrate social media data with traditional data sources such as customer surveys, focus groups, and sales data. It can also understand trends and customer perceptions of its products; and create informative reports to assist its marketing managers and product designers.

Diff: 2 Blooms: Understand Topic: What is Business Analytics?

LO1: State some typical examples of business applications in which analytics would be beneficial.

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25) What are the three components of decision support systems (DSS)?

Answer: DSSs include three components: Data management - The data management component includes databases for storing data and allows the user to input, retrieve, update, and manipulate data.

Model management - The model management component consists of various statistical tools and management science models and allows the user to easily build, manipulate, analyze, and Communication system - The communication system component provides the interface necessary for the user to interact with the data and model management components.

Diff: 2 Blooms: Remember Topic: Evolution of Business Analytics LO1: Summarize the evolution of business analytics and explain the concepts of business intelligence, operations research and management science, and decision support systems.

26) Explain how data are used by accountants, economists, and operations managers.

Answer: Following are the ways data are used: Accountants conduct audits to determine whether figures reported on a firm's balance sheet fairly represent the actual data by examining samples (that is, subsets) of accounting data, such Economists use data to help companies understand and predict population trends, interest rates, industry performance, consumer spending, and international trade.

Operations managers use data on production performance, manufacturing quality, delivery times, order accuracy, supplier performance, productivity, costs, and environmental compliance to manage their operations.

Diff: 2 Blooms: Remember Topic: Data for Business Analytics LO1: State examples of how data are used in business.

27) Data used in business analytics need to be reliable and valid. Explain.

Answer: Sample data do not always reflect reality. People do not always behave the same when observed, nor do they always act as they say they act. Poor data can result in poor decisions.

Hence, care must be taken when working with data, and every effort should be made to ensure that data are sufficiently accurate.

Diff: 2 Blooms: Remember Topic: Data for Business Analytics LO1: State examples of how data are used in business.

28) Why do predictive decision models incorporate uncertainty?

Answer: The future is always uncertain. Uncertainty is imperfect knowledge of what will happen; risk is associated with the consequences of what actually happens. Even though uncertainty may exist, there may be no risk. However, risk is an outcome of uncertainty, though not always. Thus, many predictive models incorporate uncertainty and help decision makers

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analyze the risks associated with their decisions.

Diff: 2 Blooms: Understand Topic: Models in Business Analytics LO1: Explain the difference between uncertainty and risk.

29) Which of the following is not a challenge faced by organizations that want to develop analytics capabilities?

A) a lack of understanding of how to use analytics.

B) competing business priorities.

C) understanding benefits versus perceived costs of analytics studies.

D) difficulty in getting good data and sharing information.

Answer: C Diff: 1 Blooms: Remember Topic: What is Business Analytics?

LO1: Explain why analytics is important in today’s business environment.

30) Prescriptive analytics: A) summarizes data into meaningful charts and reports that can be standardized or customized.

B) identifies patterns and relationships existing in large data sets.

C) uses data to determine a course of action to be executed in a given situation.

D) detects patterns in historical data and extrapolates them forward in time.

Answer: C Diff: 2 Blooms: Remember Topic: Descriptive, Predictive, and Prescriptive Analytics LO1: Illustrate examples of descriptive, predictive, and prescriptive analytics.

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Use the table below to answer the following question(s).

Fiberia Accessories, a clothing retailer, is planning to introduce a new line of sweaters as part of the winter collection for $65 with an inventory of 1500. The main selling season is 60 days between November and December. The store then sells the remaining units in a clearance sale at 65 percent discount. Out of the 60 main retail days, Fiberia sells the sweaters at full retail price for only 45 days, while giving a discount of 25 percent for the remaining 15 days. The demand functions a, and b are given as 79.5 and 1.1 respectively.

Marked Down Pricing Model for Fiberia Accessories's new sweater Data Retail Price Inventory Selling Season (days) Days at Full Retail Intermediate Markdown Clearance Markdown Demand Function A B

$65 1500 60 45 25 percent 65 percent 79.5 1.1

31) What is the average daily sale during the full retail sales period?

A) 15 B) 33.33 C) 8 D) 24.55 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Models in Business Analytics LO1: Illustrate examples of descriptive, predictive, and prescriptive models.

32) Calculate the total number of units sold during the full retail sales period.

A) 33.33 B) 520 C) 187.5 D) 360 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Copyright © 2020 Pearson Education, Inc.

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Topic: Models in Business Analytics LO1: Illustrate examples of descriptive, predictive, and prescriptive models.

33) Calculate the total revenue during the full retail sales period.

A) $23,400 B) $16,200 C) $2,880 D) $17,550 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Models in Business Analytics LO1: Illustrate examples of descriptive, predictive, and prescriptive models.

34) Calculate the daily sales during the discount sales period.

A) 39.28 B) 133.3 C) 388.13 D) 25.88 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Models in Business Analytics LO1: Illustrate examples of descriptive, predictive, and prescriptive models.

35) Calculate the total units sold during the discount sales period.

A) 388.13 B) 25.88 C) 133.3 D) 39.28 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Models in Business Analytics LO1: Illustrate examples of descriptive, predictive, and prescriptive models.

36) Calculate the total revenue during the discount sales period.

A) $4,478.91 B) $18,921.09

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C) $10,042.73 D) $43,321.09 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Models in Business Analytics LO1: Illustrate examples of descriptive, predictive, and prescriptive models.

37) Calculate the revenue for the clearance sales period.

A) $18,921.09 B) $23,400 C) $48,871.88 D) $17,105.16 Answer: D Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Models in Business Analytics LO1: Illustrate examples of descriptive, predictive, and prescriptive models.

38) Calculate the total revenue for the new line of sweaters.

A) $59,426.25 B) $48,871.88 C) $23,400 D) $43,231.09 Answer: A Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Models in Business Analytics LO1: Illustrate examples of descriptive, predictive, and prescriptive models.

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Use the table below to answer the following question(s).

In the spreadsheet below, there is data on the price, cost, demand, and quantity produced for an item. There are also different "what if" values that can help a manager to calculate costs and revenue with variability in demand.

1 2 3 4 5 6 7 8 9 10

A Profit Model

B

Data Unit Price ($) Unit Cost ($) Fixed Cost ($) Demand Quantity Produced

50 25 550,000 60,000 55,000

C What-If Demand Values 20,000 40,000 55,000 60,000 65,000

39) Which of the following is the Excel formula to determine the number of units sold?

A) =B8 B) =MIN(0,B8,B9) C) =MIN(B8,B9) D) =MAX(0,B8,B9) Answer: C Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Models in Business Analytics LO1: Illustrate examples of descriptive, predictive, and prescriptive models.

40) If D is demand, P is the unit price, and c and d are constants (where d > 0 is the price elasticity), which of the following is a nonlinear demand prediction model?

A) D = d + (c × P) B) D = (d × P)c C) D = cd × P -d D) D = cP Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Models in Business Analytics LO1: Illustrate examples of descriptive, predictive, and prescriptive models.

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Use the chart below to answer the following two questions:

Gallons

Sales Function 920 900 880 860 840 820 800 780 760 $0

$1

$2

$3

$4

$5 Price

$6

$7

$8

$9

$10

41) What is the slope of the sales function D = a - bP? A) 4 B) 9 C) 12 D) 17 Answer: C Diff: 3 Blooms: Apply Topic: Models in Business Analytics LO1: Illustrate examples of descriptive, predictive, and prescriptive models.

42) How many gallons will be sold if the price is increased to $4.75?

A) 833.26 B) 843 C) 798.72 D) 818 Answer: B Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Models in Business Analytics LO1: Illustrate examples of descriptive, predictive, and prescriptive models.

43) What does business analytics use to help managers make better decisions?

A) data and information technology.

B) statistical analysis and quantitative methods.

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Chapter 1: Introduction to Business Analytics

C) mathematical or computer-based models.

D) all of the above.

Answer: D Diff: 1 Blooms: Remember Topic: What is Business Analytics?

LO1: Define business analytics.

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Business Analytics (Evans) Chapter 1 Appendix A1 Basic Excel Skills 1) Which of the following symbols is used to represent exponents in Excel?

A) ^ B) * C) # D) !

Answer: A Diff: 1 Blooms: Remember Topic: Excel Formulas and Addressing LO1: Find buttons and menus in the Excel 2010 ribbon.

2) Which of the following ways would 102 × 53 / 100 - 73 be represented in an Excel spreadsheet?

A) 10(2) * 5(3) / 100 ^ 73 B) 10(2) ^ 5(3) / 100 - 73 C) 10^2 * 5^3 / 100 - 73 D) 10*2 ^ 5*3 / 100 - 73 Answer: C Diff: 1 Blooms: Understand Topic: Excel Formulas and Addressing LO1: Write correct formulas in an Excel worksheet.

3) Which of the following is a difference between relative addressing and absolute addressing when using cell formulas in Excel?

A) A relative address uses a dollar sign before either the row or column label; an absolute address uses the ampersand symbol before either the row or column label.

B) A relative address uses a dollar sign before either the row or column label; an absolute address uses just the row and column label in the cell reference.

C) A relative address uses just the row and column label in the cell reference; an absolute address uses a dollar sign before either the row or column label.

D) A relative address uses only the column label in the cell reference; an absolute address uses the row.

Answer: C Diff: 2 Blooms: Remember Topic: Excel Formulas and Addressing LO1: Apply relative and absolute addressing in Excel formulas.

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Use the data given below to answer the following question(s) Below is the spreadsheet for demand prediction of a company that sells chocolates.

1 2 3 4 5 6 7 8 9 10 11

A Demand Prediction Models

B

Linear Model A B

10,000 10

Price $50 $55 $45

Demand 9,500 9,450 9,550

C

4) Given that D = a-bP, where D, is demand, "a" and "b," are linear constants, and P, is price, from the below spreadsheet, how will the formula in B9 be represented in Excel using relative addressing?

A) B4-B5*A9 B) C5-C6*A10 C) B4-B5*A10 D) B5-B6*A10 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Excel Formulas and Addressing LO1: Copy formulas from one cell to another or to a range of cells.

5) If a dollar sign is used after the column in B5 (B$5), how will the formula at B8 be represented in C9 using absolute addressing?

A) C3-B$5*C9 B) C5-C$6*B9 C) C5-C$6*C9 D) C5-C$5*B9 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Excel Formulas and Addressing LO1: Apply relative and absolute addressing in Excel formulas.

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6) If a dollar sign is used before the column label B4 ($B4), how will the formula at B10 be represented in C11 using absolute addressing?

A) $B5-C6*B11 B) $C5-C6*A10 C) $B4-C5*B11 D) $A5-C6*B11 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Excel Formulas and Addressing LO1: Apply relative and absolute addressing in Excel formulas.

7) If, in the spreadsheet, cells B9 and B10 were empty, which of the following formulas should be entered in B8 so that the formula can be dragged to B9 and B10 to obtain their correct values?

A) B4-B5*A8 B) B4-B5*$A8 C) $B4-B5*$A8 D) $B$4-$B$5*$A8 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Excel Formulas and Addressing LO1: Copy formulas from one cell to another or to a range of cells.

8) Using a $ sign before a column label ________.

A) keeps the reference to both the row and column fixed B) keeps the reference to the row fixed, but allows the column reference to change C) keeps the reference to column fixed, but allows the row reference to change D) allows both the row and column references to change Answer: C Diff: 1 Blooms: Remember AACSB: Analytic Skills Topic: Excel Formulas and Addressing LO1: Copy formulas from one cell to another or to a range of cells.

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9) To copy a formula from a single cell or range of cells down a column or across a row, first ________, click and hold the mouse on the small square in the lower right-hand corner of the cell, and drag the formula to the "target" cells which you wish to copy.

A) press Ctrl-C B) select the cell or range C) press Ctrl-Enter D) select the whole spreadsheet Answer: B Diff: 1 Blooms: Remember AACSB: Analytic Skills Topic: Excel Formulas and Addressing LO1: Copy formulas from one cell to another or to a range of cells.

10) Trace the process of copying and pasting a cell, which has a formula in it, such that the formula is not retained in the pasted cell.

A) Home - Paste - Paste Special - Paste Values B) Home - Paste - Paste Special - Paste Validation C) Home - Paste - Paste Special - Paste Formats D) Home - Paste - Paste Special - Paste Formulas Answer: A Diff: 1 Blooms: Remember Topic: Miscellaneous Excel Functions and Tools LO1: Copy formulas from one cell to another or to a range of cells.

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Use the data given below to answer the following question(s).

Below is a spreadsheet of purchase orders for a computer hardware retailer.

1 2 3

A Purchase Orders

Supplier Rex 4 Technologies Rex 5 Technologies Rex 6 Technologies Rex 7 Technologies Max's 8 Wavetech Max's 9 Wavetech Max's 10 Wavetech 11 12

B

C

D

E

F

G

H

Item Item Description Cost Graphics Card $ 89

Cost per A/P Terms Order Quantity Order (Months) No.

Order Size

35

$3115

20

AL123

Large

Monitor

$150

15

$2250

25

AL234

Small

Keyboard

$ 15

40

$600

15

AL345

Large

Speakers

$ 15

20

$300

25

AL456

Small

HD Cables

$ 5

10

$50

25

KO876

Small

Processor

$278

27

$6950

30

KO765

Large

Hard disk

$120

18

$2160

20

KO654

Small

11) To find the total order cost, what Excel formula should be used in A12?

A) =COUNT(C4:C10) B) =COUNT(C4:C7) C) =MAX(C4:C10) D) =SUM(E4:E10) Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Excel Functions LO1: Use basic and advanced Excel functions.

12) For which of the following columns can the COUNT function be performed?

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Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Excel Functions LO1: Use basic and advanced Excel functions.

13) To find the average of the total cost of orders from Rex Technologies, what Excel formula should be used in A12?

A) =AVERAGE(C4:C10) B) =AVERAGE(C4:C7) C) =AVERAGE(E4:E7) D) =AVERAGE(E4:E10) Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Excel Functions LO1: Use basic and advanced Excel functions.

14) The easiest way to locate a particular function is to select a cell and click on the Insert function button represented by ________ on the Excel ribbon.

A) fx B) Σ C) $ D) % Answer: A Diff: 1 Blooms: Remember Topic: Excel Functions LO1: Find buttons and menus in the Excel 2010 ribbon.

15) What is the Insert function in Excel?

Answer: The easiest way to locate a particular function is to select a cell and click on the Insert function button fx, which can be found under the ribbon next to the formula bar and also in the Function Library group in the Formulas tab. You may either type in a description in the search field, such as "net present value," or select a category, such as "Financial," from the drop-down box. This feature is particularly useful if you know what function to use but are not sure of what arguments to enter because it will guide you in entering the appropriate data for the function arguments.

Diff: 1 Blooms: Remember Topic: Excel Functions LO1: Use basic and advanced Excel functions.

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22 Chapter 1 Appendix A1 Basic Excel Skills

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16) The Excel function of ________ is used to find the largest value in a range of cells.

A) SUM(range) B) COUNT(range) C) MAX(range) D) COUNTIF(range, criteria) Answer: C Diff: 1 Blooms: Remember Topic: Excel Functions LO1: Apply logical functions in Excel formulas.

17) ________ measures the worth of a stream of cash flows, taking into account the time value of money.

A) Accounting rate of return B) Net present value C) Internal rate of return D) Adjusted present value Answer: B Diff: 1 Blooms: Remember Topic: Excel Functions LO1: Design simple Excel templates for descriptive analytics.

18) The ________ reflects the opportunity costs of spending funds now versus achieving a return through another investment, as well as the risks associated with not receiving returns until a later time.

A) modified internal rate of return B) payback period C) accounting rate of return D) discount rate Answer: D Diff: 1 Blooms: Remember Topic: Excel Functions LO1: Design simple Excel templates for descriptive analytics.

19) Identify the equation for calculating the net present value for a stated period of time, where Ft = cash flow in period t, and i is the discount rate.

Ft  i 2 t 0 n n

A) NPV =



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Chapter 1 Appendix A1 Basic Excel Skills

Business Analytics, 3e 23

n

B) NPV =  Ft (1  i )t t 0 n

Ft t t  0 (1  i ) n F D) NPV =  t (1  i )t t 0 i

C) NPV = 

Answer: C Diff: 1 Blooms: Remember Topic: Excel Functions LO1: Design simple Excel templates for descriptive analytics.

20) A positive NPV means that the investment will provide added value because the projected return exceeds the ________.

A) modified internal rate of return B) discount rate C) accounting rate of return D) adjusted present value Answer: B Diff: 1 Blooms: Remember Topic: Excel Functions LO1: Design simple Excel templates for descriptive analytics.

21) Describe the method of calculating the net present value (NPV) in Excel.

Answer: The Excel function NPV (rate, value1, value2,…) calculates the net present value of an investment by using a discount rate and a series of future payments (negative values) and income (positive values). Rate is the rate of discount over the length of one period (i), and value1, value2,… are 1 to 29 arguments representing the payments and income. The values must be equally spaced in time and are assumed to occur at the end of each period. The NPV investment begins one period before the date of the value1 cash flow and ends with the last cash flow in the list. The NPV calculation is based on future cash flows. If the first cash flow (such as an initial investment or fixed cost) occurs at the beginning of the first period, then it must be added to the NPV result and not included in the function arguments.

Diff: 1 Blooms: Remember Topic: Excel Template Design LO1: Design simple Excel templates for descriptive analytics.

Copyright © 2020 Pearson Education, Inc.

Business Analytics, 3e (Evans) Chapter 2: Database Analytics 1) What is a database?

A) a structured collection of related files and data B) simply a collection of data C) a data file holding a single file D) flat files used to store data Answer: A Diff: 1 Blooms: Remember Topic: Data Sets and Databases LO1: Explain the difference between a data set and a database and apply Excel range names in data files.

2) In a database, information is stored and maintained in ________.

A) fields B) measurements C) entities D) attributes Answer: C Diff: 1 Blooms: Remember Topic: Data Sets and Databases LO1: Explain the difference between a data set and a database and apply Excel range names in data files.

3) In a database file, which is organized in a two-dimensional table, the rows represent records of related data elements.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Data Sets and Databases LO1: Explain the difference between a data set and a database and apply Excel range names in data files.

4) The sort buttons in Excel can be found under: A) the Data tab in the Sort & Filter group.

B) the Home tab in the Styles group.

C) the Insert tab in the Sort group.

D) the Sort tab in the Filter group.

Answer: A Diff: 1 Copyright © 2020 Pearson Education, Inc. 24

Chapter 2: Database Analytics

Business Analytics, 3e 25

Blooms: Remember Topic: Data Queries: Tables, Sorting, and Filtering LO1: Construct Excel tables and be able to sort and filter data.

Use the data given below to answer the following question.

Following is the purchase order database of 'The Chef Says So', a restaurant in New York, over the last quarter (April-June).

Order Date 5/6/2012 4/7/2012 5/13/2012 6/10/2012 6/22/2012 5/17/2012 4/25/2012 6/1/2012 4/2/2012 5/27/2012 6/13/2012 4/30/2012 5/11/2012 6/18/2012 5/9/2012 5/30/2012 6/6/2012 4/3/2012 6/26/2012 4/23/2012 4/29/2012 4/4/2012 6/15/2012 6/25/2012 5/23/2012 6/28/2012 5/25/2012 5/1/2012

Item

Region

Supplier

Unit Cost

Steel Fork Ceramic Plate Steel Fork Silver Spoon Steel Fork Ceramic Plate Steel Fork Steel Fork Steel Fork Ceramic Plate Steel Fork Ceramic Plate Ceramic Plate Steel Fork Glass Bottle Ceramic Bowl Ceramic Plate Silver Spoon Silver Spoon Ceramic Bowl Steel Fork Ceramic Bowl Ceramic Plate Ceramic Plate Ceramic Plate Ceramic Plate Ceramic Bowl Steel Fork

Antasia Puitoria Puitoria Puitoria Almeco Antasia Puitoria Puitoria Almeco Antasia Puitoria Antasia Antasia Antasia Puitoria Antasia Puitoria Antasia Antasia Puitoria Puitoria Antasia Puitoria Puitoria Antasia Almeco Puitoria Puitoria

Peter Kane Jones Gerry Sarah Peter Audrey Jones Thomas Peter Mary Henry Philip Peter Simson Peter Mary Peter Philip Kane Simson Philip Gerry Simson Peter Sarah Jones Audrey

5.44 23.44 8.44 23.44 6.44 8.44 5.44 8.44 5.44 12.44 8.44 5.44 23.44 8.44 128.45 19.44 12.44 12.44 23.44 8.44 4.74 19.44 12.44 18.45 8.44 23.44 8.44 5.44

Copyright © 2020 Pearson Education, Inc.

Units 98 53 39 30 59 63 78 93 35 63 93 32 84 38 5 19 31 67 18 99 70 77 49 90 7 10 53 69

26 Chapter 2: Database Analytics

Order Date 4/12/2012 4/18/2012 6/30/2012 5/19/2012 4/16/2012 6/4/2012 5/2/2012 4/19/2012 6/11/2012 5/31/2012 6/2/2012 4/13/2012 5/3/2012 6/3/2012 4/17/2012

Business Analytics, 3e

Item

Region

Supplier

Unit Cost

Silver Spoon Steel Fork Ceramic Plate Glass Bottle Ceramic Bowl Ceramic Bowl Ceramic Bowl Glass Bottle Steel Fork Silver Spoon Ceramic Plate Steel Fork Ceramic Plate Ceramic Plate Ceramic Plate

Antasia Puitoria Puitoria Puitoria Antasia Puitoria Puitoria Almeco Puitoria Almeco Almeco Puitoria Puitoria Puitoria Puitoria

Henry Gerry Gerry Kane Peter Mary Kane Sarah Gerry Sarah Thomas Audrey Jones Jones Audrey

8.44 4.74 12.44 128.45 8.44 15.94 27.4 278.45 4.74 5.44 23.44 4.74 8.44 23.44 8.44

Units 99 56 83 8 65 58 45 6 10 79 60 17 14 97 31

5) Describe how to sort the data by inventory value to compute cumulative percentage of total inventory value to help the restaurateur conduct a Pareto analysis. (Assume that no damages were caused to the inventory purchased over the three months) Answer: In order to calculate inventory value of items, only Item, Unit Cost, and Units have to be retained in the table. Inventory value can be calculated by multiplying the unit cost by the number of units. Percentage and the cumulative percentage may be calculated based on the inventory values. Then, sort by Item, calculate subtotals for each Item, calculate percentages, sort the percentage in descending order and then calculate the cumulative percentages.

Item Steel Fork Ceramic Plate Steel Fork Silver Spoon Steel Fork Ceramic Plate Steel Fork Steel Fork Steel Fork

Unit Cost 5.44 23.44 8.44 23.44 6.44 8.44 5.44 8.44 5.44

Units 98 53 39 30 59 63 78 93 35

Inventory Cumulative Percentage Value Percentage 533.12 1.77646 1.77646 1242.32 4.13966 5.91612 329.16 1.09683 7.01295 703.2 2.3432 9.35616 379.96 1.2661 10.6223 531.72 1.7718 12.3941 424.32 1.41392 13.808 784.92 2.61551 16.4235 190.4 0.63445 17.0579

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Chapter 2: Database Analytics

Item Ceramic Plate Steel Fork Ceramic Plate Ceramic Plate Steel Fork Glass Bottle Ceramic Bowl Ceramic Plate Silver Spoon Silver Spoon Ceramic Bowl Steel Fork Ceramic Bowl Ceramic Plate Ceramic Plate Ceramic Plate Ceramic Plate Ceramic Bowl Steel Fork Silver Spoon Steel Fork Ceramic Plate Glass Bottle Ceramic Bowl Ceramic Bowl Ceramic Bowl Glass Bottle Steel Fork Silver Spoon Ceramic Plate Steel Fork Ceramic Plate Ceramic Plate Ceramic Plate Total

Unit Cost 12.44 8.44 5.44 23.44 8.44 128.45 19.44 12.44 12.44 23.44 8.44 4.74 19.44 12.44 18.45 8.44 23.44 8.44 5.44 8.44 4.74 12.44 128.45 8.44 15.94 27.4 278.45 4.74 5.44 23.44 4.74 8.44 23.44 8.44

Business Analytics, 3e 27

Units 63 93 32 84 38 5 19 31 67 18 99 70 77 49 90 7 10 53 69 99 56 83 8 65 58 45 6 10 79 60 17 14 97 31

Inventory Cumulative Percentage Value Percentage 783.72 2.61151 19.6695 784.92 2.61551 22.285 174.08 0.58007 22.865 1968.96 6.56097 29.426 320.72 1.0687 30.4947 642.25 2.14011 32.6348 369.36 1.23078 33.8656 385.64 1.28503 35.1506 833.48 2.77732 37.928 421.92 1.40592 39.3339 835.56 2.78425 42.1181 331.8 1.10562 43.2238 1496.88 4.98791 48.2117 609.56 2.03118 50.2428 1660.5 5.53312 55.776 59.08 0.19687 55.9728 234.4 0.78107 56.7539 447.32 1.49056 58.2444 375.36 1.25078 59.4952 835.56 2.78425 62.2795 265.44 0.8845 63.164 1032.52 3.44057 66.6045 1027.6 3.42417 70.0287 548.6 1.82805 71.8568 924.52 3.08069 74.9374 1233 4.1086 79.0461 1670.7 5.56711 84.6132 47.4 0.15795 84.7711 429.76 1.43205 86.2032 1406.4 4.68641 90.8896 80.58 0.26851 91.1581 118.16 0.39373 91.5518 2273.68 7.57636 99.1282 261.64 0.87184 100 30010.2

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28 Chapter 2: Database Analytics

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Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Data Queries: Tables, Sorting, and Filtering LO1: Construct Excel tables and be able to sort and filter data.

6) Which of the following relies on sorting data and calculating the cumulative percentage of the characteristic of interest?

A) Randolph diagram B) Anscombe's quartet C) Bland-Altman plot D) Pareto analysis Answer: D Diff: 1 Blooms: Remember Topic: Data Queries: Tables, Sorting, and Filtering LO1: Apply the Pareto Principle to analyze data.

Use the data given below to answer the following question(s).

Below is a spreadsheet of purchase orders for a computer hardware retailer.

1 2

A B Purchase Orders

C

Item Item Description Cost Graphics 4 Rex Technologies Card $ 89 5 Rex Technologies Monitor $150 6 Rex Technologies Keyboard $ 15 7 Rex Technologies Speakers $ 15 8 Max's Wavetech HD Cables $ 5 9 Max's Wavetech Processor $278 10 Max's Wavetech Hard disk $120 11 Item 12 Supplier Order Size Cost 13 Rex Technologies Large >15 14 Max's Wavetech 3

Supplier

D

E

F

G

H

Cost per A/P Terms Order Quantity Order (Months) No.

Order Size

35 15 40 20 10 27 18

Large Small Large Small Small Large Small

$3115 $2250 $600 $300 $50 $6950 $2160

20 25 15 25 25 30 20

Copyright © 2020 Pearson Education, Inc.

AL123 AL234 AL345 AL456 KO876 KO765 KO654

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7) To find the largest quantity of items ordered from Rex Technologies, what Excel formula should be used in A12?

A) =COUNTIF(D4:D10) B) =SUM(D4:D7) C) =MAX(D4:D7) D) =COUNT(D4:D7) Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Logical Functions LO1: Apply logical functions in Excel formulas.

8) To find the number of orders with A/P terms less than 25 months, what Excel formula should be used in A12?

A) =COUNTIF(F4:F10,"<25") B) =COUNT(F4:F10,25) C) =AVERAGE(F4:F10,"<25") D) =COUNTIF(F4:F10,F5) Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Logical Functions LO1: Apply logical functions in Excel formulas.

9) If purchase quantities of 25 units or higher are found to be large orders, and orders less than 25 are considered to be small, what IF function should be entered in H4 to be copied to H5:H10 to calculate each order's size?

A) =IF(D4=AND=OR=25,"Large","Small") B) =IF(D4<>25,"Small")=AND(D4=25,"Large") C) =IF(D4=25,"Large")=OR("Small") D) =IF(D4>=25,"Large","Small") Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Logical Functions LO1: Apply logical functions in Excel formulas.

10) Which of the following Database functions calculates the count of purchase orders made by Rex Technologies?

A) =DCOUNT(A3:H10,C3,A12:A13)

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30 Chapter 2: Database Analytics

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B) =DCOUNT(A4:H10,C3,A12:A13) C) =DCOUNT(A3:H10,C3,A13) D) =DCOUNT(A3:H10,A3,A12:A13) Answer: A Diff: 3 Blooms: Apply Topic: Lookup Functions for Database Queries LO1: Use database functions to extract records.

11) Which of the following Database functions calculates the count of purchase orders made by Rex Technologies for large size orders?

A) =DCOUNT(A3:H10,C3,A12:B13) B) =DCOUNT(A3:H10,”Rex Technologies”,B12:B13) C) =DCOUNT(A3:H10,C3,B12:B13) D) =DCOUNT(A4:H10,D3,A12:B13) Answer: A Diff: 3 Blooms: Apply Topic: Lookup Functions for Database Queries LO1: Use database functions to extract records.

12) Which of the following Database functions calculates the total quantity ordered in large size?

A) =DSUM(A3:H10,”Quantity”,B12:B13) B) =DSUM(A3:H10,D3,B12:B13) C) =DSUM(A3:H10,D3,A12:B13) D) =DSUM(A4:H10,D3,B12:B13) Answer: B Diff: 3 Blooms: Apply Topic: Lookup Functions for Database Queries LO1: Use database functions to extract records.

13) Which of the following Database functions calculates the total cost charged to Rex Technologies for large size orders?

A) =DSUM(A3:H10,C3,A12:B14) B) =DSUM(A4:H10,”Cost per Order”,A12:B13) C) =DSUM(A3:H10,C3,A12:B13) D) =DSUM(A3:H10,E3,A12:B13) Answer: D Diff: 3 Blooms: Apply Topic: Lookup Functions for Database Queries LO1: Use database functions to extract records.

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14) Which of the following Database functions calculates the average item cost ordered by Rex Technologies?

A) =DAVERAGE(A3:H10,C3,A12:A13) B) =DAVERAGE(A3:H10,C3,A12:B13) C) =DAVERAGE(A3:H10,”Item Cost”,A12:A14) D) =DSUM(A3:H10,C3,A12:A13)/COUNTA(A4:A10) Answer: A Diff: 3 Blooms: Apply Topic: Lookup Functions for Database Queries LO1: Use database functions to extract records.

15) Which of the following is a differentiation between calculating using the functions COUNT and COUNTIF? A) COUNT does not require a range of cells; COUNTIF requires a range of cells.

B) COUNT only requires a range of cell and can be obtained without special criteria, COUNTIF requires range and special criteria to be calculated.

C) COUNT requires a range of cells; COUNTIF does not require a range of cells, only special criteria.

D) COUNT calculates the sum of values for a range of cells; COUNTIF finds the largest value in a range of cells.

Answer: B Diff: 2 Blooms: Remember Topic: Logical Functions LO1: Apply logical functions in Excel formulas.

16) ________ is a logical function that returns one value if the condition is true and another if the condition is false.

A) OR(condition 1, condition 2…)

B) AND(condition 1, condition 2…)

C) TO(value if true, value if false) D) IF(condition, value if true, value if false) Answer: D Diff: 1 Blooms: Remember Topic: Logical Functions LO1: Apply logical functions in Excel formulas.

17) Which of the following functions is a logical function that returns TRUE if any condition is true and FALSE if not?

A) TO(value if true, value if false) B) AND(condition 1, condition 2…)

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32 Chapter 2: Database Analytics

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C) OR(condition 1, condition 2…)

D) IF(condition, value if true, value if false) Answer: C Diff: 1 Blooms: Remember Topic: Logical Functions LO1: Apply logical functions in Excel formulas.

18) Give the logical function for the following: If cell B7 equals 12, check contents of cell B10.

If cell B10 is 10, then the value of the function in the string is YES; if not, it is a blank space. If cell B7 does not equal 12, then the value of the function is 7.

A) =IF(B7=12,(AND(B10=10, "")(YES)),7) B) =IF(B10=10,(OR(B7=12,"")"YES")7) C) =IF(B7=12,(IF(B10=10,"YES", "")),7) D) =IF(B7=12,(AND(B10=10,"YES","")(B10="NO"),7) Answer: C Diff: 3 Blooms: Understand AACSB: Analytic Skills Topic: Logical Functions LO1: Apply logical functions in Excel formulas.

19) If cell G7 contains the function ________, it states that if the value in cell C3 is 9, the number 7 will be assigned to cell G7; if the value in cell C3 is not 9, the number 4 will be assigned to cell G7.

A) =IF(G7=9)(G7=7)=OR(G7=4) B) =IF(G7=7)=THEN(C3=9)=OR(C3=4) C) =IF(C3=9)(C3=7)=OR(C3=4) D) =IF(C3=9,7,4) Answer: D Diff: 2 Blooms: Understand AACSB: Analytic Skills Topic: Logical Functions LO1: Apply logical functions in Excel formulas.

20) The function ________ returns a value or reference of the cell at the intersection of a particular row and column in a given range.

A) VLOOKUP(lookup_value, table_array, col_index_num) B) INDEX(array, row_num, col_num) C) MATCH(lookup_value, lookup_array, match_type) D) HLOOKUP(lookup_value, table_array, row_index_num) Answer: B

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Diff: 1 Blooms: Remember Topic: Lookup Functions for Database Queries LO1: Use Excel lookup functions to make database queries.

21) Which of the following Lookup functions returns the relative position of an item in an array that equals a specified value in a specified order?

A) HLOOKUP(lookup_value, table_array, row_index_num) B) MATCH(lookup_value, lookup_array, match_type) C) INDEX(array, row_num, col_num) D) VLOOKUP(lookup_value, table_array, col_index_num) Answer: B Diff: 1 Blooms: Remember Topic: Lookup Functions for Database Queries LO1: Use Excel lookup functions to make database queries.

22) In a MATCH function, if the match_type = 0, then ________.

A) the function finds the largest value that is less than or equal to lookup_value B) the function finds the smallest value that is greater than or equal to lookup_value C) MATCH finds the first value that is exactly equal to lookup_value D) the values in the lookup_array must be in a particular order Answer: C Diff: 1 Blooms: Remember Topic: Lookup Functions for Database Queries LO1: Use Excel lookup functions to make database queries.

23) For which of the following MATCH functions must the values in the lookup_array be ordered in a descending order?

A) When match_type = -1 B) When match_type >1 C) When match_type = 0 D) When match_type = 1 Answer: A Diff: 1 Blooms: Remember Topic: Lookup Functions for Database Queries LO1: Use Excel lookup functions to make database queries.

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34 Chapter 2: Database Analytics

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24) Using the spreadsheet below, provide the steps in using Excel formulas in finding the cost of the first order for Item number 1345, and the total cost of all Item numbers 1345, using the Match and Index functions in Excel. Column B is sorted by item number in ascending order.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

A Purchase Orders

B

C

D

Supplier Rex Technologies Rex Technologies Rex Technologies Rex Technologies Max's Wavetech Max's Wavetech Max's Wavetech Rex Technologies Rex Technologies Rex Technologies Rex Technologies Max's Wavetech

Item No. Item Cost Quantity 1123 $ 89 35 1234 $150 15 1345 $ 15 40 1345 $ 15 20 1345 $ 5 10 1765 $278 27 1654 $120 18 1765 $ 54 56 1100 $ 71 33 1100 $ 10 14 1683 $ 7 25 1683 $100 31

E Cost per Order $3115 $2250 $ 600 $ 300 $ 50 $6950 $2160 $3024 $2343 $ 140 $ 175 $3100

Answer: To find the order cost associated with the first order for 1345, which is in column E, we have to first use the Match function, =MATCH(1345,$B$4:$B$15,0).

Accordingly, the result will be, =MATCH(1345,$B$4:$B$15,0) = 3.

In order to find the cost associated with this result, we add this function in an Index function.

Therefore, the formula for finding cost is, =INDEX($A$4:$E$15,MATCH(1345,$B$4:$B$15,0),5). …. (1) The result for this formula is, =INDEX($A$4:$E$15,MATCH(1345,$B$4:$B$15,5) = $600.

To find the total cost associated with all items under Item number: 1345, we find the last cost associated with 1345 in column E, which is given by the formula =INDEX($A$4:$E$15,MATCH(1345,$B$4:$B$15,1),5). …. (2) The result for this formula is, =INDEX($A$4:$E$15,MATCH(1345,$B$4:$B$15,1),5) = $50.

We then substitute both (1) and (2) into Excel's SUM function.

Therefore we get, =SUM(INDEX($A$4:$E$15,MATCH(1345,$B$4:$B$15,0),5):INDEX($A$4:$E$15,MATCH(1 345,$B$4:$B$15,1),5)) Therefore the total cost for all items under 1345, =SUM(INDEX($A$4:$E$15,MATCH(1345,$B$4:$B$15,0),5):INDEX($A$4:$E$15,MATCH(1 345,$B$4:$B$15,1),5)) = $950.

Diff: 3 Blooms: Apply AACSB: Analytic Skills Copyright © 2020 Pearson Education, Inc.

Chapter 2: Database Analytics

Business Analytics, 3e 35

Topic: Lookup Functions for Database Queries LO1: Use Excel lookup functions to make database queries.

25) AND(condition 1, condition 2…) is a logical function that returns TRUE if all conditions are true and FALSE if not.

Answer: TRUE Diff: 1 Blooms: Remember AACSB: Analytic Skills Topic: Logical Functions LO1: Apply logical functions in Excel formulas.

26) To use the VLOOKUP(lookup_value, table_array, col_index_num), the table must be sorted in descending order.

Answer: FALSE Diff: 1 Blooms: Remember AACSB: Analytic Skills Topic: Lookup Functions for Database Queries LO1: Use Excel lookup functions to make database queries.

27) In a MATCH function, the default value for match_type = 0.

Answer: FALSE Diff: 1 Blooms: Remember AACSB: Analytic Skills Topic: Lookup Functions for Database Queries LO1: Use Excel lookup functions to make database queries.

28) In a MATCH function, if match_type = 1, then the function finds the smallest value that is greater than or equal to lookup_value.

Answer: FALSE Diff: 1 Blooms: Remember AACSB: Analytic Skills Topic: Lookup Functions for Database Queries LO1: Use Excel lookup functions to make database queries.

29) Explain the different Lookup functions in Excel.

Answer: Excel provides some useful functions for finding specific data in a spreadsheet. These functions are useful in many applications:

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36 Chapter 2: Database Analytics

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VLOOKUP(lookup_value, table_array, col_index_num) looks up a value in the leftmost column of a table and returns a value in the same row from a column you specify. The table must be sorted in an ascending order.

HLOOKUP(lookup_value, table_array, row_index_num) looks up a value in the top row of a table and returns a value in the same column from a row you specify. The table must be sorted in an ascending order from left to right.

INDEX(array, row_num, col_num) Returns a value or reference of the cell at the intersection of a particular row and column in a given range.

MATCH(lookup_value, lookup_array, match_type) Returns the relative position of an item in an array that matches a specified value in a specified order.

Diff: 1 Blooms: Remember Topic: Lookup Functions for Database Queries LO1: Use Excel lookup functions to make database queries.

30) Which of the following is true about constructing PivotTables?

A) It is not possible to construct the PivotTable in the same worksheet.

B) Dragging a field into the Report Filter area allows addition of a third dimension to the analysis.

C) Placing a field each in the row and column labels will automatically sum the variable values in the table.

D) PivotTables cannot be duplicated by copying and pasting an existing table.

Answer: B Diff: 2 Blooms: Remember Topic: PivotTables LO1: Use PivotTables to analyze and gain insight from data.

Copyright © 2020 Pearson Education, Inc.

Business Analytics, 3e (Evans) Chapter 3: Data Visualization 1) To select a chart type in Excel from the Charts group, which tab has to be accessed?

A) Design tab B) Layout tab C) Insert tab D) Format tab Answer: C Diff: 1 Blooms: Remember Topic: Creating Charts in Microsoft Excel LO1: Create Microsoft Excel charts.

Use the data given below to answer the following question(s).

Following is the purchase order database of 'The Chef Says So', a restaurant in New York, over the last quarter (April-June).

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

A Order Date 5/6/2012 4/7/2012 5/13/2012 6/10/2012 6/22/2012 5/17/2012 4/25/2012 6/1/2012 4/2/2012 5/27/2012 6/13/2012 4/30/2012 5/11/2012 6/18/2012 5/9/2012 5/30/2012 6/6/2012 4/3/2012 6/26/2012 4/23/2012 4/29/2012 4/4/2012 6/15/2012

B Item Steel Fork Ceramic Plate Steel Fork Silver Spoon Steel Fork Ceramic Plate Steel Fork Steel Fork Steel Fork Ceramic Plate Steel Fork Ceramic Plate Ceramic Plate Steel Fork Glass Bottle Ceramic Bowl Ceramic Plate Silver Spoon Silver Spoon Ceramic Bowl Steel Fork Ceramic Bowl Ceramic Plate

C Region Antasia Puitoria Puitoria Puitoria Almeco Antasia Puitoria Puitoria Almeco Antasia Puitoria Antasia Antasia Antasia Puitoria Antasia Puitoria Antasia Antasia Puitoria Puitoria Antasia Puitoria

D E F Supplier Unit Cost Units Peter 5.44 98 Kane 23.44 53 Jones 8.44 39 Gerry 23.44 30 Sarah 6.44 59 Peter 8.44 63 Audrey 5.44 78 Jones 8.44 93 Thomas 5.44 35 Peter 12.44 63 Mary 8.44 93 Henry 5.44 32 Philip 23.44 84 Peter 8.44 38 Simson 128.45 5 Peter 19.44 19 Mary 12.44 31 Peter 12.44 67 Philip 23.44 18 Kane 8.44 99 Simson 4.74 70 Philip 19.44 77 Gerry 12.44 49

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38 Chapter 3: Data Visualization

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

A 6/25/2012 5/23/2012 6/28/2012 5/25/2012 5/1/2012 4/12/2012 4/18/2012 6/30/2012 5/19/2012 4/16/2012 6/4/2012 5/2/2012 4/19/2012 6/11/2012 5/31/2012 6/2/2012 4/13/2012 5/3/2012 6/3/2012 4/17/2012

B Ceramic Plate Ceramic Plate Ceramic Plate Ceramic Bowl Steel Fork Silver Spoon Steel Fork Ceramic Plate Glass Bottle Ceramic Bowl Ceramic Bowl Ceramic Bowl Glass Bottle Steel Fork Silver Spoon Ceramic Plate Steel Fork Ceramic Plate Ceramic Plate Ceramic Plate

Business Analytics, 3e C Puitoria Antasia Almeco Puitoria Puitoria Antasia Puitoria Puitoria Puitoria Antasia Puitoria Puitoria Almeco Puitoria Almeco Almeco Puitoria Puitoria Puitoria Puitoria

D Simson Peter Sarah Jones Audrey Henry Gerry Gerry Kane Peter Mary Kane Sarah Gerry Sarah Thomas Audrey Jones Jones Audrey

E 18.45 8.44 23.44 8.44 5.44 8.44 4.74 12.44 128.45 8.44 15.94 27.4 278.45 4.74 5.44 23.44 4.74 8.44 23.44 8.44

F 90 7 10 53 69 99 56 83 8 65 58 45 6 10 79 60 17 14 97 31

2) Describe how to and construct a line chart exhibiting the purchase order of ceramic plates over the three months.

Answer: Filter the data set by Item (Ceramic Plate). Sort the Order Date by Oldest to Newest.

Select columns A and F and choose the type of chart (Line Chart) from the Charts group under the Insert tab. Change the title and make data and formatting changes where necessary.

Diff: 3

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Blooms: Apply AACSB: Analytic Skills Topic: Creating Charts in Microsoft Excel LO1: Create Microsoft Excel charts.

3) Changes to the type of chart, data included in the chart, and chart layout and styles can be made from the Layout tab.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Creating Charts in Microsoft Excel LO1: Create Microsoft Excel charts.

4) Describe how to and construct a pie chart exhibiting the count of purchase orders by item.

Answer: Identify all the outcomes for the variable Item. Create a frequency table of the counts of purchase orders by each outcome of the variable Item using the Excel formula COUNTIF($B$2:$B$44, criteria), where criteria represents each outcome of the variable Item.

Select the entire table and choose the type of chart (Pie Chart) from the Charts group under the Insert tab. Change the title and make data and formatting changes where necessary.

Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Creating Charts in Microsoft Excel LO1: Create Microsoft Excel charts.

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5) Describe how to and construct a column chart exhibiting the total units purchased by region.

Answer: Identify all the outcomes for the variable Region. Create a frequency table of the sum of units for each outcome of the variable Region using the Excel formula SUMIF($C$2:$C$44,criteria,$F$2:$F$44), where criteria represents each outcome of the variable Region. Select the entire table and choose the type of chart (Column Chart) from the Charts group under the Insert tab. Change the title and make data and formatting changes where necessary.

Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Creating Charts in Microsoft Excel LO1: Create Microsoft Excel charts.

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6) Describe how to and construct an area chart exhibiting the units ordered by the region of Puitoria over the three months.

Answer: Filter the data set by Region (Puitoria). Sort the Order Date by Oldest to Newest. Select the columns A and F of the data set and choose the type of chart (Area Chart) from the Charts group under the Insert tab. Change the title and make data and formatting changes where necessary.

Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Creating Charts in Microsoft Excel LO1: Create Microsoft Excel charts.

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7) Describe how to and construct a scatter chart exhibiting the relationship between the unit cost and the number of units for the purchase of steel forks.

Answer: Filter the data set by Item (Steel Fork). Select the columns for Unit Cost and Units (columns E and F), and choose the type of chart (Scatter Chart) from the Charts group under the Insert tab. Change the title and make data and formatting changes where necessary.

Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Creating Charts in Microsoft Excel LO1: Create Microsoft Excel charts.

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8) Describe how to and construct a combination chart exhibiting the purchase order of ceramic plates as a line, and the unit cost as columns on the secondary axis over the three months.

Answer: Filter the data set by Item (Ceramic Plate). Sort the Order Date by Oldest to Newest.

Select columns A, E and F and choose the type of chart (Line Chart) from the Charts group under the Insert tab. Right click the unit cost line and select Change Series Chart Type. Change the Unit Cost line to column, and check the Secondary Axis box. Change the title and make data and formatting changes where necessary.

Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Creating Charts in Microsoft Excel LO1: Create Microsoft Excel charts.

9) Elaborate on the use of geographic data mapping in business analytics.

Answer: Many applications of business analytics involve geographic data. For example, problems such as finding the best location for production and distribution facilities, analyzing regional sales performance, transporting raw materials and finished goods, and routing vehicles such as delivery trucks involve geographic data. In such problems, data mapping can help in a variety of ways. Visualizing geographic data can highlight key data relationships, identify trends, and uncover business opportunities. In addition, it can often help to spot data errors and help end users understand solutions, thus increasing the likelihood of acceptance of decision models.

MapPoint is a geographic data-mapping tool that allows you to visualize data imported from Excel and other database sources and integrate them into other Microsoft Office applications.

Diff: 1 Blooms: Remember Topic: Creating Charts in Microsoft Excel LO1: Create Microsoft Excel charts.

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10) Roger wants to compare values across categories using vertical rectangles. Which of the following charts must Roger use?

A) Line chart B) Clustered column chart C) Pie chart D) Stacked column chart Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Creating Charts in Microsoft Excel LO1: Determine the appropriate chart to visualize different types of data.

11) Which of the following charts provides a useful means for displaying data over time?

A) Scatter chart B) A doughnut chart C) Pie chart D) Line chart Answer: D Diff: 1 Blooms: Remember Topic: Creating Charts in Microsoft Excel LO1: Determine the appropriate chart to visualize different types of data.

12) Philip wishes to understand the relative proportion of each data source to the total. Which of the following charts must Philip use?

A) Pie chart B) Bar chart C) Scatter chart D) Column chart Answer: A Diff: 1 Blooms: Remember Topic: Creating Charts in Microsoft Excel LO1: Determine the appropriate chart to visualize different types of data.

13) Observations consisting of pairs of variable data are required to construct a ________ chart.

A) doughnut B) scatter C) radar D) line Answer: B Diff: 1

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Blooms: Remember Topic: Creating Charts in Microsoft Excel LO1: Determine the appropriate chart to visualize different types of data.

14) Which of the following charts shows three-dimensional data?

A) Surface chart B) Column chart C) Stock chart D) Doughnut chart Answer: A Diff: 1 Blooms: Remember Topic: Creating Charts in Microsoft Excel LO1: Determine the appropriate chart to visualize different types of data.

15) Peige, a stock broker, has data consisting of price, price/earnings ratio, and market capitalization for seven different stocks on one particular day. She wishes to plot these three variables in two dimensions. Which of the following charts must Peige use?

A) Stock chart B) Surface chart C) Bubble chart D) Line chart Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Creating Charts in Microsoft Excel LO1: Determine the appropriate chart to visualize different types of data.

16) Which of the following charts allows plotting of multiple dimensions of several data series?

A) Doughnut chart B) Bubble chart C) Radar chart D) Area chart Answer: C Diff: 1 Blooms: Remember Topic: Creating Charts in Microsoft Excel LO1: Determine the appropriate chart to visualize different types of data.

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17) How does Excel distinguish between vertical and horizontal bar charts?

Answer: Excel distinguishes between vertical and horizontal bar charts, calling the former column charts and the latter bar charts. A clustered column chart compares values across categories using vertical rectangles; a stacked column chart displays the contribution of each value to the total by stacking the rectangles; and a 100% stacked column chart compares the percentage that each value contributes to a total.

Diff: 1 Blooms: Remember Topic: Creating Charts in Microsoft Excel LO1: Determine the appropriate chart to visualize different types of data.

18) After choosing the PivotTable, the PivotChart can be found on the ________ tab.

A) Design B) View C) Analyze D) Layout Answer: C Diff: 1 Blooms: Remember Topic: PivotTables LO1: Display the results of PivotTables using PivotCharts.

19) Construct a PivotChart to visualize the purchase order total units for steel forks and ceramic bowls within each region.

Answer: Choose the whole range of data set and opt for PivotChart in the Insert Tab. Set the regions as row labels and the items as column labels after filtering to include only ceramic bowl and steel fork.

Diff: 3

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Blooms: Apply AACSB: Analytic Skills Topic: PivotTables LO1: Display the results of PivotTables using PivotCharts.

20) To select data bars in Excel from the Home tab, which command would have to be accessed?

A) Find & Select under Editing group B) Conditional Formatting under Styles group C) Format under Cell group D) None of the above Answer: B Diff: 1 Blooms: Remember Topic: Other Excel Data Visualization Tools LO1: Apply data bars, color scales, icon sets, and sparklines to create other types of visualizations.

21) You may not display data bars without the data in the cells.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Other Excel Data Visualization Tools LO1: Apply data bars, color scales, icon sets, and sparklines to create other types of visualizations.

22) Color Scales are one of the options under Conditional Formatting.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Other Excel Data Visualization Tools LO1: Apply data bars, color scales, icon sets, and sparklines to create other types of visualizations.

23) How is the color-coding of quantitative data commonly called?

A) Heatmap B) Rainbow C) Scaling D) Hot & Cold Answer: A Diff: 1 Blooms: Remember Topic: Other Excel Data Visualization Tools

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LO1: Apply data bars, color scales, icon sets, and sparklines to create other types of visualizations.

24) Icon Sets can provide more information than Color Scales because they allow you to combine shapes and arrows.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Other Excel Data Visualization Tools LO1: Apply data bars, color scales, icon sets, and sparklines to create other types of visualizations.

25) How many types of Sparklines are available?

A) 2 B) 3 C) 4 D) 5 Answer: B Diff: 1 Blooms: Remember Topic: Other Excel Data Visualization Tools LO1: Apply data bars, color scales, icon sets, and sparklines to create other types of visualizations.

26) Let’s suppose you have a data set reporting the sales of five different product categories across the columns, and for each of the past four quarters, listed across the rows. Which of the following use of Sparklines would be the most appropriate?

A) Column Sparklines to compare quarterly sales across product categories and time series for each product category.

B) Line Sparklines to visualize quarterly sales across product categories, and Column Sparklines to compare time series for each product category.

C) Column Sparklines to compare quarterly sales across product categories, and Line Sparklines to visualize time series for each product category.

A) Line Sparklines to visualize quarterly sales across product categories and time series for each product category.

Answer: C Diff: 2 Blooms: Understand Topic: Other Excel Data Visualization Tools LO1: Apply data bars, color scales, icon sets, and sparklines to create other types of visualizations.

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27) Win/Loss Sparklines can only be used on quantitative data.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Other Excel Data Visualization Tools LO1: Apply data bars, color scales, icon sets, and sparklines to create other types of visualizations.

28) Complete the following sentence: a Dashboard…

A) is a visual representation of a set of key business measures.

B) is derived from the analogy of an automobile’s control panel.

C) provides important summaries of key business information.

D) is all of the above.

Answer: D Diff: 1 Blooms: Remember Topic: Dashboards LO1: Develop useful dashboards for communicating data and information.

29) Dashboards may include tabular as well as visual data to help a manager to quickly locate key information.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Dashboards LO1: Develop useful dashboards for communicating data and information.

30) What is a Key Performance Indicator?

A) A chart located in the bottom right of a dashboard.

B) An unnecessarily cluttered chart or table.

C) An important business metric.

D) None of the above.

Answer: C Diff: 1 Blooms: Remember Topic: Dashboards LO1: Develop useful dashboards for communicating data and information.

Copyright © 2020 Pearson Education, Inc.

Business Analytics, 3e (Evans) Chapter 4: Descriptive Statistics 1) Measure is the act of obtaining data associated with a metric. Measurements are the numerical values associated with a metric.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Metrics and Data Classification LO1: Define a metric and explain the concepts of measurement and measures.

2) Which of the following is an example of a measure of continuous metrics?

A) four errors revealed in an invoice B) a delivery delayed by seven days C) weight and volume of a sheet of steel D) three incomplete orders on a day Answer: C Diff: 2 Blooms: Understand Topic: Metrics and Data Classification LO1: Explain the difference between a discrete metric and continuous metric, and provide examples of each.

3) Nominal data: A) are ranked according to some relationship to one another.

B) have constant differences between observations.

C) are continuous and have a natural zero.

D) are sorted into categories according to specified characteristics.

Answer: D Diff: 1 Blooms: Remember Topic: Metrics and Data Classification LO1: Describe the four groups of data classification, categorical, ordinal, interval, and ratio, and provide examples of each.

4) Which of the following is a disadvantage of ordinal data?

A) They bear no relationship to one another.

B) They have no fixed units of measurement.

C) They have no natural zero.

D) They are not comparable with each other.

Answer: B Diff: 2 Blooms: Understand Copyright © 2020 Pearson Education, Inc. 50

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Topic: Metrics and Data Classification LO1: Describe the four groups of data classification, categorical, ordinal, interval, and ratio, and provide examples of each.

5) Which of the following allow meaningful comparison of ranges, averages and other statistics?

A) interval data B) categorical data C) ratio data D) ordinal data Answer: A Diff: 1 Blooms: Remember Topic: Metrics and Data Classification LO1: Describe the four groups of data classification, categorical, ordinal, interval, and ratio, and provide examples of each.

6) Following are the components of a data set containing purchase details of a shoe manufacturing company. Identify the ratio data.

A) Item Number B) Rank of suppliers C) Item cost D) Arrival Date Answer: C Diff: 2 Blooms: Apply Topic: Metrics and Data Classification LO1: Describe the four groups of data classification, categorical, ordinal, interval, and ratio, and provide examples of each.

7) When data are classified by the type of measurement scale, which is the strongest form of measurement?

A) nominal B) interval C) ordinal D) ratio Answer: D Diff: 1 Blooms: Remember Topic: Metrics and Data Classification LO1: Describe the four groups of data classification, categorical, ordinal, interval, and ratio, and provide examples of each.

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8) Explain statistics as defined by David Hand. What are the two ways in which Microsoft Excel supports statistical analysis?

Answer: Statistics, as defined by David Hand, is both the science of uncertainty and the technology of extracting information from data. Statistics involves collecting, organizing, analyzing, interpreting, and presenting data. A statistic is a summary measure of data. Microsoft Excel supports statistical analysis in two ways: • with statistical functions that are entered in worksheet cells directly, or embedded in formulas • with the Excel Analysis Toolpak add-in to perform more complex statistical computations.

Diff: 1 Blooms: Remember Topic: Metrics and Data Classification LO1: Explain the science of statistics and define the term statistic.

9) To construct a frequency distribution for categorical data, the A) observations that appear in each category must be summed up.

B) number of observations that appear in each category must be counted.

C) observations in each category must be multiplied by observations in the corresponding category.

D) number of observations in each category must be divided by the total number of observations in all categories.

Answer: B Diff: 2 Blooms: Remember Topic: Frequency Distributions and Histograms LO1: Construct a frequency distribution for categorical, numerical, and grouped data.

10) When constructing frequency distributions for numerical data, SUMIF is used to count the frequencies of each discrete value.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Frequency Distributions and Histograms LO1: Construct a frequency distribution for categorical, numerical, and grouped data.

11) How is a frequency distribution calculated for categorical and numerical data?

Answer: A frequency distribution is a table that shows the number of observations in each of several non-overlapping groups. Categorical variables naturally define the groups in a frequency distribution. The frequencies may be expressed as a fraction, or proportion, of the total; these are called relative frequencies. A relative frequency distribution is a tabular summary of the relative frequencies of all categories. For numerical data that consist of a small number of discrete values, frequency distributions may be constructed in a similar way as done for categorical data; COUNTIF is used to count the frequencies of each value. A graphical depiction of frequency distributions for numerical data in the form of a column chart is called a histogram.

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Diff: 2 Blooms: Remember Topic: Frequency Distributions and Histograms LO1: Construct a frequency distribution for categorical, numerical, and grouped data.

12) If a data set has 'c' number of observations, the relative frequency of category 'l' is computed as ________.

A) (frequency of category 'l') / 'c' B) 'c' × (number of observations in category 'l') C) (sum of all observations in category 'l') / 'c' D) sum of ('c' + each observation in category 'l') Answer: A Diff: 1 Blooms: Remember Topic: Frequency Distributions and Histograms LO1: Construct a relative frequency distribution and histogram.

Use the data given below to answer the following question(s).

Following is an extract from the Employee Payroll Database of HFR Informatics Inc. Employee Maria Peter George Smith Johnson Thompson Martinez Lewis Lee Taylor Carter Edwards Bailey Cooper Bill Cox Perry Flores Woods Cole

Ethnic Group Asian American White American Hispanic American Black American Alaska Native Asian American Alaska Native White American Black American Asian American Asian American Hispanic American White American White American Alaska Native Asian American Hispanic American Alaska Native White American Asian American

Gender Female Male Male Female Male Male Male Female Male Female Male Male Male Male Male Male Female Female Male Female

Rank / Grade 3 2 1 1 2 2 3 2 2 1 2 2 2 2 3 1 2 2 3 1

Copyright © 2020 Pearson Education, Inc.

Pay Scale A B C D E B A B A B C E B A E A C B E A

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13) What is the relative frequency of Grade 3 employees?

A) 4 B) 0.55 C) 0.20 D) 5 Answer: C Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Frequency Distributions and Histograms LO1: Construct a relative frequency distribution and histogram.

14) What is the relative frequency of Female employees?

A) 0.65 B) 0.75 C) 0.25 D) 0.35 Answer: D Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Frequency Distributions and Histograms LO1: Construct a relative frequency distribution and histogram.

15) A graphical depiction of a frequency distribution for numerical data in the form of a column chart is called a ________.

A) cartogram B) correlogram C) histogram D) dendogram Answer: C Diff: 1 Blooms: Remember Topic: Frequency Distributions and Histograms LO1: Construct a relative frequency distribution and histogram.

16) While constructing a histogram, how is group width calculated?

A) number of groups × (lower limit of the last group + upper limit of the first group) B) (upper limit of the last group - lower limit of the first group) / number of groups C) (upper limit of the first group + number of groups) × lower limit of the last group + number of groups) D) (lower limit of the first group - number of groups) × upper limit of the last group Answer: B

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Diff: 1 Blooms: Remember Topic: Frequency Distributions and Histograms LO1: Construct a relative frequency distribution and histogram.

Use the data given below to answer the following question.

Following is the purchase order database of 'The Chef Says So', a restaurant in New York, over the last quarter (April-June).

Order Date 5/6/2012 4/7/2012 5/13/2012 6/10/2012 6/22/2012 5/17/2012 4/25/2012 6/1/2012 4/2/2012 5/27/2012 6/13/2012 4/30/2012 5/11/2012 6/18/2012 5/9/2012 5/30/2012 6/6/2012 4/3/2012 6/26/2012 4/23/2012 4/29/2012 4/4/2012 6/15/2012 6/25/2012 5/23/2012 6/28/2012 5/25/2012 5/1/2012

Item Steel Fork Ceramic Plate Steel Fork Silver Spoon Steel Fork Ceramic Plate Steel Fork Steel Fork Steel Fork Ceramic Plate Steel Fork Ceramic Plate Ceramic Plate Steel Fork Glass Bottle Ceramic Bowl Ceramic Plate Silver Spoon Silver Spoon Ceramic Bowl Steel Fork Ceramic Bowl Ceramic Plate Ceramic Plate Ceramic Plate Ceramic Plate Ceramic Bowl Steel Fork

Region Antasia Puitoria Puitoria Puitoria Almeco Antasia Puitoria Puitoria Almeco Antasia Puitoria Antasia Antasia Antasia Puitoria Antasia Puitoria Antasia Antasia Puitoria Puitoria Antasia Puitoria Puitoria Antasia Almeco Puitoria Puitoria

Supplier Peter Kane Jones Gerry Sarah Peter Audrey Jones Thomas Peter Mary Henry Philip Peter Simson Peter Mary Peter Philip Kane Simson Philip Gerry Simson Peter Sarah Jones Audrey

Unit Cost 5.44 23.44 8.44 23.44 6.44 8.44 5.44 8.44 5.44 12.44 8.44 5.44 23.44 8.44 128.45 19.44 12.44 12.44 23.44 8.44 4.74 19.44 12.44 18.45 8.44 23.44 8.44 5.44

Copyright © 2020 Pearson Education, Inc.

Units 98 53 39 30 59 63 78 93 35 63 93 32 84 38 5 19 31 67 18 99 70 77 49 90 7 10 53 69

56 Chapter 4: Descriptive Statistics

Order Date 4/12/2012 4/18/2012 6/30/2012 5/19/2012 4/16/2012 6/4/2012 5/2/2012 4/19/2012 6/11/2012 5/31/2012 6/2/2012 4/13/2012 5/3/2012 6/3/2012 4/17/2012

Item Silver Spoon Steel Fork Ceramic Plate Glass Bottle Ceramic Bowl Ceramic Bowl Ceramic Bowl Glass Bottle Steel Fork Silver Spoon Ceramic Plate Steel Fork Ceramic Plate Ceramic Plate Ceramic Plate

Business Analytics, 3e

Region Antasia Puitoria Puitoria Puitoria Antasia Puitoria Puitoria Almeco Puitoria Almeco Almeco Puitoria Puitoria Puitoria Puitoria

Supplier Henry Gerry Gerry Kane Peter Mary Kane Sarah Gerry Sarah Thomas Audrey Jones Jones Audrey

Unit Cost 8.44 4.74 12.44 128.45 8.44 15.94 27.4 278.45 4.74 5.44 23.44 4.74 8.44 23.44 8.44

Units 99 56 83 8 65 58 45 6 10 79 60 17 14 97 31

17) Construct a relative frequency distribution for items in the purchase order database and show the proportions of the frequencies visually using a pie chart.

Answer: In a new table, list out the items and use the COUNTIF function to calculate the frequencies. The relative frequency may be calculated as: (frequency of an item) / total number of observations Items Steel Fork Ceramic Plate Silver Spoon Glass Bottle Ceramic Bowl Total

Frequency 13 15 5 3 7 43

Relative Frequency 0.3 0.35 0.12 0.07 0.16 1

The pie chart can be constructed for the items with their corresponding relative frequencies.

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Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Frequency Distributions and Histograms LO1: Construct a relative frequency distribution and histogram.

18) Not specifying a Bin Range will not allow Excel to automatically determine bin values for the frequency distribution and histogram.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Frequency Distributions and Histograms LO1: Construct a relative frequency distribution and histogram.

19) Fewer groups provide a "coarser" histogram.

Answer: TRUE Diff: 2 Blooms: Remember Topic: Frequency Distributions and Histograms LO1: Construct a relative frequency distribution and histogram.

20) What is the cumulative relative frequency of employees on a 'A to D' pay scale?

A) 1.00 B) 0.80 C) 0.30 D) 0.60 Answer: B Diff: 3

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Blooms: Apply AACSB: Analytic Skills Topic: Frequency Distributions and Histograms LO1: Compute cumulative relative frequencies.

21) What is the cumulative relative frequency of Ranks 1 and 2?

A) 0.80 B) 0.15 C) 0.30 D) 0.25 Answer: A Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Frequency Distributions and Histograms LO1: Compute cumulative relative frequencies.

22) Which of the following represents the proportion of the total number of observations that fall at or below the upper limit of each group?

A) Percentile B) Pareto chart C) Frequency distribution D) Cumulative relative frequency Answer: D Diff: 1 Blooms: Remember Topic: Frequency Distributions and Histograms LO1: Compute cumulative relative frequencies.

23) The Excel 2010 function ________ computes the kth percentile of data in the range specified in the array field, where k is in the range 0 to 1, inclusive.

A) PERCENTILE.INC(array, k) B) PERCENTILE(array + k) C) PERCENTILE.IF(array, k) D) PERCENTILE(SUM(array), k) Answer: A Diff: 1 Blooms: Remember Topic: Percentiles and Quartiles LO1: Find percentiles and quartiles for a data set.

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Use the data given below to answer the following question(s).

Following is an extract from the Cost per Order Database of Grogtes LLC. Item Category

Item ID

Item Cost

Units

Nuts Screws Nuts Screwdriver Nuts Screws Nuts Nuts Nuts Screws Nuts Screws Screws Nuts Nails Bolts Screws Screwdriver Screwdriver Bolts Nuts Bolts Screws Screws Screws Screws Bolts Nuts Screwdriver Nuts Screws Nailgun pack

N101 S101 N102 SD101 N102 S102 N101 N102 N101 S103 N102 S101 S101 N102 NG101 B101 S103 SD102 SD101 B102 N103 B101 S103 S104 S102 S101 B102 N101 SD103 N103 S103 NG101

$2.44 $20.44 $5.44 $20.44 $3.44 $5.44 $2.44 $5.44 $2.44 $9.44 $5.44 $2.44 $20.44 $5.44 $125.45 $16.44 $9.44 $9.44 $20.44 $5.44 $1.74 $16.44 $9.44 $15.45 $5.44 $20.44 $5.44 $2.44 $5.44 $1.74 $9.44 $125.45

94 49 35 26 55 59 74 89 31 59 89 28 80 34 1 15 27 63 14 95 66 73 45 86 3 6 49 65 95 52 79 4

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Cost per Order $229.36 $1,001.56 $190.40 $531.44 $189.20 $320.96 $180.56 $484.16 $75.64 $556.96 $484.16 $68.32 $1,635.20 $184.96 $125.45 $246.60 $254.88 $594.72 $286.16 $516.80 $114.84 $1,200.12 $424.80 $1,328.70 $16.32 $122.64 $266.56 $158.60 $516.80 $90.48 $745.76 $501.80

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Item Category

Item ID

Item Cost

Units

Bolts Bolts Bolts Nails Nuts Screwdriver Screws Nuts Screws Screws Screws

B102 B103 B104 NG102 N103 SD104 S101 N103 S102 S101 S102

$5.44 $12.94 $24.40 $275.45 $1.74 $2.44 $20.44 $1.74 $5.44 $20.44 $5.44

61 54 41 2 6 75 56 13 10 93 27

Cost per Order $331.84 $698.76 $1,000.40 $550.90 $10.44 $183.00 $1,144.64 $22.62 $54.40 $1,900.92 $146.88

24) Which of the following observations is closest to the 87th percentile of costs per order?

A) 75 SD104 screwdrivers for $183.00 B) 66 N103 nuts for $114.84 C) 73 B101 bolts for $1,200.12 D) 49 S101 screws for $1,001.56 Answer: D Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Percentiles and Quartiles LO1: Find percentiles and quartiles for a data set.

25) Which of the following does the 38th percentile of the costs per order indicate?

A) 62% of the costs per order are more than or equal to $190.40.

B) 38% of the costs per order are less than or equal to $189.20.

C) 62% of the costs per order are less than or equal to $484.16.

D) 38% of the costs per order are more than or equal to $501.80.

Answer: B Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Percentiles and Quartiles LO1: Find percentiles and quartiles for a data set.

26) Which of the following observations is closest to the third quartile?

A) 35 N102 nuts for $190.40 B) 59 S103 screws for $556.96 C) 13 N103 nuts for $22.62 Copyright © 2020 Pearson Education, Inc.

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D) 2 NG102 nailgun packs for $550.90 Answer: B Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Percentiles and Quartiles LO1: Find percentiles and quartiles for a data set.

27) Which of the following does the second quartile of the costs per order indicate?

A) 2% of the costs per order are less than or equal to $114.84.

B) 20% of the costs per order are less than or equal to $1,200.12.

C) 5% of the costs per order are less than or equal to $229.36.

D) 50% of the costs per order are less than or equal to $286.16.

Answer: D Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Percentiles and Quartiles LO1: Find percentiles and quartiles for a data set.

28) What is the rank of the 42nd percentile of the costs per order ?

A) 17 B) 13.35 C) 19 D) 33.75 Answer: C Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Percentiles and Quartiles LO1: Find percentiles and quartiles for a data set.

29) Which of the following is true about quartiles?

A) The 25th percentile is called the fourth quartile.

B) One-fourth of the data fall below the fourth quartile.

C) Three-fourths of the data are below the third quartile.

D) The 50th quartile is the third percentile.

Answer: C Diff: 2 Blooms: Remember Topic: Percentiles and Quartiles LO1: Find percentiles and quartiles for a data set.

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30) Which of the following will give the value for the third quartile?

A) PERCENTILE.INC(array, 0.75) B) QUARTILE.INC(array, 0.75) C) DECILE.INC(array, 0.30) D) QUARTILE.INC(array, 0.25) Answer: A Diff: 2 Blooms: Remember Topic: Percentiles and Quartiles LO1: Find percentiles and quartiles for a data set.

31) Which of the following is true about cross-tabulation?

A) All subcategories together must constitute the complete data set.

B) A cross-tabulation table is often called a latent class model.

C) Each observation can be classified into many subcategories.

D) The table displays the number of categorical variables between two observations.

Answer: A Diff: 2 Blooms: Remember Topic: Cross-Tabulations LO1: Construct a cross-tabulation (contingency table).

32) The purpose of sampling is to ________.

A) enumerate all the values in the population B) measure all items of interest for a particular interest or investigation C) obtain sufficient information to draw a valid inference about a population D) calculate all variables and observations within a population Answer: C Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: Explain the difference between a population and a sample.

33) In statistical notation, the elements of a data set are typically labeled as ________.

A) summation operators B) letters in capitals C) Greek letters D) subscripted variables Answer: D Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: Understand statistical notation.

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34) According to statistical notations, what does Σ stand for?

A) to act as a summation operator B) to represent sample statistics C) to represent population measures D) to represent the number of items in a population Answer: A Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: Understand statistical notation.

35) Which of the following measures of location is calculated using the formula , where n is the number of observations?

A) midrange B) sample mean C) mode D) median Answer: B Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: List different measures of location.

36) Which of the following is true from the equation: = 0, where 𝑥̅ is the mean of the sample?

A) The sum of the deviations above the mean are the same as the sum of the deviations below the mean B) Half the data lie above the mean of the values C) The specific set of values does not have any outliers affecting the mean D) Half the data lie below the mean of the values Answer: A Diff: 2 Blooms: Remember Topic: Descriptive Statistical Measures LO1: Compute the mean, median, mode, and midrange of a set of data.

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Use the table below to answer the following question(s).

Below is a table showing the costs per order of items bought by a computer hardware store.

Supplier Aloham Technologies Aloham Technologies Aloham Technologies Aloham Technologies Aloham Technologies Aloham Technologies MindRoot Hardwares MindRoot Hardwares MindRoot Hardwares MindRoot Hardwares

Item Description Monitors Hard Disks Power Supply Graphics Card Processor Speakers Flashdrive Graphics Card CD-ROM Bluetooth Device

Cost per Order $250 $220 $88 $300 $325 $88 $9 $299 $88 $80

37) Calculate the mean cost per order.

A) $220.54 B) $174.70 C) $159 D) $88 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Descriptive Statistical Measures LO1: Compute the mean, median, mode, and midrange of a set of data.

38) Calculate the mode for the cost per order data.

A) $174.17 B) $325 C) $88 D) $206.5 Answer: C Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Descriptive Statistical Measures LO1: Compute the mean, median, mode, and midrange of a set of data.

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39) Calculate the median for the cost per order data.

A) $325 B) $154 C) $174.17 D) $88 Answer: B Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Descriptive Statistical Measures LO1: Compute the mean, median, mode, and midrange of a set of data.

40) One of the measures of location is calculated as 88. Which of the following measures of location corresponds to this value?

A) mean B) mode C) median D) midrange Answer: B Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Descriptive Statistical Measures LO1: List different measures of location.

41) The measure of location that specifies the middle value when the data are arranged from least to greatest is the ________.

A) outlier B) mean C) median D) mode Answer: C Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: List different measures of location.

42) Which of the following is true for a median?

A) A median is only meaningful for interval or ordinal data and not for ratio data.

B) Medians can be calculated no matter how the data is arranged.

C) Medians are affected by outliers.

D) For an even number of observations, the median is the mean of the two middle numbers.

Answer: D

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Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: List different measures of location.

43) Which of the following is a difference between a mean and a median?

A) A mean divides the data half above it and half below it; a median does not.

B) A median is not affected by outliers; a mean is affected by outliers.

C) A mean is an observation that occurs most frequently; a median is the average of all observations.

D) A median is not meaningful for ratio data; a mean is meaningful to ratio data.

Answer: B Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: List different measures of location.

44) The ________ is the observation that occurs most frequently.

A) mode B) mean C) outlier D) median Answer: A Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: List different measures of location.

45) Which of the following is true for a mode?

A) Modes are the mid values of data arranged from least to greatest.

B) Modes are affected by outliers.

C) Modes cannot be used in data having repetitious values.

D) The highest bar in a histogram is its mode.

Answer: D Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: List different measures of location.

46) The ________ is the average of the greatest and least values in the data set.

A) mean B) median

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C) midrange D) mode Answer: C Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: List different measures of location.

47) Which of the following types of conditions is most likely to render a midrange value useless?

A) having repetitious values in the data set B) having the data arranged from least to greatest in value C) having a small sample size D) having extreme values in a data Answer: D Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: List different measures of location.

48) Which of the following is a similarity between a midrange and a mean?

A) Both measures are calculated using all the values in a data set.

B) Both measures are affected by outliers.

C) Both measures divide the data into two equal halves.

D) Both measures can only be used for small sample sizes.

Answer: B Diff: 1 Blooms: Understand Topic: Descriptive Statistical Measures LO1: List different measures of location.

49) Which of the following is an example of a measure of dispersion?

A) median B) mode C) variance D) midrange Answer: C Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: List different measures of dispersion.

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50) Which of the following describes dispersion in statistics?

A) the degree of variation in the data B) the central value in the data C) the frequency of values in the data D) the measure of outliers in the data Answer: A Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: List different measures of dispersion.

51) The difference between the first and third quartiles is referred to as the ________.

A) standard deviation B) variance C) interquartile range D) midrange Answer: C Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: List different measures of dispersion.

52) Which of the following is true of midspread?

A) It is an example of a measure of location.

B) It is calculated by finding the difference between the highest and lowest values in the data set.

C) It is affected by extreme values.

D) It is calculated using only the middle 50% of the data.

Answer: D Diff: 1 Blooms: Understand Topic: Descriptive Statistical Measures LO1: List different measures of dispersion.

53) Which of the following describes variance?

A) It is the difference between the maximum value and the minimum value in the data set.

B) It is the difference between the first and third quartiles of a data set.

C) It is the average of the squared deviations of the observations from the mean.

D) It is the average of the greatest and least values in the data set.

Answer: C Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: List different measures of dispersion.

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54) Which of the following is true of variance?

A) The formula to calculate variance of a population is not the same as the formula to calculate variance of a sample.

B) Its value is inversely proportional to the degree to which the data is spread from the mean.

C) It only requires the middle 50% of data to be calculated.

D) It is the square root of standard deviation.

Answer: A Diff: 1 Blooms: Understand Topic: Descriptive Statistical Measures LO1: List different measures of dispersion.

55) Which of the following describes standard deviation?

A) It is the average of the greatest and least values in the data set.

B) It is the square root of the variance.

C) It is the difference between the first and third quartiles of a data set.

D) It is the average of the squared deviations of the observations from the mean.

Answer: B Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: List different measures of dispersion.

56) ________ states that for any set of data, the proportion of values that lie within k standard deviations (k > 1) of the mean is at least 1 - 1/k2.

A) Prime number theorem B) Bertrand's postulate C) Oppermann's conjecture D) Chebyshev's theorem Answer: D Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: Explain Chebyshev's theorem.

57) Using Chebyshev's theorem for standard deviation, calculate the percentage of data that lie within five standard deviations of the mean.

A) 89% B) 75% C) 96% D) 50% Answer: C Diff: 2

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Blooms: Apply AACSB: Analytic Skills Topic: Descriptive Statistical Measures LO1: Explain Chebyshev's theorem.

58) In the equation Cp = (upper specification - lower specification)/total variation, what does Cp denote?

A) capacity variation index B) capability pattern C) process capability index D) capability push Answer: C Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: List different measures of dispersion.

59) Which of the following is the z-score equation for the ith observation?

A) zt = B) zi = C) z1= D) zi = Answer: B Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: Compute a standardized value (z-score) for observations in a data set.

60) In the z-score formula, which of the following is true if the value in the numerator is a negative value?

A) that the xi value lies to the left of the mean B) that the mean is of lesser value than the xi value C) that the mean is of negative value D) that the numerator value cannot be divided by the standard deviation Answer: A Diff: 2 Blooms: Understand

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Topic: Descriptive Statistical Measures LO1: Compute a standardized value (z-score) for observations in a data set.

61) A z-score of 1.0 means that ________.

A) the observation is -1.0 standard deviation to the right of the mean B) the observation is -1.0 standard deviation to the left of the mean C) the observation has no deviation from the mean D) the observation is 1.0 standard deviation to the right of the mean Answer: D Diff: 2 Blooms: Understand Topic: Descriptive Statistical Measures LO1: Compute a standardized value (z-score) for observations in a data set.

62) Which of the following is the equation for calculating the coefficient of variation (CV)?

A) CV = standard deviation/mean B) CV = standard deviation - z-score/mean (total variation) C) CV = value of observation's distance from mean/standard deviation D) CV = mean/(standard deviation)2 Answer: A Diff: 2 Blooms: Understand Topic: Descriptive Statistical Measures LO1: Define and compute the coefficient of variation.

63) How is the return to risk described in financial statistics?

A) as the relative measure of the distance an observation is from the mean B) as the reciprocal of coefficient of variation C) as the square root of variance D) as the ratio of excess returns to its standard deviation Answer: B Diff: 1 Blooms: Understand Topic: Descriptive Statistical Measures LO1: Define and compute the coefficient of variation.

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64) Describe and construct a cross-tabulation showing the region-wise percentage breakdown of purchase of glass bottles and silver spoons and visually represent the data in a 3-D column chart.

Counts: Region Almeco Antasia Puitoria

Glass Bottle 6 0 13

Silver Spoon 79 184 30

Grand Total 85 184 43

Percentages by Region: Region Glass Bottle Almeco 7% Antasia 0% Puitoria 30%

Silver Spoon 93% 100% 70%

Grand Total 100% 100% 100%

Answer: Construct a pivot table with regions as the row labels and filtering the items to include only glass bottle and silver spoon. Compute the percentage purchase within each region and construct a chart on that data.

Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: PivotTables LO1: Use PivotTables to analyze and gain insight from data.

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65) In finance, the ________ is the ratio of a fund's excess returns (annualized total returns minus Treasury bill returns) to its standard deviation.

A) field ratio B) Sortino ratio C) Calmar ratio D) Sharpe ratio Answer: D Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: Define and compute the coefficient of variation.

66) Calculate the coefficient of variation from the following data: z-score = 1.32; standard deviation = 0.173; mean = 4.7; total variation = 0.6 A) 27.16 B) 156.66 C) 0.04 D) -0.5 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Descriptive Statistical Measures LO1: Define and compute the coefficient of variation.

67) Which of the following values of the coefficients of variation of stocks represents the least risky stock?

A) 1.0 B) 0.005 C) 0.5 D) 0.045 Answer: B Diff: 2 Blooms: Understand Topic: Descriptive Statistical Measures LO1: Define and compute the coefficient of variation.

68) Which of the following describes a positively skewed histogram?

A) a histogram that tails off toward the right B) a histogram that has no fluctuation in mass C) a histogram where more mass tails off toward the left D) a histogram where mass is only concentrated in the middle Answer: A

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Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: Explain the nature of skewness and kurtosis in a distribution.

69) The ________ measures the degree of asymmetry of observations around the mean.

A) coefficient of variation B) return to risk factor C) coefficient of skewness D) coefficient of kurtosis Answer: C Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: Explain the nature of skewness and kurtosis in a distribution.

70) The coefficient of skewness is computed as ________.

A) CS =

)3

B) CS =

C) CS =

D) CS = Answer: D Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: Interpret the coefficients of skewness and kurtosis.

71) Which of the following is true of the coefficient of skewness (CS)?

A) If the CS is positive, the distribution of values tails off to the left.

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B) If the CS value is between 0.5 and 1, the skewness is considered to be moderate.

C) If the CS is closer to zero, the degree of skewness is considered to be high.

D) If the CS value is between -0.5 and -1, the skewness is considered negligible.

Answer: B Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: Interpret the coefficients of skewness and kurtosis.

72) In statistics, ________ refers to the peakedness or flatness of a histogram.

A) Sharpe ratio B) entropy rate C) Markov chain D) kurtosis Answer: D Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: Explain the nature of skewness and kurtosis in a distribution.

73) Which of the following cases require the mean of a sample to be calculated using the formula x

where N represents the sample size?

A) the sample has no mode value B) there is direct access to the raw data C) sample data are grouped in a frequency distribution D) the coefficient of skewness is 1 or less than -1 Answer: C Diff: 1 Blooms: Understand Topic: Computing Descriptive Statistics for Frequency Distributions LO1: Calculate the mean, variance, and standard deviation for grouped data.

74) The ________ is a formal statistical measure for categorical data, such as defects or errors in quality control applications or consumer preferences in market research.

A) variance B) proportion C) mean D) skewness Answer: B

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Diff: 1 Blooms: Remember Topic: Descriptive Statistics for Categorical Data: The Proportion LO1: Calculate a proportion.

75) ________ is a measure of the linear association between two variables, X and Y. A) Kurtosis B) Proportion C) Skewness D) Covariance Answer: D Diff: 1 Blooms: Remember Topic: Measures of Association LO1: Explain the importance of understanding relationships between two variables. Explain the difference between covariance and correlation.

76) Which of the following formula is used to compute covariance between two variables X and Y? N

 ( x   )( y   ) i

A) cov (X,Y) = i 1

x

i

y

N

N

 (x   ) i

B) cov (X,Y) = i 1

2

x

N ( x   x )2 C) cov (X,Y) =  i i 1 ( yi   y ) N

N

D) cov (X,Y) =

 (x   ) i 1

i

2

x

N2

Answer: A Diff: 1 Blooms: Remember Topic: Measures of Association LO1: Explain the importance of understanding relationships between two variables. Explain the difference between covariance and correlation.

77) Which of the following is true of covariance, between two variables, when one of the deviations from the mean is positive and the other is negative?

A) the degree of linear association is high between the two variables B) there is no covariance between the two variables

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C) the covariance will be negative D) the covariance will be positive Answer: C Diff: 2 Blooms: Understand Topic: Measures of Association LO1: Explain the importance of understanding relationships between two variables. Explain the difference between covariance and correlation.

78) ________ is a measure of the linear relationship between two variables, X and Y, which does not depend on the units of measurement.

A) Kurtosis B) Proportion C) Skewness D) Correlation Answer: D Diff: 1 Blooms: Remember Topic: Measures of Association LO1: Explain the importance of understanding relationships between two variables. Explain the difference between covariance and correlation.

79) Which of the following is the equation used for computing the sample correlation coefficient?

A) rxy = cov(X,Y)(sxsy) B) rxy = C) rxy = D) rxy = Answer: B Diff: 1 Blooms: Remember Topic: Measures of Association LO1: Calculate measures of covariance and correlation.

80) For two variables, a positive correlation coefficient indicates ________.

A) a linear relationship exists for which one variable increases as the other also increases B) a linear relationship exists for one variable that increases while the other decreases

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C) that the two variables have no linear relationship with each other D) a nonlinear relationship with no linear correlation between the two variables Answer: A Diff: 2 Blooms: Understand Topic: Measures of Association LO1: Calculate measures of covariance and correlation.

Use the spreadsheet below to answer the following question(s).

Below is the table showing rate of shoes sold per day and the highest-priced shoe sold that day for a one-week period. The rate of shoes sold per day (X) and the price of the shoes (Y).

Shoes sold in % (X) 15 27 10 13 25 9 18

Price (Y) $48 $55 $40 $88 $53 $47 $40

81) Use Excel to calculate the mean for X. A) 16.71 B) 7.04 C) 2.67 D) 0.02 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Descriptive Statistical Measures LO1: Compute the mean, median, mode, and midrange of a set of data.

82) Use Excel to calculate the variance of X. A) 271.33 B) 16.47 C) 49.57 D) 7.04 Answer: C Diff: 2

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Blooms: Apply AACSB: Analytic Skills Topic: Descriptive Statistical Measures LO1: Compute the range, interquartile range, variance, and standard deviation of a set of data.

83) Use Excel to calculate the standard deviation for Y. A) 49.57 B) 16.47 C) 7.04 D) 2.6 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Descriptive Statistical Measures LO1: Compute the range, interquartile range, variance, and standard deviation of a set of data.

84) Use Excel to calculate the covariance between variables X and Y. A) 2.67 B) 0.02 C) 16.71 D) 7.04 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Measures of Association LO1: Calculate measures of covariance and correlation.

85) Use Excel to calculate the z-score of X observation 27.

A) -0.24 B) 0 C) 0.18 D) 1.46 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Descriptive Statistical Measures LO1: Compute a standardized value (z-score) for observations in a data set.

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86) Use Excel to calculate the coefficient of variation of X. A) 0.42 B) 0.31 C) 7.04 D) 16.47 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Descriptive Statistical Measures LO1: Define and compute the coefficient of variation.

87) Use Excel to calculate the correlation between variables X and Y. A) 16.47 B) 0.02 C) 16.71 D) 7.04 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Measures of Association LO1: Calculate measures of covariance and correlation.

88) Calculate the standard deviation for cost per order in the following table.

Observation X1 X2 X3 X4 X5 X6 X7

Cost per order $ 1345 $ 4364 $ 1768 $ 2278 $ 4332 $ 2984 $ 3326

Answer: The formula for standard deviation, S =

where n, is the number of

observations. (xi - )2 is the square of the difference between each observation minus the mean.

In order to calculate the standard deviation, we must first calculate the mean order.

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of all the cost per

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=

, where,

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is the sum of observations, n, the number of observations.

Therefore, = 20397 / 7 = 2913.86.

2

Now, we have to calculate

) , which is calculated by adding all the squares of each

observation minus the mean.

Observation X1 X2 X3 X4 X5 X6 X7 Sum Count Mean Variance Standard Deviation Therefore,

Cost per order in $ 1345 4364 1768 2278 4332 2984 3326

(xi - mean) -1568.86 1450.14 -1145.86 -635.86 1418.14 70.14 412.14

20397 7 2913.86 1411240.14

(xi - mean)2 2461312.73 2102914.31 1312988.59 404314.31 2011129.16 4920.02 169861.73 8467440.86

1187.96 )2 = 8467440.86

From this variance can be calculated using

= 8467440.86 / 6 = 1411240.14

Standard Deviation is the square root of variance, therefore, standard deviation = 1411240.14 = 1187.96.

Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Descriptive Statistical Measures LO1: Compute the range, interquartile range, variance, and standard deviation of a set of data.

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89) Below is the data collected from a manufacturing process for a part whose dimensions are specified as 4.00 ± 0.1 centimeters. Calculate the process capability index within three standard deviations of the mean.

Manufacturing Measurements 4.78 3.99 5.02 4.23 4.57 4.44 5.18 Answer: The process capability index, denoted as Cp = upper specification - lower specification / total variation.

Manufacturing Measurements (Xi - mean {X}) (Xi - mean {X})2 4.78 0.18 0.032 Mean 4.6 Standard 3.99 -0.61 0.37 Deviation 0.424 5.02 0.42 0.18 Variance 0.18 4.23 -0.37 0.14 Mean -3*Stdev 3.33 4.57 -0.03 0.00099 Mean +3*Stdev 5.87 4.44 -0.16 0.03 Total Variation 2.54 5.18 0.58 0.33 Lower Specification 3.9 Upper Sum 1.08 Specification 4.1 Specification Range 0.2 Cp

.08

In order to calculate the process capability index, the mean of the measurements should be first calculated using the formula: sum of all measurements / number of measurements.

The mean is found to be: 4.6.

From the mean, we calculate variation using the formula observations.

; where n is the number of

)2 is the sum of all the squares of each observation minus the mean.

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The variation is found to be: 0.18.

The standard deviation is the square root of variance, therefor, standard deviation = 0.42.

0.18 =

Now Mean - 3*Stdev, and Mean + 3*Stdev are calculated.

Mean - 3*Stdev = 4.6 × 3(0.44) = 3.33, and, Mean + 3*Stdev = 4.6 + 3(0.44) = 5.87.

Therefore total variation = (Mean + 3*Stdev) - (Mean - 3*Stdev) = 5.87 - 3.33 = 2.54.

The process capability index, Cp, is then calculated as 0.2 / 2.54 = 0.08.

Therefore, Cp = 0.08.

Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Descriptive Statistical Measures LO1: Compute the range, interquartile range, variance, and standard deviation of a set of data.

90) The table below shows the sales per day at a grocery store over a period of a week. Calculate the z-score for sales on Day 4.

Day 1 2 3 4 5 6 7

Sales per day in $ (Xi) 5000 5304 6430 7889 5333 6109 6734

Answer: Z-score is calculated using the formula, z4 =, where s is the standard deviation, xi are observations, is the mean of the observation.

Day 1 2 3 4 5 6 7 Sum

Sales per day (Xi - mean in $ (Xi) {X}) 5000 -1114.14 5304 -810.14 6430 315.86 7889 1774.86 5333 -781.14 6109 -5.14 6734 619.86 42799

(Xi - mean {X})^2 1241314.31 656331.45 99765.73 3150117.88 610184.16 26.44898 384222.88 6141962.86

z-score -1.10 -0.80 0.31 1.75 -0.77 -0.005 0.61

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Mean Variance Standard Deviation

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6114.14 1023660.48 1011.76

First, the mean has to be calculated using the formula =

, n is the number of

observations, and x are number of observations.

The mean is calculated to be: 42799/7 = 6114.14.

From the mean we calculate the variance using the formula s2 =

, where (xi - )2 is

the sum of the squares of observations minus the mean.

Therefor variance is calculated as 6141962.86/6 = 1023660.48.

Standard deviation is the square root of variance, therefor, standard deviation = 1011.76.

Now, the z-score for the 4th day can be calculated as 1774.86/1011.76 = 1.75.

Therefore, z4 = 1.75.

Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Descriptive Statistical Measures LO1: Compute a standardized value (z-score) for observations in a data set.

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=

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91) The table below shows the daily frequency of female customers at a particular ice cream shop during discount sale periods. The data is collected for 5 days. Calculate the mean for the data.

Female Customer Frequency Days (x) 1 2 3 4 5

Frequency (f) 0 5 8 11 18

Answer: For grouped data, mean, =

, where n is the number of observations, and fixi

is individual frequencies multiplied by the corresponding number of days.

Female Customer Frequency Days (x) 1 2 3 4 5 Sum

Frequency (f) Frequency*Days 0 0 5 10 8 24 11 44 18 90 42 168 Mean

4

First we multiply individual frequencies by their corresponding number of day. Then we add the multiplied values to obtain Here,

.

=168.

n is calculated to be 42.

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Therefore, the mean, = 168/42 = 4. = 4.

Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Computing Descriptive Statistics for Frequency Distributions LO1: Calculate the mean, variance, and standard deviation for grouped data.

92) The following table lists the amounts paid in mortgages as a percentage of the household income in the town Aponia. Calculate the variance and standard deviation of the data, if mean is given as 22.4%. The percentage (x) values are estimated as midpoints of each percentage range.

Mortgage as a percentage of household income in Aponia Group in % 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60

Percentage Number of (x) households (f) 5 4567 15 6562 25 3356 35 2975 45 1644 55 1376

Answer: For grouped data such as this, variance, s2 = frequencies, and,

, where n is the sum of

is the sum of all the squares of each observation minus the mean.

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Since mean is given,

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is calculated to be 453.9.

Note that the square of the deviations from the mean is divided by 10000 to simplify the calculations.

Sum of frequencies is calculated to be 20480.

Substituting these values in the variance formula, we get, S2 = 453.9/20479 = 0.022.

Therefore, the variance value is 0.02.

Standard deviation is the square root of variance, therefore, standard deviation, s = Therefore, the standard deviation value is 0.15.

Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Computing Descriptive Statistics for Frequency Distributions LO1: Calculate the mean, variance, and standard deviation for grouped data.

= 0.15.

93) A sample is a subset of a population.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: Explain the difference between a population and a sample.

94) One of the properties of the mean is that the sum of the deviations of each observation from the mean is zero.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures

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LO1: Compute the mean, median, mode, and midrange of a set of data.

95) For an odd number of observations, the median is the mean of the two middle numbers.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: Compute the mean, median, mode, and midrange of a set of data.

96) The larger the variance, the more the data are spread out from the mean.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: Compute the range, interquartile range, variance, and standard deviation of a set of data.

97) According to the empirical rules of standard deviation in statistics, approximately 68% of the observations will fall within three standard deviations of the mean.

Answer: FALSE Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Descriptive Statistical Measures LO1: State the Empirical Rules and apply them to practical data.

98) Two different sets of data can never have the same z-scores.

Answer: FALSE Diff: 1 Blooms: Understand Topic: Descriptive Statistical Measures LO1: Compute a standardized value (z-score) for observations in a data set.

99) In stock trading, the higher the coefficient of variation for the stock, the smaller the relative risk is for the return provided.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: Define and compute the coefficient of variation.

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100) Skewness describes the lack of symmetry of data.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: Explain the nature of skewness and kurtosis in a distribution.

101) The value of a coefficient of skewness falling between 0.5 and -0.5 indicates relative symmetry.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: Interpret the coefficients of skewness and kurtosis.

102) If the distribution of observations are such that mode < median < mean, the histogram would be said to be negatively skewed.

Answer: FALSE Diff: 1 Blooms: Understand Topic: Descriptive Statistical Measures LO1: Explain the nature of skewness and kurtosis in a distribution.

103) Two variables can only have a statistical relationship if there is a cause-and-effect factor between them.

Answer: FALSE Diff: 1 Blooms: Understand Topic: Measures of Association LO1: Explain the importance of understanding relationships between two variables. Explain the difference between covariance and correlation.

104) A correlation of 0 indicates that the two variables have no linear relationship with each other.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Measures of Association LO1: Calculate measures of covariance and correlation.

105) According to the interquartile range, extreme outliers are more than 3*IQR away from the left of Q1 or to the right of Q3.

Answer: TRUE

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Diff: 1 Blooms: Remember Topic: Outliers LO1: Identify outliers in data.

106) State the three empirical rules in standard deviation.

Answer: The three empirical rules in standard deviation are: 1. Approximately 68% of the observations will fall within one standard deviation of the mean, or between x̅ - s and x̅ + s 2. Approximately 95% of the observations will fall within one standard deviation of the mean, or between x̅ - 2s and x̅ + 2s 3. Approximately 99.7% of the observations will fall within one standard deviation of the mean, or between x̅ - 3s and x̅ + 3s Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: State the Empirical Rules and apply them to practical data.

107) Give an account of Excel's Descriptive Statistics Tool.

Answer: Excel provides a useful tool for basic data analysis, Descriptive Statistics. Click on Data Analysis in the Analysis group under the Data tab in the Excel menu bar. Select Descriptive Statistics from the list of tools. You need to enter only the range of the data, which must be in a single row or column. If the data are in multiple columns, the tool treats each row or column as a separate data set, depending on which you specify. This means that if you have a single data set arranged in a matrix format, you would have to stack the data in a single column before applying the Descriptive Statistics tool. Check the box Labels in First Row if labels are included in the input range. You may choose to save the results in the current worksheet or in a new one. For basic summary statistics, check the box Summary statistics; you need not check any others. One important point to note about the use of the tools in the Analysis Toolpak versus Excel functions is that while Excel functions dynamically change as the data in the spreadsheet are changed, the results of the Analysis Toolpak tools do not.

Diff: 1 Blooms: Remember Topic: Descriptive Statistical Measures LO1: Use the Excel Descriptive Statistics tool to summarize data.

108) What are the different interpretations for correlation coefficient values?

Answer: A correlation of 0 indicates that the two variables have no linear relationship to each other. Thus, when one variable changes, we cannot reasonably predict what the other variable might do. A positive correlation coefficient indicates a linear relationship for which one variable increases as the other also increases. A negative correlation coefficient indicates a linear relationship for which one variable that increases while the other decreases.

Diff: 1

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Blooms: Remember Topic: Measures of Association LO1: Calculate measures of covariance and correlation.

109) How can outliers be identified in a data set?

Answer: Outliers can make a significant difference in the results we obtain from statistical analyses.

The first thing to do is to check the data for possible errors, such as a misplaced decimal point or an incorrect transcription to a computer file. Histograms can help to identify possible outliers visually.

The empirical rule and z-scores can also be used to identify an outlier as one that is more than three standard deviations from the mean. Outliers can also be identified based on the interquartile range.

"Mild" outliers are often defined as being between 1.5*IQR and 3*IQR to the left of Q1 or to the right of Q3, and "extreme" outliers, as more than 3*IQR away from these quartiles.

Diff: 1 Blooms: Remember Topic: Outliers LO1: Identify outliers in data.

110) What is statistical thinking? How is it important to making business decisions?

Answer: Statistical thinking is a philosophy of learning and action for improvement that is based on the principles that (1) all work occurs in a system of interconnected processes, (2) variation exists in all processes, and (3) better performance results from understanding and reducing variation.

Understanding business processes provides the context for determining the effects of variation and the proper type of action to be taken. Any process contains many sources of variation.

Statistical analysis can provide better insight into the facts and nature of relationships among the many factors that may have contributed to an event and enable managers to make better decisions.

Diff: 2 Blooms: Understand AACSB: Analytic Skills Topic: Statistical Thinking in Business Decisions LO1: State the principles of statistical thinking.

111) Which of the following can be used to quickly create cross-tabulations?

A) Frequency distribution B) COUNTIF function C) PivotTable D) Sort & Filter Answer: C Diff: 1 Blooms: Remember Topic: PivotTables LO1: Use PivotTables to analyze and gain insight from data.

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Business Analytics, 3e (Evans) Chapter 5: Probability Distributions and Data Modeling 1) Which of the following is true about the classical definition of probability?

A) It is based on judgment and experience.

B) If the process that generates the outcomes is known, probabilities can be deduced from theoretical arguments.

C) The probability that an outcome will occur is simply the relative frequency associated with that outcome.

D) It is based on observed data.

Answer: B Diff: 1 Blooms: Knowledge Topic: Basic Concepts of Probability LO1: Explain the concept of probability and provide examples of the three definitional perspectives of probability.

2) John and Mike were offered mints. What is the probability that at least John or Mike would respond favorably? (Hint: Use the classical definition).

A) B) C) D) Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Basic Concepts of Probability LO1: Use probability rules and formulas to perform probability calculations.

3) Consider an event X comprised of three outcomes whose probabilities are Compute the probability of the complement of the event.

A) B) C) D) Copyright © 2020 Pearson Education, Inc. 92

,

, and

.

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Answer: A Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Basic Concepts of Probability LO1: Use probability rules and formulas to perform probability calculations.

Use the data given below to answer the following question(s).

In an event X, the probability of rolling a sum of 8 on two dice is rolling an 11 is rolling a 9 is

while the probability of

. In another event Y, the probability of rolling a 2 is , and the probability of rolling a 4 is

, the probability of

.

4) What is the probability that either event X or Y occurs?

A) B) C) D) Answer: B Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Basic Concepts of Probability LO1: Use probability rules and formulas to perform probability calculations.

5) What is probability that neither X nor Y will occur?

A) B) C) D) Answer: D Diff: 3 Blooms: Apply Copyright © 2020 Pearson Education, Inc.

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AACSB: Analytic Skills Topic: Basic Concepts of Probability LO1: Use probability rules and formulas to perform probability calculations.

6) Consider an event Z that includes all outcomes of rolling two dice whose sum is odd. What is the probability that either event Y or Z occurs?

A) B) C) D) Answer: B Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Basic Concepts of Probability LO1: Use probability rules and formulas to perform probability calculations.

7) Which of the following computes the probability of an event P given that event Q is known to have occurred?

A) P(P|Q) = P(P and Q) / P(Q) B) P(Q|P) = P(Q) - P(P) C) P(P|Q) = P(Q) - P(P or Q) D) P(Q|P) = P(P or Q) - P(Q) Answer: A Diff: 1 Blooms: Knowledge Topic: Basic Concepts of Probability LO1: Explain conditional probability and how it can be applied in a business context.

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Use the data given below to answer the following question(s).

15 students were asked to choose between the broad categories of Arts, Science, and Math as their preferred area of study.

Respondent Gender Preference 1 Female Arts 2 Male Science 3 Male Math 4 Female Arts 5 Female Math 6 Male Science 7 Male Math 8 Male Math 9 Female Arts 10 Male Arts 11 Male Science 12 Female Science 13 Female Math 14 Male Arts 15 Female Arts 8) What is the probability that a respondent is male and prefers Arts?

A) B) C) D) Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Basic Concepts of Probability LO1: Use probability rules and formulas to perform probability calculations.

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9) What is the probability that a respondent prefers Science given that the respondent is female?

A) B) C) D) Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Basic Concepts of Probability LO1: Use probability rules and formulas to perform probability calculations.

10) Use the multiplication law of probability to compute the probability that the respondent is male and prefers Math.

A) B) C) D) Answer: D Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Basic Concepts of Probability LO1: Apply the multiplication law of probability.

11) Identify the correct statement from the following.

A) The events that a respondent is female and chooses Math are not independent.

B) All events are independent of each other.

C) The events that a respondent is male and chooses Science are not dependent.

D) The events that a respondent is female and that she chooses Science are independent.

Answer: A Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Basic Concepts of Probability LO1: Determine if two events are independent using probability arguments.

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12) Which of the following will hold true if events X and Y are independent?

A) P(X) = P(Y) × P(X and Y) B) P(Y) = P(X|Y) C) P(X and Y) = [P(X) + P(Y)] - P(X or Y) D) P(X) = P(X|Y) Answer: D Diff: 2 Blooms: Knowledge Topic: Basic Concepts of Probability LO1: Determine if two events are independent using probability arguments.

13) Which of the following is a continuous random variable?

A) the outcomes of rolling two dice B) the time to complete a specific task C) the number of new hires in a year D) the number of hits on a Web site link Answer: B Diff: 2 Blooms: Understand Topic: Random Variables and Probability Distributions LO1: Explain the difference between a discrete and a continuous random variable.

14) While rolling two dice, what is the probability of rolling a sum of 7 or more?

A) B) C) D) Answer: A Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Discrete Probability Distributions LO1: Use the cumulative distribution function to compute probabilities over intervals.

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15) The ________ of a random variable corresponds to the notion of the mean, or average, for a sample.

A) mode B) variance C) expected value D) standard deviation Answer: C Diff: 1 Blooms: Knowledge Topic: Discrete Probability Distributions LO1: Compute the expected value and variance of a discrete random variable.

16) For a discrete random variable X, which of the following computes the expected value?

A) B) C) D) Answer: B Diff: 1 Blooms: Knowledge Topic: Discrete Probability Distributions LO1: Compute the expected value and variance of a discrete random variable.

17) Which of the following is a weighted average of the squared deviations from the expected value?

A) skewness B) mean difference C) kurtosis D) variance Answer: D Diff: 1 Blooms: Knowledge Topic: Discrete Probability Distributions LO1: Compute the expected value and variance of a discrete random variable.

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18) Which of the following formulas will compute the variance of a discrete random variable X? A) ∑

𝑥 − 𝐸[𝑋]

B) ∑

𝐸[𝑋] 𝑓(𝑥 )

C) ∑

𝑥 − 𝐸[𝑋] 𝑓(𝑥 )

D) ∑

𝑥 𝑓(𝑥 )

Answer: C Diff: 1 Blooms: Knowledge Topic: Discrete Probability Distributions LO1: Compute the expected value and variance of a discrete random variable.

19) Which of the following is true about variance?

A) It measures the uncertainty of a random variable.

B) Higher variance implies low uncertainty.

C) It is the square root of a random variable's standard deviation.

D) It is the weighted average of all possible outcomes.

Answer: A Diff: 2 Blooms: Understand Topic: Discrete Probability Distributions LO1: Compute the expected value and variance of a discrete random variable.

20) Which of the following characterizes a random variable having two possible outcomes, each with a constant probability of occurrence?

A) Beta distribution B) Bernoulli distribution C) Poisson distribution D) Binominal distribution Answer: B Diff: 1 Blooms: Knowledge Topic: Discrete Probability Distributions LO1: Calculate probabilities for the Bernoulli, binomial, and Poisson distributions, using the probability mass function and Excel functions.

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21) Which of the following is the probability mass function of the Bernoulli distribution?

A) B)

C) D) Answer: A Diff: 1 Blooms: Knowledge Topic: Discrete Probability Distributions LO1: Calculate probabilities for the Bernoulli, binomial, and Poisson distributions, using the probability mass function and Excel functions.

22) The binominal distribution: A) is a discrete distribution used to model the number of occurrences in some unit of measure.

B) assumes that the average number of occurrences per unit is a constant and that occurrences are independent.

C) is symmetric irrespective of the value of the probability of success.

D) models n independent replications of a Bernoulli experiment, each with a probability p of success.

Answer: D Diff: 2 Blooms: Understand Topic: Discrete Probability Distributions LO1: Calculate probabilities for the Bernoulli, binomial, and Poisson distributions, using the probability mass function and Excel functions.

23) Which of the following is true of the binomial distribution?

A) The expected value of the binomial distribution is np(1 - p), where n is the number of experiments and p is the probability of success.

B) The binomial distribution can assume different shapes and amounts of skewness, depending on the parameters.

C) In Excel's binomial distribution function, setting cumulative to TRUE will provide the probability mass function for a specified value.

D) The expected value of the binomial distribution is λ, a constant.

Answer: B Diff: 2 Blooms: Understand

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Topic: Discrete Probability Distributions LO1: Calculate probabilities for the Bernoulli, binomial, and Poisson distributions, using the probability mass function and Excel functions.

Use the data given below to answer the following question(s).

On an average, the number of students that choose to study Arts subjects at Greyin Tide University is 17 each year. (Hint: Use Poisson distribution formula).

24) What is the probability that exactly 13 students will take up Arts in the coming year?

A) 0.08795 B) 0.20087 C) 0.04798 D) 0.06585 Answer: D Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Discrete Probability Distributions LO1: Calculate probabilities for the Bernoulli, binomial, and Poisson distributions, using the probability mass function and Excel functions.

25) What is the probability of 8 takers or less for Arts subjects in the coming year?

A) 0.00716 B) 0.01260 C) 0.03164 D) 0.04744 Answer: B Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Discrete Probability Distributions LO1: Calculate probabilities for the Bernoulli, binomial, and Poisson distributions, using the probability mass function and Excel functions.

26) A probability density function: A) is the probability distribution of discrete outcomes.

B) suggests that the probability that a random variable assumes a specific value must be positive.

C) characterizes outcomes of a continuous random variable.

D) can yield negative values depending on the values of the random variable, X. Answer: C Diff: 1 Blooms: Knowledge+

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Topic: Continuous Probability Distributions LO1: List the key properties of probability density functions.

27) Which of the following is true about probability density functions?

A) A graph of the density function must lie at or below the x-axis.

B) The total area under the density function below the x-axis is 2.0.

C) It calculates the probability of a random variable lying within a certain interval.

D) P (a) x P (b) is the area under the density function between two numbers a and b.

Answer: C Diff: 2 Blooms: Understand Topic: Continuous Probability Distributions LO1: List the key properties of probability density functions.

28) Which of the following characterizes a continuous random variable for which all outcomes between some minimum and maximum value are equally likely?

A) exponential distribution B) uniform distribution C) normal distribution D) lognormal distribution Answer: B Diff: 1 Blooms: Knowledge Topic: Continuous Probability Distributions LO1: Use the probability density and cumulative distribution functions to calculate probabilities for a uniform distribution.

29) Which of the following is true of normal distributions?

A) The mean, median, and mode are all equal.

B) Its measure of skewness is always greater than 1.

C) The range of the random variable X is bounded.

D) Mathematical formulas make it easier to compute normal distributions.

Answer: A Diff: 2 Blooms: Remember Topic: Continuous Probability Distributions LO1: Describe the normal and standard normal distributions and use Excel functions to calculate probabilities.

30) The exponential distribution: A) has the density function f (x) = e-λx , for x ≥ 0.

B) models the time between randomly occurring events.

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C) has an expected value λ.

D) is described by the familiar bell-shaped curve.

Answer: B Diff: 2 Blooms: Knowledge Topic: Continuous Probability Distributions LO1: Describe properties of the exponential distribution and compute probabilities.

Use the data given below to answer the following question(s).

At a casino, a combination of two spinners is used to decide the winner based on the sum of scores from spinning. The spinners each have four colored spaces - red, yellow, blue, and green.

Red = 1, Yellow = 2, Blue = 3, and Green = 4 31) What is the probability that the spinners land on colors summing up to exactly 3?

Answer: There are 16 outcomes. The following is a breakdown of all possible sums and their frequencies.

Outcome x Frequency f(x) 2 10.0625 3 20.1250 4 30.1875 5 40.2500 6 30.1875 7 20.1250 8 10.0625

F(x) 0.0625 0.1875 0.3750 0.6250 0.8125 0.9375 1.0000

The probability that the spinners land on colors summing up to exactly 3 = 0.1250 Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Discrete Probability Distributions LO1: Calculate probabilities for the Bernoulli, binomial, and Poisson distributions, using the probability mass function and Excel functions.

32) Compute the expected value of the random variable that denotes the possible summed scores from the two spinners.

Answer: For a discrete random variable X, the expected value, denoted E[X], is the weighted average of all possible outcomes, where the weights are the probabilities:

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E[X] = Outcome, x

Frequency 2 3 4 5 6 7 8

1 2 3 4 3 2 1

Probability, f(x) xf(x) 1/16 1/8 3/16 1/4 3/16 1/8 1/16 Expected value

1/8 3/8 3/4 5/4 9/8 7/8 1/2 5

Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Discrete Probability Distributions LO1: Compute the expected value and variance of a discrete random variable.

33) Compute the variance of the random variable that denotes the possible summed scores from the two spinners.

Answer: The variance, Var[X], of a discrete random variable X as a weighted average of the squared deviations from the expected value: Var[X] = Outcome, X Probability, f(x) xf(x) (x-E[X]) (x-E[X])2 (x-E[X])2f(x) 2 1/16 1/8 -3 9 9/16 3 1/8 3/8 -2 4 1/2 4 3/16 3/4 -1 1 3/16 5 1/4 5/4 0 0 0 6 3/16 9/8 1 1 3/16 7 1/8 7/8 2 4 1/2 8 1/16 1/2 3 9 9/16 Expected Value 5 Variance 2 1/2 Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Discrete Probability Distributions LO1: Compute the expected value and variance of a discrete random variable.

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Use the data given below to answer the following question(s).

The profit from selling folding tables varies uniformly each quarter between $1,500 and $2,300.

34) What is the probability that profit will be less than $1,900?

Answer:

F(1,900) = (1,900 - 1,500) / (2,300 - 1,500) = 0.50 Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Continuous Probability Distributions LO1: Use the probability density and cumulative distribution functions to calculate probabilities for a uniform distribution.

35) What is the probability that profit will be between $2,000 and $2,200?

Answer: P(2,000 ≤ X ≤ 2,200) = P(X ≤ 2,200) - P(X ≤ 2,000) = F(2,200) - F(2,000)

Since quarterly profit here follows a uniform distribution

, where a =

$1,500 and b = $2,300, the probability that profit will be between $2,000 and $2,200 = = 0.25 Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Continuous Probability Distributions LO1: Use the probability density and cumulative distribution functions to calculate probabilities for a uniform distribution.

36) If P(X|Y) = P(X), it implies that event Y is dependent on event X. Answer: FALSE Diff: 1 Blooms: Knowledge Topic: Basic Concepts of Probability LO1: Determine if two events are independent using probability arguments.

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37) The expected value and variance of the Poisson distribution are equal to λ.

Answer: TRUE Diff: 1 Blooms: Knowledge Topic: Discrete Probability Distributions LO1: Calculate probabilities for the Bernoulli, binomial, and Poisson distributions, using the probability mass function and Excel functions.

38) The Excel function NORM.DIST finds probabilities for the standard normal distribution.

Answer: FALSE Diff: 1 Blooms: Knowledge Topic: Continuous Probability Distributions LO1: Describe the normal and standard normal distributions and use Excel functions to calculate probabilities.

39) How are probability, experiment, outcome, and sample space related to each other?

Answer: Probability is the likelihood that an outcome will occur. An experiment is a process that results in an outcome. The outcome of an experiment is a result that is observed. The collection of all possible outcomes of an experiment is called the sample space.

Diff: 1 Blooms: Knowledge Topic: Basic Concepts of Probability LO1: Explain the concept of probability and provide examples of the three definitional perspectives of probability.

40) What are the properties of a probability mass function?

Answer: A probability mass function has the properties that (1) the probability of each outcome must be between 0 and 1 and (2) the sum of all probabilities must add to 1; that is, 0 ≤ f(xi) ≤ 1, for all i

Diff: 2 Blooms: Understand Topic: Discrete Probability Distributions LO1: Verify the properties of a probability mass function.

41) Explain the similarity between the formulas for computing population mean and expected value of discrete random variable X. Answer: For a discrete random variable X, the expected value, denoted E[X], is the weighted average of all possible outcomes, where the weights are the probabilities:

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The population mean can be computed using the formula: μ= If this formula is written as the sum of xi multiplied by (fi / N), then fi / N can be thought of as the probability of xi. Then this expression for the mean has the same basic form as the expected value formula.

Diff: 2 Blooms: Understand Topic: Discrete Probability Distributions LO1: Compute the expected value and variance of a discrete random variable.

42) How can normal probabilities be computed using Excel? Given the cumulative probability, how can the value of the random variable be found?

Answer: The Excel 2010 function NORM.DIST(x, mean, standard_deviation, cumulative) computes normal probabilities. NORM.DIST(x, mean, standard_deviation, TRUE) calculates the cumulative probability F (x) = P (X ≤ x) for a specified mean and standard deviation. The Excel function NORM.INV(probability, mean, standard_dev) can be used to compute the value of x if the cumulative probability is known. In this function, probability is the cumulative probability value corresponding to the value of x which is sought.

Diff: 2 Blooms: Understand Topic: Continuous Probability Distributions LO1: Describe the normal and standard normal distributions and use Excel functions to calculate probabilities.

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Business Analytics, 3e (Evans) Chapter 6: Sampling and Estimation 1) A ________ is a description of the approach that is used to obtain samples from a population prior to any data collection activity.

A) population frame B) sampling weight C) sampling plan D) probability interval Answer: C Diff: 1 Blooms: Remember Topic: Statistical Sampling LO1: Describe the elements of a sampling plan.

2) Which of the following is true of judgment sampling?

A) It selects samples based on expert opinion.

B) It selects samples based on ease of data collection.

C) It selects samples based on random procedures.

D) It selects samples based on full representation of all subsets in a population.

Answer: A Diff: 1 Blooms: Remember Topic: Statistical Sampling LO1: Explain the difference between subjective and probabilistic sampling 3) Which of the following types of sampling involves using random procedures to select a sample?

A) judgment sampling B) probabilistic sampling C) subjective sampling D) convenience sampling Answer: B Diff: 1 Blooms: Remember Topic: Statistical Sampling LO1: Explain the difference between subjective and probabilistic sampling 4) ________ involves selecting items from a population so that every subset of a given size has an equal chance of being selected.

A) Convenience sampling B) Subjective sampling C) Judgment sampling D) Simple random sampling Copyright © 2020 Pearson Education, Inc. 108

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Answer: D Diff: 1 Blooms: Remember Topic: Statistical Sampling LO1: Explain the difference between subjective and probabilistic sampling 5) Which of the following sampling methods bases its selection of samples on the ease of data collection?

A) probabilistic sampling B) judgment sampling C) simple random sampling D) convenience sampling Answer: D Diff: 1 Blooms: Remember Topic: Statistical Sampling LO1: Explain the difference between subjective and probabilistic sampling 6) Which of the following describes periodic sampling?

A) It is a sampling method based solely on expert opinion.

B) It is a sampling method based on selecting a time and then sampling the products after that time.

C) It is a sampling method based on selecting every nth item from a population.

D) It is a sampling method exclusively used for population that is divided into subsets.

Answer: C Diff: 1 Blooms: Remember Topic: Statistical Sampling LO1: Explain how to conduct simple random sampling and use Excel to find a simple random sample from an Excel database

7) ________ sampling applies to populations that are divided into natural subsets and allocates the appropriate proportion of samples to each subset.

A) Systematic B) Stratified C) Cluster D) Continuous process Answer: B Diff: 1 Blooms: Remember Topic: Statistical Sampling LO1: Explain systematic, stratified, and cluster sampling and sampling from a continuous process.

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8) ________ is based on dividing a population into subgroups, sampling a set of subgroups, and conducting a complete census within the subgroups sampled.

A) Cluster sampling B) Continuous process sampling C) Judgment sampling D) Systematic sampling Answer: A Diff: 1 Blooms: Remember Topic: Statistical Sampling LO1: Explain systematic, stratified, and cluster sampling and sampling from a continuous process.

9) In sampling, ________ involves assessing the value of an unknown population parameter– such as a population mean, population proportion, or population variance–using sample data.

A) distribution B) randomization C) estimation D) substitution Answer: C Diff: 1 Blooms: Remember Topic: Estimating Population Parameters LO1: Explain the importance of unbiased estimators

10) From the standard deviation formula,

∑ ̅

, identify the estimator.

A) s2 B) σ2 C) 𝑥̅ D) s Answer: A Diff: 1 Blooms: Remember Topic: Topic: Estimating Population Parameters LO1: Explain the importance of unbiased estimators 11) A(n) ________ is a single number derived from sample data that is used to estimate the value of a population parameter.

A) confidence interval B) frequentist interference C) interval estimate D) point estimate

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Answer: D Diff: 1 Blooms: Remember Topic: Topic: Estimating Population Parameters LO1: Explain the importance of unbiased estimators 12) For which of the following is the value of the estimator said to be biased?

A) if the expected value of the estimator does not equal the population parameter B) if the expected value of the estimator equals the population parameter C) only if the expected value of the estimator is zero D) only if the expected value of the estimator goes below zero Answer: A Diff: 1 Blooms: Remember Topic: Topic: Estimating Population Parameters LO1: Explain the importance of unbiased estimators 13) Which of the following is true of an unbiased estimator value?

A) The expected value will align perfectly with the population mean.

B) The expected value will not equal the population's parameters.

C) The expected value will not be greater than zero.

D) The expected value will equal the population's parameter.

Answer: D Diff: 1 Blooms: Remember Topic: Topic: Estimating Population Parameters LO1: Explain the importance of unbiased estimators.

14) Which of the following accurately describes a sampling distribution of the mean?

A) It is the mean of any one sample from a group of related populations of different sizes.

B) It is the mean distribution of any one sample from a group of samples of varying sizes from a population.

C) It is the mean of half the samples from a related group of populations.

D) It is the distribution of the means of all possible samples of fixed size n from a population.

Answer: D Diff: 1 Blooms: Remember Topic: Sampling Distributions LO1: Define the sampling distribution of the mean.

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15) Which of the following is the inherent reason why sampling errors occur?

A) because samples represent the whole population B) because samples are only a subset of the population C) because samples never provide enough data to estimate standard deviation D) because the means cannot be accurately estimated using samples Answer: B Diff: 1 Blooms: Understand Topic: Topic: Estimating Population Parameters LO1: Describe the difference between sampling error and nonsampling error 16) ________ are statistical errors that are due to the sample not representing the target population adequately.

A) Parallax errors B) Sampling errors C) Nonsampling errors D) Quantization errors Answer: C Diff: 1 Blooms: Understand Topic: Topic: Estimating Population Parameters LO1: Describe the difference between sampling error and nonsampling error.

17) The means of all possible samples of a fixed size n from some population will form a distribution which is known as the ________.

A) corollary of the mean B) sampling distribution of the mean C) standard error of the mean D) point estimate Answer: B Diff: 1 Blooms: Remember Topic: Sampling Distribution LO1: Define the sampling distribution of the mean.

18) Which of the following is the equation for calculating the standard error of the mean?

A) B) 𝑥 − 𝑥̅ 𝑛 C) 𝜎√𝑛 D) 𝜎/√𝑛 Copyright © 2020 Pearson Education, Inc.

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Answer: D Diff: 1 Blooms: Remember Topic: Sampling Distribution LO1: Calculate the standard error of the mean.

19) Which of the following is implied from the standard error of the mean formula?

A) that true means of populations can be found easier than those of samples B) that standard deviation increases with increase in sample size C) that larger sample sizes provide greater accuracy in estimating the true population mean D) that the true mean of the population can only be calculated using smaller sample sizes Answer: C Diff: 1 Blooms: Remember Topic: Sampling Distribution LO1: Calculate the standard error of the mean.

20) The Ransin Sports Company has noted that the size of individual customer orders is normally distributed with a mean of $112 and a standard deviation of $9. Which of the following is the answer for the probability that the next individual who buys a product will make a purchase of more than $116?

A) 71% B) 48% C) 33% D) 42% Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Sampling Distributions LO1: Define the sampling distribution of the mean.

21) The Ransin Sports Company has noted that the size of individual customer orders is normally distributed with a mean of $112 and a standard deviation of $9. If a soccer team of 11 players were to make the next batch of orders, what would be the standard error of the mean?

A) 1.64 B) 2.71 C) 3.67 D) 0.82 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills

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Topic: Sampling Distributions LO1: Define the sampling distribution of the mean.

22) The Ransin Sports Company has noted that the size of individual customer orders is normally distributed with a mean of $112 and a standard deviation of $9. If a soccer team of 11 players were to make the next batch of orders, what is the probability that the mean purchase would exceed $116?

A) 11% B) 3% C) 33% D) 7% Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Sampling Distributions LO1: Define the sampling distribution of the mean.

23) ________ states that if the sample size is large enough, the sampling distribution of the mean is approximately normally distributed, regardless of the distribution of the population and that the mean of the sampling distribution will be the same as that of the population.

A) Chebyshev's theorem B) Central limit theorem C) Prime number theorem D) Oppermann's conjecture Answer: B Diff: 1 Blooms: Remember Topic: Sampling Distributions LO1: Explain the practical importance of the central limit theorem.

24) The central limit theorem states that if the population is normally distributed, then the ________.

A) mean of the population can be calculated without using samples B) standard error of the mean will not vary from the population mean C) sampling distribution of the mean will vary from sample to sample D) sampling distribution of the mean will also be normal for any sample size Answer: D Diff: 1 Blooms: Understand Topic: Sampling Distributions LO1: Explain the practical importance of the central limit theorem.

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25) Which of the following is a difference between interval estimates and point estimates?

A) Point estimates cannot be used to calculate statistical error, while interval estimate is used to calculate statistical error.

B) Point estimates provide only a single value for a sample, while interval estimates provide a range of values.

C) Point estimates indicate the magnitude of potential error in the estimate, while interval estimates don't.

D) Point estimates on an average provide more information than interval estimates.

Answer: B Diff: 2 Blooms: Understand Topic: Interval Estimates LO1: Explain how an interval estimate differs from a point estimate.

26) A ________ is a range of values between which the value of the population parameter is believed to be, along with a probability that the interval correctly estimates the true population parameter.

A) point estimate B) frequentist interference C) confidence interval D) fiducial inference Answer: C Diff: 1 Blooms: Remember Topic: Interval Estimates LO1: Define and give examples of confidence intervals.

27) A 100(1-α)% confidence interval for the population mean μ based on a sample of size n with a sample mean 𝑥̅ and a known population standard deviation σ is given by ________.

A) x  za / 2(n  1)( n ) B) x

( / n ) za /2

C) x / ( / n ) D) x  za / 2 ( / n ) Answer: D Diff: 1 Blooms: Remember Topic: Interval Estimates LO1: Define and give examples of confidence intervals.

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28) For the formula for calculating the confidence level with known standard deviation, the value ________ represents the value of a standard normal random variable with a cumulative probability of 1 - α / 2.

A) σ / √𝑛 B) za/2 C) D) xi Answer: B Diff: 1 Blooms: Remember Topic: Interval Estimates LO1: Define and give examples of confidence intervals.

29) The ________ is a family of probability distributions with a shape similar to the standard normal distribution.

A) log-normal distribution B) Gaussian q-distribution C) frequentist interference D) t-distribution Answer: D Diff: 1 Blooms: Remember Topic: Interval Estimates LO1: Describe the difference between the t-distribution and the normal distribution.

30) Which of the following is a difference between the t-distribution and the standard normal distribution?

A) The t-distribution cannot be calculated without a known standard deviation, while the standard normal distributions can be.

B) The standard normal distribution's confidence levels are wider than those of the t-distribution.

C) The t-distribution has a larger variance than the standard normal distribution.

D) The standard normal distribution is dependent on parameters like degrees of freedom, while tdistribution is not.

Answer: C Diff: 2 Blooms: Understand Topic: Interval Estimates LO1: Describe the difference between the t-distribution and the normal distribution.

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31) Which of the following is true of the t-distribution?

A) It has narrower confidence intervals than the standard normal distribution.

B) It is only used to calculate confidence intervals where there is no known population standard deviation.

C) It converges to the standard normal distribution as degrees of freedom increase.

D) It does not require parameters such as degrees of freedom.

Answer: C Diff: 2 Blooms: Understand Topic: Interval Estimates LO1: Describe the difference between the t-distribution and the normal distribution.

32) Which of the following is true of calculating confidence intervals for larger samples?

A) For larger samples, the t-distribution is indistinguishable from the standard normal distribution.

B) For larger samples, both the t-distribution and the standard normal distribution require standard deviation values to be calculated.

C) For larger samples, the degrees of freedom cannot be calculated accurately.

D) For larger samples, only z-values provide a true sampling distribution of the mean.

Answer: A Diff: 2 Blooms: Understand Topic: Interval Estimates LO1: Describe the difference between the t-distribution and the normal distribution.

33) Which of the following types of distributions use z-values to establish confidence intervals?

A) Gaussian q-distribution B) t-distribution C) log-normal distribution D) standard normal distribution Answer: D Diff: 1 Blooms: Remember Topic: Interval Estimates LO1: Define and give examples of confidence intervals.

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Use the table below to answer the following question(s).

The historical data of Velvetta Inc., a healthcare products manufacturer, have shown that in a production process for filling bottles of shampoo, variance in the volume is constant; however, clogs in the filling machine often affect the mean volume. The historical standard deviation is 5 milliliters. In filling 250-milliliter bottles, a sample of 20 found a mean volume of 242 milliliters.

Velvetta Inc. Shampoo Production Alpha Value Standard Deviation Sample Size Sample Mean

0.05 5 20 242

34) Based on the data in the table above, calculate the margin of error at 95% confidence interval.

A) 1.84 B) 2.19 C) 2.51 D) 1.96 Answer: B Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Interval Estimates LO1: Define and give examples of confidence intervals.

35) Calculate the 𝑧 / value at a 95% confidence interval.

A) 1.64 B) 1.84 C) 1.96 D) 2.19 Answer: C Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Interval Estimates LO1: Define and give examples of confidence intervals.

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36) From the table above, determine the cumulative probability for z at a 95% confidence level.

A) 0.975 B) 0.950 C) 1 D) 0.987 Answer: A Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Interval Estimates LO1: Define and give examples of confidence intervals.

37) From the table above, calculate the lower confidence interval estimate at a confidence level of 95% A) 239.49 B) 240.16 C) 239.81 D) 240.04 Answer: C Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Interval Estimates LO1: Define and give examples of confidence intervals.

38) The formula for a 100(1 - α)% confidence interval for the mean μ when the population standard deviation is unknown is ________.

A) /(σ / √𝑛) B) ± tα/2n-1(s / √𝑛) C) ± zα/2 (σ/ √𝑛) D) Answer: B Diff: 1 Blooms: Remember Topic: Interval Estimates LO1: Calculate confidence intervals for population means and proportions using the formulas in the chapter and the appropriate Excel functions.

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39) In which of the following cases is a proportion of the observations of a sample used in estimating the confidence interval?

A) when the degrees of freedom are too large B) when a true sampling distribution cannot be estimated C) when the population standard deviation is known D) when variables have only two possible outcomes Answer: D Diff: 1 Blooms: Remember Topic: Interval Estimates LO1: Use and visualize confidence intervals to draw conclusions about population parameters.

40) In the equation for calculating a confidence interval for a proportion, p± za/2 does

, what

represent?

A) the mean for the sampling distribution of the proportion B) the degree of freedom for the sampling distribution of the proportion C) the standard error for the sampling distribution of the proportion D) the estimator for sampling distribution of the proportion Answer: C Diff: 1 Blooms: Remember Topic: Interval Estimates LO1: Use and visualize confidence intervals to draw conclusions about population parameters.

41) A ________ is one that provides a range for anticipating the value of a new observation from the same population.

A) prediction interval B) confidence interval C) t-distribution D) standard normal distribution Answer: A Diff: 1 Blooms: Remember Topic: Interval Estimates LO1: Compute a prediction interval and explain how it differs from a confidence interval.

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42) Which of the following is true of prediction intervals?

A) It provides estimates for variables that can have only two possible outcomes.

B) It is associated with the distribution of a random variable.

C) It provides an interval estimate of a population parameter.

D) It is associated with the sampling distribution of a statistic.

Answer: B Diff: 2 Blooms: Understand Topic: Prediction Intervals LO1: Compute a prediction interval and explain how it differs from a confidence interval.

43) Which of the following is true of the equation [n ≥ (zα/2)

2

] for computing the sample

size required to achieve a desired confidence interval half-width for a proportion?

A) The sample size calculated will only be an approximation.

B) The standard deviation need not be calculated first in order to compute the sample size.

C) The value for π is always set at 1.

D) The most conservative estimate for π is 0.5.

Answer: D Diff: 1 Blooms: Understand Topic: Confidence Interval and Sample Size LO1: Compute sample sizes needed to ensure a confidence interval for means and proportions with a specified margin of error.

44) The table below shows the weights of female individuals in Catherine's family. Calculate the sample variance in the weights, and the standard deviation.

Weights of female individuals in Catherine's family (in lbs) 163 160 155 161 158 155 149 151 158 171 Answer: Sample variance is calculated by the formula, s2 =

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… (1)

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Where, n = number of samples is the sum of individual samples minus the sample mean.

N= 10, 𝑥̅ = (163+160+155+161+158+155+149+151+158+171) / 10 = 158.1 Therefore substituting the values in equation (1), and by simplifying the values, we get,

=24.01+3.61+9.61+8.41+.01+9.61+82.81+50.41+.01+166.41 / 9 =354.9 / 9 =39.43.

Therefore, total variance is 39.43.

Standard deviation is the positive square root of variance.

Therefore, standard deviation = = 6.28.

Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Estimating Population Parameters LO1: Explain how the average, standard deviation, and distribution of means of samples changes as the sample size increases.

45) The table below shows the number of goals scored by the Huntington Soccer Club in their league for the past 12 years. Calculate the standard error of the mean of the data given that the variance of the data is 50.45 Goals Scored by the Huntington Soccer Club for the past 12 years Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 Year 11 Year 12

45 51 33 40 30 38 49 52 46 43 40 50

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Answer: Standard error of the mean is calculated by the formula …(1), where is the standard deviation of the data, and n is the number of samples.

Standard deviation is the positive square root of variance, and since we have the variance value as 50.45, the standard deviation is =7.10 n = 12…(2) σ =7.10…(3) Substituting (2) and (3) in (1), we get 7.10 / = 2.05 Therefore the standard error of the mean = 2.05 Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Sampling Distributions LO1: Calculate the standard error of the mean.

46) Convenience sampling is an example of a probabilistic sampling method.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Statistical Sampling LO1: State two types of subjective samplin.

47) Estimators are the measures used to estimate population parameters.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Estimating Population Parameters LO1: Explain the importance of unbiased estimators 48) Point estimates do not provide any indication of the magnitude of the potential error in the estimate.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Estimating Population Parameters LO1: Explain how an interval estimate differs from a point estimate 49) The simple random sampling method is the only statistical sampling method that does not include sampling errors.

Answer: FALSE Diff: 1 Blooms: Remember

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Topic: Sampling Distributions LO1: Describe the difference between sampling error and nonsampling error.

50) A confidence interval is a range of values between which the value of the population parameter is believed to be.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Interval Estimates LO1: Define and give examples of confidence intervals.

51) As the number of degrees of freedom increases, the t-distribution converges to the standard normal distribution.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Interval Estimates LO1: Describe the difference between the t-distribution and the normal distribution.

52) For any sample of fixed size n, the true standard deviation of the sampling distribution of the mean is the standard deviation of the population.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Interval Estimates LO1: Describe the difference between the t-distribution and the normal distribution.

53) A confidence interval is associated with the sampling distribution of a statistic.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Prediction Intervals LO1: Define and give examples of confidence intervals.

54) As the sample size increases, the width of the confidence interval decreases.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Confidence Intervals and Sample Size LO1: Explain how confidence intervals change as the level of confidence increases or decreases.

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55) Explain selecting a sample using the continuous process sampling methods.

Answer: Selecting a sample from a continuous manufacturing process can be accomplished in two main ways. First, select a time at random; then select the next n items produced after that time. Second, select n times at random; then select the next item produced after each of these times. The first approach generally ensures that the observations will come from a homogeneous population; however, the second approach might include items from different populations if the characteristics of the process should change over time.

Diff: 1 Blooms: Remember Topic: Statistical Sampling LO1: Explain systematic, stratified, and cluster sampling, and sampling from a continuous process.

56) Give an account of biased and unbiased estimators in sampling methods.

Answer: Statisticians develop many types of estimators, and from a theoretical as well as a practical perspective, it is important that they "truly estimate" the population parameters they are supposed to estimate. Suppose that we perform an experiment in which we repeatedly sampled from a population and computed a point estimate for a population parameter. Each individual point estimate will vary from the population parameter; however, we would hope that the longterm average (expected value) of all possible point estimates would equal the population parameter. If the expected value of an estimator equals the population parameter it is intended to estimate, the estimator is said to be unbiased. If this is not true, the estimator is called biased and will not provide correct results.

Diff: 1 Blooms: Remember Topic: Estimating Population Parameters LO1: Explain the importance of unbiased estimators.

57) What is a confidence interval in sampling?

Answer: Confidence interval estimates provide a way of assessing the accuracy of a point estimate. A confidence interval is a range of values between which the value of the population parameter is believed to be, along with a probability that the interval correctly estimates the true (unknown) population parameter. This probability is called the level of confidence, denoted by 1 -α, where α is a number between 0 and 1. The level of confidence is usually expressed as a percent; common values are 90%, 95%, or 99%.

Diff: 1 Blooms: Remember Topic: Interval Estimates LO1: Define and give examples of confidence intervals.

58) Compare between the t-distribution and the standard normal distribution.

Answer: The t-distribution is actually a family of probability distributions with a shape similar to the standard normal distribution. Different t-distributions are distinguished by an additional

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parameter, degrees of freedom (df). The t-distribution has a larger variance than the standard normal, thus making confidence intervals wider than those obtained from the standard normal distribution, in essence correcting for the uncertainty about the true standard deviation, which is not known. As the number of degrees of freedom increases, the t-distribution converges to the standard normal distribution. When sample sizes get to be as large as 120, the distributions are virtually identical; even for sample sizes as low as 30 to 35, it becomes difficult to distinguish between the two. Thus, for large sample sizes, many people use z-values to establish confidence intervals even when the standard deviation is unknown.

Diff: 2 Blooms: Remember Topic: Interval Estimates LO1: Describe the difference between the t-distribution and the normal distribution.

59) Compare between a prediction interval and a confidence interval.

Answer: A prediction interval is one that provides a range for predicting the value of a new observation from the same population. This is different from a confidence interval, which provides an interval estimate of a population parameter, such as the mean or proportion. A confidence interval is associated with the sampling distribution of a statistic, but a prediction interval is associated with the distribution of the random variable itself.

Diff: 2 Blooms: Remember Topic: Prediction Intervals LO1: Compute a prediction interval and explain how it differs from a confidence interval.

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Business Analytics, 3e (Evans) Chapter 7: Statistical Inference 1) Which of the following propositions describes an existing theory or belief?

A) standard deviation B) null hypothesis C) proportion D) alternative hypothesis Answer: B Diff: 1 Blooms: Remember Topic: Hypothesis Testing LO1: Explain the difference between the null and alternative hypotheses.

2) Which of the following is the initial step in conducting a hypothesis test?

A) collecting data and calculating a test statistic B) selecting a level of significance C) identifying the population parameter of interest D) determining a decision rule Answer: C Diff: 1 Blooms: Remember Topic: Hypothesis Testing LO1: List the steps in the hypothesis-testing procedure.

3) Which of the following is a valid one-sample hypothesis test?

A) H0: population parameter ≠ constant vs. H1: population parameter = constant B) H0: population parameter > constant vs. H1: population parameter ≤ constant C) H0: population parameter < constant vs. H1: population parameter ≥ constant D) H0: population parameter = constant vs. H1: population parameter ≠ constant Answer: D Diff: 1 Blooms: Remember Topic: One-Sample Hypothesis Tests LO1: State the proper forms of hypotheses for one-sample hypothesis tests.

4) A manufacturer wishes to determine if the average profit from the sale of his product exceeds $6,710. Which of the following is the appropriate hypothesis test?

A) H0: population mean profit from sale > $6,710 vs. H1: population mean profit from sale ≤ $6,710 B) H0: population mean profit from sale ≤ $6,710 vs. H1: population mean profit from sale > $6,710 Copyright © 2020 Pearson Education, Inc. 127

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C) H0: population mean profit from sale < $6,710 vs. H1: population mean profit from sale ≥ $6,710 D) H0: population mean profit from sale ≥ $6,710 vs. H1: population mean profit from sale < $6,710 Answer: B Diff: 2 Blooms: Apply Topic: One-Sample Hypothesis Tests LO1: Correctly formulate hypotheses 5) Which of the following is true about determining the proper form of the hypotheses?

A) H0 is statistically proved true while testing B) failure to reject H0 proves H1 wrong C) H0 is always assumed to be true in testing D) H1 is always assumed to be true in testing Answer: C Diff: 2 Blooms: Understand Topic: One-Sample Hypothesis Tests LO1: Correctly formulate hypotheses 6) Which of the following is a Type I error?

A) the null hypothesis is actually true, and the hypothesis test correctly fails to reject it B) the null hypothesis is actually false, but the test incorrectly fails to reject it C) the null hypothesis is actually false, and the test correctly rejects it D) the null hypothesis is actually true, but the hypothesis test incorrectly rejects it Answer: D Diff: 2 Blooms: Remember Topic: One-Sample Hypothesis Tests LO1: Explain the difference between Type I and Type II errors.

7) Robin Inc. feared that the average company loss is running beyond $34,000. It initially conducted a hypothesis test on a sample extracted from its database. The hypothesis was formulated as H0: average company loss $34,000 vs. H1: average company loss > $34,000. The test resulted in favor of Robin Inc.'s loss not exceeding $34,000. Detailed study of company accounts later revealed that the average company loss had run up to $37,896. Which of the following errors were made during the hypothesis test?

A) Type III error B) Type II error C) Type I error D) Type IV error

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Answer: B Diff: 1 Blooms: Apply Topic: One-Sample Hypothesis Tests LO1: Explain the difference between Type I and Type II errors.

8) Type II error occurs when the test: A) correctly fails to reject an actually true null hypothesis.

B) incorrectly fails to reject an actually false null hypothesis.

C) correctly rejects an actually false null hypothesis.

D) incorrectly rejects an actually true null hypothesis.

Answer: B Diff: 2 Blooms: Remember Topic: One-Sample Hypothesis Tests LO1: Explain the difference between Type I and Type II errors.

9) Level of significance is the probability of: A) incorrectly rejecting an actually true null hypothesis.

B) correctly failing to reject an actually true null hypothesis.

C) incorrectly failing to reject an actually false null hypothesis.

D) correctly rejecting an actually false null hypothesis.

Answer: A Diff: 1 Blooms: Remember Topic: One-Sample Hypothesis Tests LO1: Explain the difference between Type I and Type II errors.

10) The confidence coefficient is denoted by: A) α B) 1 - β C) β D) 1 - α Answer: D Diff: 1 Blooms: Remember Topic: One-Sample Hypothesis Tests LO1: Explain the difference between Type I and Type II errors.

11) What is the confidence coefficient when the level of significance is 0.03?

A) 0.9700 B) 0.0376

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C) 0.7924 D) 0.7776 Answer: A Diff: 1 Blooms: Apply Topic: One-Sample Hypothesis Tests LO1: Explain the difference between Type I and Type II errors.

12) Which of the following denotes the power of the test?

A) α B) 1 - β C) β D) 1 - α Answer: B Diff: 1 Blooms: Remember Topic: One-Sample Hypothesis Tests LO1: Explain the difference between Type I and Type II errors.

13) Which of the following probabilities gives the confidence coefficient?

A) P(rejecting H0 | H0 is true) B) P(not rejecting H0 | H0 is false) C) P(rejecting H0 | H0 is false) D) P(not rejecting H0 | H0 is true) Answer: D Diff: 1 Blooms: Remember Topic: One-Sample Hypothesis Tests LO1: Explain the difference between Type I and Type II errors.

14) Identify the power of the test from the following probabilities.

A) P(rejecting H0 | H0 is true) B) P(not rejecting H0 | H0 is false) C) P(rejecting H0 | H0 is false) D) P(not rejecting H0 | H0 is true) Answer: C Diff: 1 Blooms: Remember Topic: One-Sample Hypothesis Tests LO1: Explain the difference between Type I and Type II errors.

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15) Which of the following is true about the value of the power of the test?

A) low value will enable valid conclusions to be made B) small sample sizes generate a low value of the power of the test C) low value will help in detecting small differences in sample statistics D) small sample sizes incur higher costs than large sample sizes Answer: B Diff: 1 Blooms: Remember Topic: One-Sample Hypothesis Tests LO1: State how to increase the power of a test.

16) Which of the following is the test statistic for a one-sample test for mean when the population standard deviation is unknown?

A) t = B) z = C) z = D) t = Answer: A Diff: 1 Blooms: Remember Topic: One-Sample Hypothesis Tests LO1: Choose the proper test statistic for hypothesis tests involving means and proportions.

17) The average cost for the sample of 5 sales of a product is = $230 and the sample standard deviation is s = $17.50. The hypothesized mean is μ0 = $250. Compute the value of the test statistic.

A) -2.56 B) -4.00 C) -1.67 D) -3.87 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: One-Sample Hypothesis Tests LO1: Choose the proper test statistic for hypothesis tests involving means and proportions.

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18) For a one-tailed test, the critical value: A) divides the sampling distribution into three parts.

B) is the number of standard errors away from the sample mean.

C) helps determine if the test statistic falls in the rejection region or not.

D) fails to reject the null hypothesis if the test statistic exceeds the critical value.

Answer: C Diff: 2 Blooms: Understand Topic: One-Sample Hypothesis Tests LO1: Explain how to draw a conclusion for one- and two-tailed hypothesis tests.

19) Which of the following is true about the rejection region?

A) The rejection region is chosen to determine the probability of a Type I error.

B) With a true null hypothesis, the test statistic falls into the rejection region.

C) If the test statistic is in the nonrejection region, the null hypothesis is rejected.

D) The rejection region occurs in the tails of the sampling distribution of the test statistic.

Answer: D Diff: 2 Blooms: Understand Topic: One-Sample Hypothesis Tests LO1: Explain how to draw a conclusion for one- and two-tailed hypothesis tests.

20) Which of the following is true about one-tailed and two-tailed tests?

A) For standard normal and t-distributions, which have a mean of zero, lower-tail critical values are negative and upper-tail critical values are positive.

B) For an upper one-tailed test, if the test statistic is greater than the critical value, the decision would be to fail to reject the null hypothesis.

C) For a lower one-tailed test, if the test statistic is less than the critical value, the decision would be to fail to reject the null hypothesis.

D) For a two-tailed test, if the test statistic is either greater than the upper critical value or less than the lower critical value, the decision would be to fail to reject the null hypothesis.

Answer: A Diff: 2 Blooms: Understand Topic: One-Sample Hypothesis Tests LO1: Explain how to draw a conclusion for one- and two-tailed hypothesis tests.

Use the data given below to answer the following question(s).

In a lower one-tailed hypothesis test, chosen level of significance = 0.10, sample size = 55, and ttest statistic = -1.76.

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21) What is the observed level of significance?

A) 0.4605 B) 0.4191 C) 0.0379 D) 0.0420 Answer: D Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: One-Sample Hypothesis Tests LO1: Use p-values to draw conclusions about hypothesis tests.

22) Which of the following is the conclusion?

A) This is a high probability and the conclusion is difficult.

B) The null hypothesis is rejected.

C) There are many sampling errors.

D) The null hypothesis cannot be rejected.

Answer: B Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: One-Sample Hypothesis Tests LO1: Use p-values to draw conclusions about hypothesis tests.

23) Which of the following computes the test statistic for a one-sample test for proportions?

A) z = B) z = C) z = D) z = Answer: C Diff: 1 Blooms: Remember Topic: One-Sample Hypothesis Tests LO1: Choose the proper test statistic for hypothesis tests involving means and proportions.

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24) For a two-sample hypothesis which tests for differences in population parameters (1) and (2), a two-tailed test seeks evidence that: A) population parameter (2) is larger than parameter (1).

B) population parameter (2) is the same as parameter (1).

C) population parameter (2) is smaller than parameter (1).

D) population parameters (1) and (2) do not belong to the same data.

Answer: B Diff: 1 Blooms: Remember Topic: Two-Sample Hypothesis Tests LO1: State the proper forms of hypotheses for two-sample hypothesis tests.

25) For a two-sample hypothesis test for differences in population parameters (1) and (2), which of the following is the correct form of an upper-tailed test?

A) H0: population parameter (1) - population parameter (2) ≥ 0 vs. H1: population parameter (1) - population parameter (2) < 0 B) H0: population parameter (1) - population parameter (2) > 0 vs. H1: population parameter (1) - population parameter (2) ≤ 0 C) H0: population parameter (1) - population parameter (2) < 0 vs. H1: population parameter (1) - population parameter (2) > 0 D) H0: population parameter (1) - population parameter (2) ≤ 0 vs. H1: population parameter (1) - population parameter (2) > 0 Answer: D Diff: 1 Blooms: Remember Topic: Two-Sample Hypothesis Tests LO1: State the proper forms of hypotheses for two-sample hypothesis tests.

26) In a two-sample test for differences in means, the hypotheses are of the form: A) B) C) D) Answer: B Diff: 1 Blooms: Remember Topic: Two-Sample Hypothesis Tests LO1: State the proper forms of hypotheses for two-sample hypothesis tests.

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27) For a lower-tail test, the p-value in the output from an Excel tool: A) is correct if the test-statistic is negative.

B) is the difference from 1.0 if the test-statistic is negative.

C) is correct if the test-statistic is zero.

D) is correct if the test-statistic is positive.

Answer: A Diff: 1 Blooms: Remember Topic: Two-Sample Hypothesis Tests LO1: Select and use Excel Analysis ToolPak procedures for two-sample hypothesis tests.

28) Which of the following Excel tools is used for a two-sample test for equality of variances?

A) Excel F-test Two-sample for variances B) Excel z-test: Two-sample for means C) Excel t-test: Two-sample assuming unequal variances D) Excel t-test: Two-sample assuming equal variances Answer: A Diff: 1 Blooms: Remember Topic: Two-Sample Hypothesis Tests LO1: Select and use Excel Analysis ToolPak procedures for two-sample hypothesis tests.

29) While testing for equality of variances, which of the following formulae gives the F-test statistic?

A)

-

B) C) D)

௦భమ

௦మమ Answer: D Diff: 1 Blooms: Remember Topic: Analysis of Variance (ANOVA) LO1: Explain the purpose of analysis of variance.

30) In statistical terminology, the variable of interest is called a ________.

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D) test-statistic Answer: C Diff: 1 Blooms: Remember Topic: Analysis of Variance (ANOVA) LO1: Explain the purpose of analysis of variance.

31) Which of the following is true while applying the Excel ANOVA tool?

A) The specified input range of data must be separated.

B) The sample size for each factor level must be the same.

C) The input range must be a rectangular region that contains all data.

D) Level of significance need not be specified.

Answer: C Diff: 1 Blooms: Understand Topic: Analysis of Variance (ANOVA) LO1: Use the Excel ANOVA tool to conduct an analysis of variance test.

32) In order to reject the null hypothesis, the F-test statistic must be greater than the ________.

A) p-value B) variance C) df D) F crit Answer: D Diff: 1 Blooms: Remember Topic: Analysis of Variance (ANOVA) LO1: Use the Excel ANOVA tool to conduct an analysis of variance test.

33) Which of the following tests is used to determine if two categorical variables are independent?

A) Chi-square test B) t-test C) z-test D) ANOVA Answer: A Diff: 1 Blooms: Remember Topic: Chi-Square Test for Independence LO1: Conduct and interpret the results of a chi-square test for independence.

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34) Which of the following is true about chi-square distribution?

A) It is a special distribution and is denoted by (C2).

B) It is characterized by degrees of freedom.

C) It is computed using the Excel function CHISQ.INV.TEST. D) It has a left-tail area equal to the expected value of the sample.

Answer: B Diff: 1 Blooms: Understand Topic: Chi-Square Test for Independence LO1: Conduct and interpret the results of a chi-square test for independence.

35) Which of the following 2016 Excel functions computes the p-value for the chi-square test?

A) CHISQ.INV.RT B) CHIDIST C) CHI.SQ D) CHISQ.TEST Answer: D Diff: 1 Blooms: Remember Topic: Chi-Square Test for Independence LO1: Conduct and interpret the results of a chi-square test for independence.

Use the data given below to answer the following question(s).

The following extract from a manufacturer's database shows a sample of 10 suppliers, their transportation charges, and the estimated and actual total costs of supplying materials. (Note: Assume a significance level of 0.05 wherever necessary.)

Supplier Peter John Martin Philip Mark Thomas Jaison David Carter Leonard

Transportation Charges 340 560 480 290 370 520 350 430 510 270

Estimated Total Cost 4,500 4,500 4,500 4,500 4,500 4,500 4,500 4,500 4,500 4,500

Actual Total Cost 4,680 4,790 5,110 4,780 4,810 4,770 5,250 4,930 5,010 4,810

36) Conduct the appropriate type of one-sample test-statistic to determine whether the average transportation charge is less than $430.

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H0: population mean transportation charges ≥ $430 vs. H1: population mean transportation charges < $430 Average transportation charges for a sample of 10 suppliers ( ) = $412 Sample standard deviation (s) = $102.18 Hypothesized mean (μ0) = $430 t = ( - μ0) / (s /✓n) = (412 - 430) / (102.18 /✓ 10) = (-18) / (32.31) = -0.56 The sample mean is 0.56 standard errors below the hypothesized value of 430. Since -0.56 > than Critical t -2.1318, there is insufficient evidence to conclude that the average transportation charges is below $430.

Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: One-Sample Hypothesis Tests LO1: Choose the proper test statistic for hypothesis tests involving means and proportions.

37) Conduct the appropriate type of one-sample test-statistic to determine whether the average transportation charge is less than $430. Apply a decision rule using the observed level of significance and draw a conclusion.

Answer: If the true mean is 430, then the p-value is the probability of obtaining a test statistic of - 0.56 or less.

Using the Excel function TDIST(-0.56,9,TRUE), p-value = 0.2946.

Decision rule: Whenever p-value < chosen level of significance α, reject the null hypothesis and otherwise fail to reject it.

Because p-value is not less than α = 0.05, the null hypothesis cannot be rejected. There is about a 30% chance that the test statistic would be -0.56 or smaller if the null hypothesis was true. This is a fairly high probability, so it would be difficult to conclude that the true mean is less than 430. The fact that the sample mean is less than the hypothesized value can be attributed to sampling error alone.

Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: One-Sample Hypothesis Tests LO1: Use p-values to draw conclusions about hypothesis tests.

38) On studying the database, the manufacturer found out that the average difference between the estimated and actual total costs was $394. Based on the sample data, can the manufacturer conclude that the average difference between the estimated and actual total costs is different from zero?

Answer: If μD denotes the population mean difference between the estimated and actual total costs, then the null and the alternative hypotheses are of the form, H0: μD = 0 vs. H1: μD ≠ 0.

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t-Test: Paired Two Sample for Means

The above output from the Excel tool shows the critical values are ± 2.26. Since t Stat -6.97 is much smaller than the lower critical value -2.26, the null hypothesis is rejected. It can be concluded that the mean of the differences between the estimated and the actual total costs is statistically significant. The p-value 0.0001 too is essentially zero verifying this conclusion.

Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Two-Sample Hypothesis Tests LO1: State the proper forms of hypotheses for two-sample hypothesis tests. Select and use Excel Analysis ToolPak procedures for two-sample hypothesis tests.

39) During a study, individuals were asked to rate a product on a scale of 1-5. From the following data, help the researcher determine whether any significant differences exist in opinions among individuals from different regions. (Note: Assume a significance level of 0.05 wherever necessary.)

Quintasia 3 4 2 5 1 5 3

Paraland Bayundera 1 5 4 1 2 3 2 2 3 2 5 5 5 1 1 4 4 2

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Answer: The null hypothesis for ANOVA is that the population means of all groups are equal; the alternative hypothesis is that at least one mean differs from the rest: H0: μ1 = μ2 = μ3 vs. H1: at least the mean from one region is different from others Anova: Single Factor

From the above results of the ANOVA test, F = 0.16 and F crit = 3.443. Clearly, F < F crit, which means that the null hypothesis cannot be rejected. It can be concluded that we do not have enough information to state that there are no significant differences in the opinions among the individuals from different regions. The p-value 0.8492 being greater than the chosen level of significance verifies the conclusion.

Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Analysis of Variance (ANOVA) LO1: Use the Excel ANOVA tool to conduct an analysis of variance test.

40) Using the following data, test for the independence of the variables. (Note: Assume a significance level of 0.05 wherever necessary.)

Respondent 1 2 3 4 5 6 7 8 9

Gender Female Male Male Female Female Male Male Male Female

Breakfast Preference Fruits Cereal Milk Fruits Milk Cereal Milk Milk Fruits

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10 11 12 13 14 15

Male Male Female Female Male Female

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Fruits Cereal Cereal Milk Fruits Fruits

Answer: The chi-square test for independence tests the following hypotheses: H0: the two categorical variables are independent H1: the two categorical variables are dependent Cross-tabulation table:

Expected Frequency Female Male Grand Total

Cereal Fruits Milk 1.87 2.80 2.33 2.13 3.20 2.67 4.00 6.00 5.00

The chi-square statistic is computed as X2 =

Grand Total 7.00 8.00 15.00 , where fo is the observed frequency, and

fe is the expected frequency.

Chi Square Statistic Cereal Fruits Milk Grand Total Female 0.40 0.51 0.05 0.96 Male 0.36 0.45 0.04 0.85 Grand Total 0.76 0.96 0.09 1.81 From the above table of calculations, the value of the chi-square statistic is 1.81.

From the cross-tabulation table, the number of rows r = 2 and number of columns c = 3.

Degrees of freedom = (r-1)(c-1) = (2-1)(3-1) = 2. Chi-square critical = 5.991. p-value = 0.4049 The chi-square test returned a p-value greater than the chosen level of significance. Therefore, the null hypothesis cannot be rejected. We cannot state that the categorical variables are dependent.

Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Chi-Square Test for Independence LO1: Conduct and interpret the results of a chi-square test for independence.

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41) In conducting a hypothesis test, what is usually to be proven statistically is identified as the null hypothesis.

Answer: FALSE Diff: 1 Blooms: Remember Topic: One-Sample Hypothesis Tests LO1: Explain the difference between the null and alternative hypotheses.

42) If the alternative hypothesis includes the symbol <, the rejection region is in the upper tail.

Answer: FALSE Diff: 1 Blooms: Remember Topic: One-Sample Hypothesis Tests LO1: Explain how to draw a conclusion for one- and two-tailed hypothesis tests.

43) For a two-sample test for means with the population variance being known, the Excel procedure used is the Excel z-test.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Two-Sample Hypothesis Tests LO1: Select and use Excel Analysis ToolPak procedures for two-sample hypothesis tests.

44) In a two-sample test for means with the population variance being known, the z-test uses a test statistic that is based on the standard normal distribution.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Two-Sample Hypothesis Tests LO1: Explain how to draw a conclusion for one- and two-tailed hypothesis tests.

45) The first step in a chi-square test is to compute the observed frequency between each cell of the cross-tabulation if the two variables are independent.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Chi-Square Test for Independence LO1: Conduct and interpret the results of a chi-square test for independence.

46) What are the four different outcomes of hypothesis testing?

Answer: Hypothesis testing can result in one of four different outcomes:

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• The null hypothesis is actually true, and the hypothesis test correctly fails to reject it.

• The null hypothesis is actually false, and the hypothesis test correctly rejects it.

• The null hypothesis is actually true, but the hypothesis test incorrectly rejects it (called Type I error).

• The null hypothesis is actually false, but the hypothesis test incorrectly fails to reject it (called Type II error).

Diff: 2 Blooms: Remember Topic: One-Sample Hypothesis Tests LO1: List the four possible outcome results from a hypothesis test.

47) How do test statistics for two-sample tests vary depending on whether the population standard deviations are known, and if not, whether they are assumed to be equal?

Answer: Selection of the proper test statistic for a two-sample test for means depends on whether the population standard deviations are known, and if not, whether they are assumed to be equal.

• Population variance is known. In Excel 2010, choose z-Test: Two-Sample for Means from the Data Analysis menu. This test uses a test statistic that is based on the standard normal distribution.

• Population variance is unknown and assumed unequal. From the Data Analysis menu, choose t-test: Two-Sample Assuming Unequal Variances. The test statistic for this case has a tdistribution.

• Population variance unknown but assumed equal. In Excel, choose t-test: Two-Sample Assuming Equal Variances. The test statistic also has a t-distribution, but it is different from the unequal variance case.

Diff: 2 Blooms: Understand Topic: Two-Sample Hypothesis Tests LO1: Select and use Excel Analysis ToolPak procedures for two-sample hypothesis tests.

48) For a two-sample test, explain the procedure used when it is difficult to justify the assumption that the variances of each population are equal.

Answer: Only rarely are the population variances known; also, it is often difficult to justify the assumption that the variances of each population are equal. Therefore, in most practical situations, the t-test: Two-Sample Assuming Unequal Variances is used. This procedure also works well with small sample sizes if the populations are approximately normal. It is recommended that the size of each sample be approximately the same and total 20 or more. If the populations are highly skewed, then larger sample sizes are recommended.

Diff: 2 Blooms: Understand Topic: Two-Sample Hypothesis Tests LO1: Select and use Excel Analysis ToolPak procedures for two-sample hypothesis tests.

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49) Explain the assumptions underlying ANOVA along with their violations.

Answer: ANOVA requires assumptions that the m groups or factor levels being studied represent populations whose outcome measures: • are randomly and independently obtained, • are normally distributed, and • have equal variances.

If these assumptions are violated, then the level of significance and the power of the test can be affected. If sample sizes are equal, violation of the third assumption does not have serious effects on the statistical conclusions; however, with unequal sample sizes, it can. A nonparametric test may be used when the assumptions underlying ANOVA are violated.

Diff: 2 Blooms: Understand Topic: Analysis of Variance (ANOVA) LO1: List the assumptions of ANOVA. 50) Why is testing for independence important for businesses?

Answer: A common problem in business is to determine whether two categorical variables are independent. With sample data, sampling error can make it difficult to properly assess independence of categorical variables. The joint probabilities would never be expected to be exactly the same as the product of the marginal probabilities because of sampling error even if the two variables are statistically independent. Testing for independence is important in marketing applications.

Diff: 2 Blooms: Understand Topic: Chi-Square Test for Independence LO1: Conduct and interpret the results of a chi-square test for independence.

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Business Analytics, 3e (Evans) Chapter 8: Trendlines and Regression Analysis 1) A regression model that involves a single independent variable is called ________.

A) single regression B) unit regression C) simple regression D) individual regression Answer: C Diff: 1 Blooms: Remember Topic: Simple Linear Regression LO1: Explain the purpose of regression analysis and provide examples in business.

2) Regression models of ________ data focus on predicting the future.

A) missing B) time-series C) panel D) cross-sectional Answer: B Diff: 1 Blooms: Remember Topic: Simple Linear Regression LO1: Explain the purpose of regression analysis and provide examples in business.

The following table exhibits the age of antique furniture and the corresponding prices. Use the table to answer the following question(s). (Hint: Use scatter diagram and the Excel Trendline tool where necessary).

Number Value of years ($) 78 930 91 1010 83 970 159 1950 134 1610 210 2880 88 980 178 2010 124 1370 72 900

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3) What is the relationship between the age of the furniture and their values?

A) Nonlinear B) Linear C) Curvilinear D) No relationship Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Simple Linear Regression LO1: Use a scatter chart to identify the type of relationship between two variables.

4) Which of the following is true of linear functions used in predictive analytical models?

A) It is used when the rate of change in a variable decreases or increases quickly and then levels out.

B) It is used when there is a steady decrease or increase over a range of a variable.

C) It is used when there is increase at a specific rate.

D) It is used when there is a rise or fall at a constantly increasing rate.

Answer: B Diff: 2 Blooms: Remember Topic: Data-Driven Modeling LO1: List the common types of mathematical functions used in predictive modeling.

5) ________ are mathematical functions used in predictive analytical models which define phenomena that increase at a specific rate, and is represented by the formula y = axb A) Exponential functions B) Power functions C) Polynomial functions D) Logarithmic functions Answer: B Diff: 1 Blooms: Remember Topic: Modeling Relationships and Trends in Data LO1: List the common types of mathematical functions used in predictive modeling.

6) Which of the following mathematical functions, used in predictive analytical models, is represented by the formula y = ax3 + bx2 + cx + d?

A) exponential functions B) power functions C) logarithmic functions D) polynomial functions Answer: D

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Diff: 1 Blooms: Remember Topic: Modeling Relationships and Trends in Data LO1: List the common types of mathematical functions used in predictive modeling.

7) In ________ functions, represented by y = abx, y rises or falls at constantly increasing rates.

A) logarithmic B) power C) exponential D) polynomial Answer: C Diff: 1 Blooms: Remember Topic: Data-Driven Modeling LO1: List the common types of mathematical functions used in predictive modeling.

8) In Excel's Trendline tool, the value of the________ gives the measure of fit of the line to the data.

A) linear function B) R-squared C) moving average D) set intercept Answer: B Diff: 1 Blooms: Remember Topic: Data-Driven Modeling LO1: Apply the Excel Trendline tool to fit models to data.

9) Which of the following is true of the R-squared (R2) value in Excel's Trendline function?

A) A value of 1.0 for R2 indicates maximum deviation of the data from the line.

B) If the value of R2 is above 1.0, the line will be at a perfect fit for the data.

C) The value of R2 will always be between -1 and 1.

D) As the value of R2 gets higher, the line will be a better fit for the data.

Answer: D Diff: 1 Blooms: Remember Topic: Data-Driven Modeling LO1: Apply the Excel Trendline tool to fit models to data.

10) Which of the following equations correctly expresses the relationship between the two variables?

A) Value = (-181.16) + 13.493 × Number of years Copyright © 2020 Pearson Education, Inc.

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B) Number of years = Value / 12.537 C) Value = (459.34 / Number of years) × 4.536 D) Number of years = (17.538 × Value) / (-157.49) Answer: A Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Simple Linear Regression LO1: Use the Excel Trendline tool to find the best-fitting simple linear regression model.

11) What is the expected value for a 90 year-old piece of furniture?

A) $1002.45 B) $997.98 C) $934.56 D) $1033.21 Answer: D Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Simple Linear Regression LO1: Use the Excel Trendline tool to find the best-fitting simple linear regression model.

12) In a linear relationship, which of the following accounts for the many possible values of the dependent variable that vary around the mean?

A) the coefficient of the dependent variable X B) the value of the intercept ß0 C) the random error term ε D) the standard error SYX Answer: C Diff: 1 Blooms: Remember Topic: Simple Linear Regression LO1: Explain how least-squares regression finds the best-fitting regression model.

13) Which of the following is true about the observed errors associated with estimating the value of the dependent variable using the regression line?

A) They are the horizontal distances between slopes and y-intercepts.

B) The errors are also referred to as critical values.

C) They are always maximized by the regression lines.

D) The errors can be negative or positive.

Answer: D Diff: 2 Blooms: Understand

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Topic: Simple Linear Regression LO1: Explain how least-squares regression finds the best-fitting regression model.

14) For an independent variable Y, the error associated with the ith observation is: A) ei = Yi - Ŷi B) Yi = (ei)2 - Ŷi C) (Ŷi)2 ei = Yi D) ei = (Yi + Ŷi)2 Answer: A Diff: 1 Blooms: Remember Topic: Simple Linear Regression LO1: Explain how least-squares regression finds the best-fitting regression model.

Use the data given below to answer the following question(s).

Following is an extract from the database of a construction company. The table shows the height of walls in feet and the cost of raising them. The estimated simple linear regression equation is given as Ŷ = b0 + b1X. (Hint: Use Excel functions).

Height (ft)

Cost ($) 4 670 3 430 7 810 9 1100 6 790 8 880 5 760 11 1200

15) What is the value of the coefficient b0?

A) -2.25321 B) 0.010697 C) 254.8371 D) 86.81704 Answer: C Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Simple Linear Regression LO1: Use Excel functions to find least-squares regression coefficients.

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16) What is the value of the coefficient b1?

A) 86.81704 B) 254.8371 C) 0.010697 D) -2.14625 Answer: A Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Simple Linear Regression LO1: Use Excel functions to find least-squares regression coefficients.

17) What is the estimated cost of raising a 10-inch wall?

A) 1505.786 B) 1103.578 C) 968.6109 D) 1123.008 Answer: D Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Simple Linear Regression LO1: Use Excel functions to find least-squares regression coefficients.

18) Which of the following statements is true when using the Excel Regression tool?

A) The range for the independent variable values must be specified in the box for the Input Y Range.

B) Checking the option Constant is Zero forces the intercept to zero.

C) The Regression tool can be found in the Tools tab under Insert group.

D) Adding an intercept term reduces the analysis' fit to the data.

Answer: B D’ff: 2 Blooms: Understand Topic: Simple Linear Regression LO1: Use the Excel Regression tool for both single and multiple linear regressions.

19) Which of the following generates a scatter chart in Excel with the values predicted by the regression model included?

A) Trendline B) Residual Plots C) R Square D) Line Fit Plots Answer: D

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Diff: 1 Blooms: Remember Topic: Simple Linear Regression LO1: Use the Excel Regression tool for both single and multiple linear regressions.

20) Which of the following is true about Excel outputs Multiple R? A) It is often referred to as the coefficient of determination.

B) A value of 0 indicates positive correlation.

C) A negative slope of the regression line denotes a positive Multiple R. D) It is another name for the sample correlation coefficient, r.

Answer: D Diff: 1 Blooms: Remember Topic: Simple Linear Regression LO1: Interpret the regression statistics of the Excel Regression tool.

21) The R2 value: A) is the variability of the observed Y-values from the predicted values.

B) indicates that as the independent variable increases, the intercept term does too.

C) gives the proportion of variation in the dependent variable that is explained by the independent variable.

D) transforms the cumulative probability scale (vertical axis) so that the graph of the cumulative normal distribution is a straight line.

Answer: C Diff: 1 Blooms: Remember Topic: Simple Linear Regression LO1: Interpret the regression statistics of the Excel Regression tool.

22) For a simple linear regression model, significance of regression is: A) a measure of how well the regression line fits the data.

B) a hypothesis test of whether the true regression coefficient ß1 is zero.

C) a statistic that modifies the value of R2 by incorporating the sample size and the number of explanatory variables in the model.

D) the variability of the observed Y-values from the predicted values.

Answer: B Diff: 1 Blooms: Remember Topic: Simple Linear Regression LO1: Interpret significance of regression from the Excel Regression tool output.

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23) Which of the following Excel functions is applied to test for significance of regression?

A) COVAR B) ANOVA C) SINH D) TREND Answer: B Diff: 1 Blooms: Remember Topic: Simple Linear Regression LO1: Interpret significance of regression from the Excel Regression tool output.

24) While testing hypotheses for regression coefficients, the t-test for the slope is expressed as: A) t = B) t = C) t = D) t = Answer: A Diff: 1 Blooms: Remember Topic: Simple Linear Regression LO1: Draw conclusions for tests of hypotheses about regression coefficients.

25) ________ provide information about the unknown values of the true regression coefficients, accounting for sampling error.

A) Standard errors B) Confidence intervals C) Adjusted R Squares D) P-values Answer: B Diff: 1 Blooms: Remember Topic: Simple Linear Regression LO1: Interpret confidence intervals for regression coefficients 26) Standard residuals: A) help detect outliers that may bias the results of a regression analysis.

B) cause differences in the regression equation by changing the slope and intercept.

C) point out the ranges for the population intercept and slope at a 95% confidence level.

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D) provide information for testing hypothesis associated with the intercept and slope.

Answer: A Diff: 2 Blooms: Remember Topic: Residual Analysis and Regression Assumptions LO1: Calculate standard residuals.

27) A(n) ________ is an extreme value that is different from the rest of the data.

A) critical value B) standard error C) expected value D) outlier Answer: D Diff: 1 Blooms: Remember Topic: Residual Analysis and Regression Assumptions LO1: Calculate standard residuals.

28) While checking for linearity by examining the residual plot, the residuals must: A) exhibit a linear trend.

B) form a parabolic shape.

C) be randomly scattered.

D) be below the x-axis.

Answer: C Diff: 1 Blooms: Remember Topic: Residual Analysis and Regression Assumptions LO1: Calculate standard residuals.

29) Which of the following is true when testing for normality of errors?

A) Normality is verified by inspecting for a bell-shaped distribution.

B) It is easier to evaluate normality with small sample sizes.

C) A scatter diagram of the whole data is always used to verify normality.

D) Errors are normally distributed when the scatter diagram shows a straight-line distribution.

Answer: A Diff: 1 Blooms: Remember Topic: Residual Analysis and Regression Assumptions LO1: List the assumptions of regression analysis and describe methods to verify them.

30) ________ means that the variation about the regression line is constant for all values of the independent variable.

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A) Autocorrelation B) Normality of errors C) Homoscedasticity D) Linearity Answer: C Diff: 1 Blooms: Remember Topic: Residual Analysis and Regression Assumptions LO1: List the assumptions of regression analysis and describe methods to verify them.

31) Which of the following helps in evaluation of autocorrelation?

A) Breusch-Pagan test B) Durbin-Watson statistic C) Hosmer-Lemeshow test D) Cochran-Mantel-Haenszel statistics Answer: B Diff: 1 Blooms: Remember Topic: Residual Analysis and Regression Assumptions LO1: List the assumptions of regression analysis and describe methods to verify them.

32) In multiple regression, R Square is referred to as the: A) multiple correlation coefficient.

B) coefficient of autocorrelation.

C) coefficient of multiple determination.

D) multiple significance coefficient.

Answer: C Diff: 1 Blooms: Remember Topic: Multiple Linear Regression LO1: Explain the differences in the Excel Regression tool output for simple and multiple linear regression models.

33) Which of the following is true about multiple linear regression?

A) It is a linear regression model with more than one dependent variable.

B) The regression coefficients are called fractional regression coefficients.

C) It uses least squares to estimate the intercept and slope coefficients.

D) The ANOVA tests for the significance of each variable separately.

Answer: C Diff: 1 Blooms: Understand Topic: Multiple Linear Regression

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LO1: Explain the differences in the Excel Regression tool output for simple and multiple linear regression models.

34) When using the t-statistic in multiple regression to determine if a variable should be removed: 2 A) R will increase if the variable is removed.

B) if |t| > 1, the standard error will decrease.

C) a large number of independent variables is convenient.

D) if |t| < 1, the standard error will increase.

Answer: A Diff: 2 Blooms: Understand Topic: Building Good Regression Models LO1: Apply a systematic approach to build good regression models.

35) When two or more independent variables in the same regression model can predict each other better than the dependent variable, the condition is referred to as ________.

A) autocorrelation B) heteroscedasticity C) multicollinearity D) homoscedasticity Answer: C Diff: 1 Blooms: Remember Topic: Building Good Regression Models LO1: Explain the importance of understanding multicollinearity in regression models.

36) Which of the following is true about multicollinearity?

A) The effect of a dependent variable on another becomes difficult to isolate.

B) Regression coefficients become clearer and are easier to interpret.

C) P-values reduce significantly leading to rejection of null hypothesis.

D) It is best measured using the statistic variance inflation factor (VIF).

Answer: D Diff: 1 Blooms: Remember Topic: Building Good Regression Models LO1: Explain the importance of understanding multicollinearity in regression models.

37) Categorical variables that have been coded are called ________.

A) limited dependent variables B) dummy variables C) instrumental variables

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D) observable variables Answer: B Diff: 1 Blooms: Remember Topic: Regression with Categorical Independent Variables LO1: Build regression models for categorical data using dummy variables.

38) Interaction is: A) the principle of having a model with maximum explanatory variables.

B) the process of coding categorical variables.

C) a measure to determine the correlation between dependent variables.

D) the dependence between two independent variables.

Answer: D Diff: 1 Blooms: Remember Topic: Regression with Categorical Independent Variables LO1: Test for interactions in regression models with categorical variables.

39) How many additional dummy variables are required if a categorical variable has 4 levels?

A) 2 B) 3 C) 1 D) 4 Answer: B Diff: 1 Blooms: Understand Topic: Regression with Categorical Independent Variables LO1: Build regression models for categorical data using dummy variables.

40) When a scatter chart of data shows a nonlinear relationship, the nonlinear model can be expressed as: A) Y = β0 + β1X + β2X2 + ε B) Y = β0 + β1X + (β2X)2 + ε C) Y = β0 + β1X + β2X D) Y = β0 + β1X2 + β2X2 + ε Answer: A Diff: 1 Blooms: Remember Topic: Regression Models with Nonlinear Terms LO1: Identify when curvilinear regression models are more appropriate than linear models.

41) In a quadratic regression model, the ________ represents the curvilinear effect.

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A) slope of the linear term B) error term C) slope of the quadratic term D) R Square Answer: C Diff: 1 Blooms: Remember Topic: Regression Models with Nonlinear Terms LO1: Identify when curvilinear regression models are more appropriate than linear models.

Use the data given below to answer the following question(s).

Following is an extract from a firm's database detailing the number of hours spent on the job by employees and their corresponding pay. (Note: Assume a level of significance of 0.05 wherever necessary.)

Hours spent on the job Salary ($) 4 340 12 850 7 570 5 470 11 820 8 610 9 630 13 900 10 800 6 480 42) Construct a scatter diagram and use the Excel Trendline tool to find the best-fitting simple linear regression model.

Answer:

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Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Simple Linear Regression LO1: Use the Excel Trendline tool to fit models to data.

43) Is the hours spent on the job a statistically significant variable in explaining the variation in pay of employees? (Hint: Use Regression tool).

Answer: Hypothesis test for significance of regression: H0 : β1 = 0 H1 : β1 ≠ 0 where, β1 is the slope of the intercept.

Significance F, that is, the p-value associated with the hypothesis test is essentially zero (2.525 × 10-7). Therefore, assuming a level of significance of 0.05, the null hypothesis must be rejected and conclude that the slope–the coefficient for number of hours spent on the job–is not zero. This means that work hours is a statistically significant variable in explaining the variation in employee pay.

Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Simple Linear Regression LO1: Interpret significance of regression from the Excel Regression tool output.

44) Draw conclusions for test of hypothesis for regression coefficients.

Answer: Hypothesis test for regression coefficients: H0 : β1 = 0 H1 : β1 ≠ 0 where, β1 is the slope of the intercept.

The t-test for the slope: t=

= 61.27272727 / 3.868357187 = 15.83946991

Because the P-value for both coefficients is essentially zero, it can be concluded that neither coefficient is statistically equal to zero.

Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Simple Linear Regression LO1: Draw conclusions for tests of hypotheses about regression coefficients.

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45) Interpret the confidence intervals.

Answer: A 95% confidence interval for the intercept is [46.15, 206.22]. Similarly, a 95% confidence interval for the slope is [52.35, 70.19]. Although the regression model is Ŷ = 126.18 + 61.273X, the confidence intervals suggest a bit of uncertainty about predictions using the model. Although, it can be estimated that an employee who spent 10.5 hours on the job will receive a pay of 126.18 + (61.273 × 10.5) = $769.5465, if the true parameters are at the extremes of the confidence intervals, the estimate might be as low as 46.15 + (52.35 × 10.5) = $595.825 or as high as 206.22 + (70.19 × 10.5) = $943.215.

Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Simple Linear Regression LO1: Interpret confidence intervals for regression coefficients 46) Interpret residual output.

Answer: From the data, the first observation has a salary of $340 and the regression model predicts $371.27. Thus the residual is 340 - 371.27 = - $31.27. By dividing this residual by its standard deviation, the standardized residual for the first observation is - 0.944. This means that the first observation is about 0.94 standard deviations below the regression line. There are no standardized residuals outside of ± 3 standard deviations. It can be concluded that there are no outliers.

Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Residual Analysis and Regression Assumptions LO1: Calculate standard residuals.

47) In predictive analysis models, a second-order polynomial has only one hill or valley.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Modeling Relationships and Trends in Data LO1: List the common types of mathematical functions used in predictive modeling.

48) Excel's Trendline feature cannot be used in modeling trends which include time variables.

Answer: FALSE Diff: 1 Blooms: Understand Topic: Modeling Relationships and Trends in Data LO1: Use the Excel Trendline tool to fit models to data.

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49) The best-fitting line maximizes the residuals.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Simple Linear Regression LO1: Explain how least-squares regression finds the best-fitting regression model.

50) Creating a scatter chart with an added trendline is visually superior to the scatter chart generated by line fit plots.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Simple Linear Regression LO1: Use a scatter chart to identify the type of relationship between two variables.

51) The standard error may be assumed to be large if the data are clustered close to the regression line.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Simple Linear Regression LO1: Interpret the regression statistics of the Excel Regression tool.

52) An increase in adjusted R2 indicates that the regression model has improved.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Building Good Regression Models LO1: Interpret the regression statistics of the Excel Regression tool.

53) A good regression model has the fewest number of explanatory variables providing an adequate interpretation of the dependent variable.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Building Good Regression Models LO1: Apply a systematic approach to build good regression models.

54) Why is regression analysis necessary in business? What categories of regression models are used?

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Answer: Regression analysis is a tool for building statistical models that characterize relationships among a dependent variable and one or more independent variables, all of which are numerical. Two broad categories of regression models are used often in business settings: (1) regression models of cross-sectional data and (2) regression models of time-series data, in which the independent variables are time, or some function of time, and the focus is on predicting the future. Time-series regression is an important tool in forecasting.

Diff: 2 Blooms: Remember Topic: Simple Linear Regression LO1: Explain the purpose of regression analysis and provide examples in business.

55) When are logarithmic functions used in predictive analysis?

Answer: Logarithmic functions are used when the rate of change in a variable increases or decreases quickly and then levels out, such as with diminishing returns to scale. Logarithmic functions are often used in marketing models where constant percentage increases in advertising, for instance, result in constant, absolute increases in sales.

Diff: 1 Blooms: Remember Topic: Modeling Relationships and Trends in Data LO1: List the common types of mathematical functions used in predictive modeling.

56) While conducting regression analysis, how is constructing a normal probability plot useful?

Answer: While conducting regressions analysis using the Excel Regression tool, a normal probability plot for the dependent variable may be chosen to be constructed. It transforms the cumulative probability scale (vertical axis) so that the graph of the cumulative normal distribution is a straight line. The closer the points are to a straight line, the better the fit to a normal distribution.

Diff: 2 Blooms: Understand Topic: Simple Linear Regression LO1: Use the Excel Regression tool for both single and multiple linear regressions.

57) Briefly explain the assumptions on which the statistical hypothesis tests associated with regression analysis are predicated.

Answer: The statistical hypothesis tests associated with regression analysis are predicated on some key assumptions about the data.

(1) Linearity: This is usually checked by examining a scatter diagram of the data or examining the residual plot. If the model is appropriate, then the residuals should appear to be randomly scattered about zero, with no apparent pattern.

(2) Normality of errors: Regression analysis assumes that the errors for each individual value of X are normally distributed, with a mean of zero.

(3) Homoscedasticity: This means that the variation about the regression line is constant for all values of the independent variable.

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(4) Independence of errors: Residuals should be independent for each value of the independent variable.

Diff: 1 Blooms: Remember Topic: Residual Analysis and Regression Assumptions LO1: List the assumptions of regression analysis and describe methods to verify them.

58) List the systematic approach to build good multiple regression models.

Answer: (1) Construct a model with all available independent variables. Check for significance of the independent variables by examining the p-values.

(2) Identify the independent variable having the largest p-value that exceeds the chosen level of significance.

(3) Remove the variable identified in step 2 from the model and evaluate adjusted R2. (Don't remove all variables with p-values that exceed α at the same time, but remove only one at a time.)

(4) Continue until all variables left in the model are significant.

Diff: 1 Blooms: Remember Topic: Building Good Regression Models LO1: Apply a systematic approach to build good regression models.

59) Explain the concept of curvilinear regression model.

Answer: Linear regression models are not appropriate for every situation. A scatter chart of the data might show a nonlinear relationship, or the residuals for a linear fit might result in a nonlinear pattern. In such cases, a nonlinear model is proposed to explain the relationship. For instance, a second-order polynomial model would be: Y = β0 + β1X + β2X2 + ε Sometimes this is called a curvilinear regression model. In this model, β1 represents the linear effect of X on Y, and β2 represents the curvilinear effect. However, although this model appears to be quite different from ordinary linear regression models, it is still linear in the parameters. In other words, all terms are a product of a beta coefficient and some function of the data, which are simply numerical values. In such cases least squares can still be applied to estimate the regression coefficients.

Diff: 2 Blooms: Understand Topic: Regression Models with Nonlinear Terms LO1: Identify when curvilinear regression models are more appropriate than linear models.

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Business Analytics, 3e (Evans) Chapter 9: Forecasting Techniques 1) The Delphi method used for forecasting: A) obtains forecasts through a comparative analysis with a previous situation.

B) uses measures that are believed to influence the behavior of a variable that the researcher wishes to forecast.

C) uses a single measure that weights multiple indicators and provides a measure of overall expectation.

D) uses a panel of experts, whose identities are typically kept confidential from one another, to respond to a sequence of questionnaires.

Answer: D Diff: 1 Blooms: Remember Topic: Qualitative and Judgmental Forecasting LO1: Explain how judgmental approaches are used for forecasting.

2) Before launching a new line of toys, Toys Inc. used the method of historical analogy to obtain a forecast. In this scenario, Toys Inc.: A) noted the behavior of its current customers while they use their products.

B) used a panel of experts, whose identities were kept confidential from one another, to respond to a sequence of questionnaires.

C) noted the consumer response to similar previous products to marketing campaigns and used the responses as a basis to predict how the new marketing campaign might fare.

D) used a brainstorming session among a group of experts to draw new ideas.

Answer: C Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Qualitative and Judgmental Forecasting LO1: Explain how judgmental approaches are used for forecasting.

3) In forecasting, what is an index?

A) It is a single measure that weights multiple indicators and provides a measure of overall expectation.

B) It is a stream of historical data, such as weekly sales.

C) It is a time series that does not have trend, seasonal, or cyclical effects but is relatively constant and only exhibits random behavior.

D) It is a measure that provides a complete forecast.

Answer: A Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Qualitative and Judgmental Forecasting Copyright © 2020 Pearson Education, Inc. 163

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LO1: Explain how judgmental approaches are used for forecasting.

4) What is a stream of historical data known as?

A) a time series B) an index C) a complex number D) an orthopole Answer: A Diff: 1 Blooms: Remember Topic: Statistical Forecasting Models LO1: List different types of statistical forecasting models.

5) Time-series models may exhibit seasonal effects or cyclical effects. A seasonal effect differs from a cyclical effect in that a seasonal effect: A) has no trend, is relatively constant, and only exhibits random behavior.

B) describes ups and downs over a time frame such as several years.

C) is one that repeats at fixed intervals of time, typically a year, month, week, or day.

D) is based on analysis of historical time-series data and are predicated on the assumption that the future is an extrapolation of the past.

Answer: C Diff: 2 Blooms: Understand Topic: Statistical Forecasting Models LO1: List different types of statistical forecasting models.

6) The data for the number of hand-held gaming devices sold for the past 5 weeks are 15 units, 20 units, 25 units, 30 units, and 17 units respectively. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects; thus, a moving average model would be appropriate. Setting k = 3 the three-period moving average forecast for week 6 is ________.

A) 20 units B) 24 units C) 30 units D) 17 units Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Stationary Time Series LO1: Apply moving average and exponential smoothing models to stationary time series.

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7) If the actual value of a time series at time t and the forecast value for time t is denoted by At and Ft respectively, then the formula for the mean absolute deviation over a range of forecasted values is ________.

A) MAD =

B) MAD =

C) MAD =

D) MAD = Answer: A Diff: 1 Blooms: Remember Topic: Forecasting Models for Stationary Time Series LO1: State three error metrics used for measuring forecast accuracy and explain the differences among them.

8) Identify the formula used to calculate the root mean square error over a range of forecasted values, if the actual value of the time series at time t and the forecast value for time t are denoted

by At and Ft respectively.

A) RMSE =

B) RMSE =

C) RMSE =

D) RMSE =

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Answer: C Diff: 1 Blooms: Remember Topic: Forecasting Models for Stationary Time Series LO1: State three error metrics used for measuring forecast accuracy and explain the differences among them.

9) The actual value of the time series at time t and the forecast value for time t is denoted by At and Ft respectively. What is the formula used for calculating the mean absolute percentage error over a range of forecasted values?

A) MAPE =

∑

∑

B) MAPE = C) MAPE =

∑

|

|

∑

D) MAPE =

× 100

Answer: D Diff: 1 Blooms: Remember Topic: Forecasting Models for Stationary Time Series LO1: State three error metrics used for measuring forecast accuracy and explain the differences among them.

Use the data given below to answer the following question(s).

The table provided below gives the sales details of the number of android smart phones at an electronic retail store for the past 6 weeks. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. The simple moving average value of k is set at 2.

Week 1 2 3 4 5 6

Units sold 88 44 54 65 72 85

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10) For the given data, the simple moving average mean absolute deviation is ________.

A) 0.21 B) 20.12 C) 14.25 D) 207.13 Answer: C Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Stationary Time Series LO1: State three error metrics used for measuring forecast accuracy and explain the differences among them.

11) For the given data, what is the value of the simple moving average mean square error?

A) 0.21 B) 20.12 C) 14.25 D) 207.13 Answer: D Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Stationary Time Series LO1: State three error metrics used for measuring forecast accuracy and explain the differences among them.

12) Using the data, determine the value of the simple moving average root mean square error.

A) 0.21 B) 14.39 C) 20.12 D) 207.13 Answer: B Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Stationary Time Series LO1: State three error metrics used for measuring forecast accuracy and explain the differences among them.

13) For the given data, calculate the value of the simple moving average mean absolute percentage error.

A) 20.90 B) 23.45

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C) 14.39 D) 25.56 Answer: A Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Stationary Time Series LO1: State three error metrics used for measuring forecast accuracy and explain the differences among them.

14) If the smoothing constant is assumed to be 0.7, and setting F1 and F2 = A1, the exponential smoothing sales forecast for week 7 is approximately ________.

A) 50 phones B) 80 phones C) 60 phones D) 70 phones Answer: B Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Stationary Time Series LO1: State three error metrics used for measuring forecast accuracy and explain the differences among them.

Answer the following question(s) using exponential smoothing after having optimized α at 0.1 increments.

15) Calculate the value of the mean absolute percentage error for the given data.

A) 20.90 B) 16.60 C) 21.72 D) 29.97 Answer: D Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Stationary Time Series LO1: State three error metrics used for measuring forecast accuracy and explain the differences among them.

16) Which of the following is the value of the root mean square error for the given data?

A) 11.56 B) 21.77

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C) 13.87 D) 20.13 Answer: B Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Stationary Time Series LO1: State three error metrics used for measuring forecast accuracy and explain the differences among them.

17) What is the forecasted value for the 3rd week?

A) 53 phones B) 64 phones C) 71 phones D) 49 phones Answer: A Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Stationary Time Series LO1: State three error metrics used for measuring forecast accuracy and explain the differences among them.

18) What is the difference between the forecasted and the actual value for the 3rd week?

A) 1 phones B) 6 phones C) 4 phones D) 3 phones Answer: A Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Stationary Time Series LO1: State three error metrics used for measuring forecast accuracy and explain the differences among them.

19) What is the forecasted value for the 7th week?

A) 53 phones B) 82 phones C) 71 phones D) 49 phones Answer: B Diff: 3 Blooms: Apply

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AACSB: Analytic Skills Topic: Forecasting Models for Stationary Time Series LO1: State three error metrics used for measuring forecast accuracy and explain the differences among them.

20) In the linear trend equation, Ft+k = at + btk, at is known as the ________.

A) level B) trend C) slope D) forecast Answer: A Diff: 1 Blooms: Remember Topic: Forecasting Models for Time Series with a Linear Trend LO1: Apply double exponential smoothing models to time series with a linear trend.

21) In the linear trend equation Ft+k = at + btk, identify the term that signifies the trend.

A) bt B) k C) at D) Ft + k Answer: A Diff: 1 Blooms: Remember Topic: Forecasting Models for Time Series with a Linear Trend LO1: Apply double exponential smoothing models to time series with a linear trend.

22) What is the formula used to calculate the value of at in the linear trend equation Ft+k = at + btk while using double exponential smoothing?

A) at = β(bt - bt-1) + (1 -β)bt-1 B) at = αFt-1 + (1 - α)(at +1 + bt+1) C) at = αFt + (1 - α)(at -1 + bt-1) D) at = β(bt + bt-1) + (1 + γ)bt-1 Answer: C Diff: 1 Blooms: Remember Topic: Forecasting Models for Time Series with a Linear Trend LO1: Apply double exponential smoothing models to time series with a linear trend.

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23) What is the formula used to calculate the value of bt in the linear trend equation Ft+k = at + btk while using double exponential smoothing?

A) bt = β(bt - bt-1) + (1 -β)bt-1 B) bt = αFt-1 + (1 - α)(at +1 + bt+1) C) bt = αFt + (1 - α)(at -1 + bt-1) D) bt = β(at - at-1) + (1 -β)bt-1 Answer: D Diff: 1 Blooms: Remember Topic: Forecasting Models for Time Series with a Linear Trend LO1: Apply double exponential smoothing models to time series with a linear trend.

Use the data given below to answer the following question(s).

The worldwide sales of cars from 1981-1990 are shown in the table below. Given: α = 0.2 and β = 0.15 (Hint: Use XLMiner) Year 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990

Units sold in thousands 888 900 1000 1200 1100 1300 1250 1150 1100 1200

24) Calculate the value of the mean absolute percentage error using double exponential smoothing for the given data.

A) 1.80 B) 8.10 C) 91.27 D) 11976.17 Answer: B Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Time Series with a Linear Trend LO1: Apply double exponential smoothing models to time series with a linear trend.

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25) Identify the value of the mean square error using double exponential smoothing for the given set of data.

A) 8.10 B) 1.80 C) 91.27 D) 11976.17 Answer: D Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Time Series with a Linear Trend LO1: Apply double exponential smoothing models to time series with a linear trend.

26) Using double exponential smoothing, calculate the value of the mean absolute deviation for the given data.

A) 8.10 B) 1.80 C) 91.27 D) 11976.17 Answer: C Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Time Series with a Linear Trend LO1: Apply double exponential smoothing models to time series with a linear trend.

27) Using double exponential smoothing, find the value of the root mean square error for the given data.

A) 8.10 B) 91.27 C) 11976.17 D) 109.44 Answer: D Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Time Series with a Linear Trend LO1: Apply double exponential smoothing models to time series with a linear trend.

28) Which of the following equations is the trend line equation for the given data? (Note: the fitted model assumes that the years are numbered 1 through 10, not the actual dates.)

A) 60.123x + 481.56 B) 48.16x + 481.86

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C) 32.17x + 931.87 D) 57.15x + 503.81 Answer: C Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Time Series with a Linear Trend LO1: Apply regression-based forecasting to time series with a linear trend.

29) For the given data, what is the sales forecast for the year 1992 (in thousands)?

A) 1256.87 B) 1317.91 C) 1285.74 D) 1350.08 Answer: B Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Time Series with a Linear Trend LO1: Apply regression-based forecasting to time series with a linear trend.

Use the data given below to answer the following question(s).

The worldwide sales of cars from 1981-1990 are shown in the table below. Given: α = 0.2, γ = 0.05, and season length = 1. (Hint: Use XLMiner).

Year 1 2 3 4 5 6 7 8 9 10

Units sold in thousands 750 823 1034 1945 1556 1300 1346 1150 967 1200

30) Calculate the value of the mean absolute percentage error using the Holt-Winters no-trend model for the given data.

A) 8.10 B) 18.39 C) 21.70 Copyright © 2020 Pearson Education, Inc.

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D) 10.97 Answer: C Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Time Series with a Linear Trend LO1: Use Holt-Winters and regression models to forecast time series with seasonality.

31) Determine the value of the mean absolute deviation using the Holt-Winters no-trend model for the given data.

A) 367.35 B) 18.39 C) 21.70 D) 252.55 Answer: D Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Time Series with a Linear Trend LO1: Use Holt-Winters and regression models to forecast time series with seasonality.

32) Which of the following is the value of the root mean square error for the given data?

A) 252.55 B) 367.35 C) 21.70 D) 109.76 Answer: B Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Time Series with a Linear Trend LO1: Use Holt-Winters and regression models to forecast time series with seasonality.

33) Which of the following is the forecast value for the 6th year?

A) 1256.06 B) 1328.04 C) 1321.31 D) 1327.24 Answer: B Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Time Series with a Linear Trend

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LO1: Use Holt-Winters and regression models to forecast time series with seasonality.

34) If the given time series has no trend and no seasonality, the most appropriate forecasting model to determine the forecast of the time series is the ________ model.

A) single moving average B) Holt-Winters no-trend smoothing C) double exponential smoothing D) Holt-Winters additive Answer: A Diff: 1 Blooms: Remember Topic: Forecasting Time Series with Seasonality LO1: Identify the appropriate choice of forecasting model based on the characteristics of a time series.

35) If the given time series has a trend and no seasonality, the most appropriate forecasting model to determine the forecast of the time series is the ________ model.

A) single exponential smoothing B) Holt-Winters no trend smoothing C) double exponential smoothing D) Holt-Winters additive Answer: C Diff: 1 Blooms: Remember Topic: Forecasting Time Series with Seasonality LO1: Identify the appropriate choice of forecasting model based on the characteristics of a time series.

36) If the given time series has a trend and seasonality, the most appropriate forecasting model to determine the forecast of the time series is the ________ model.

A) multiple regression B) Holt-Winters no trend smoothing C) double exponential smoothing D) Holt-Winters multiplicative Answer: D Diff: 1 Blooms: Remember Topic: Forecasting Time Series with Seasonality LO1: Identify the appropriate choice of forecasting model based on the characteristics of a time series.

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Use the data given below to answer the following question(s).

The table below provides the sales data for JD Inc. for the year 1998. Given: α = 0.2, β = 0.15, and γ = 0.05 (Hint: Use an additive Holt-Winters model.)

Umbrella Sales of JD Inc. Year Month Units 1 Jan 3980 1 Feb 4000 1 Mar 4740 1 April 4720 1 May 4920 1 Jun 5140 1 July 4640 1 Aug 4520 1 Sep 4480 1 Oct 4690 1 Nov 4210 1 Dec 4418 2 Jan 4380 2 Feb 4400 2 Mar 5140 2 April 5120 2 May 5320 2 Jun 5540 2 July 5040 2 Aug 4920 2 Sep 4880 2 Oct 5090 2 Nov 4610 2 Dec 4818 37) Using an appropriate Holt-Winters trend model, calculate the value of the mean absolute percentage error for the given data.

A) 8.10 B) 330.01 C) 384.83 D) 7.21 Answer: D Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Time Series with a Linear Trend LO1: Apply Holt-Winters forecasting models to time series with both trend and seasonality.

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38) What is the value of the mean absolute deviation for the given data?

A) 8.10 B) 340.73 C) 14.82 D) 7.62 Answer: B Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Time Series with a Linear Trend LO1: Apply Holt-Winters forecasting models to time series with both trend and seasonality.

39) Calculate the value of the mean square error using an appropriate Holt-Winters trend model for the given data.

A) 8.10 B) 346.26 C) 140942.78 D) 7.62 Answer: C Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Time Series with a Linear Trend LO1: Apply Holt-Winters forecasting models to time series with both trend and seasonality.

40) What will be the predicted sales for umbrellas for the month of February of year 2?

A) 4530.19 B) 4648.21 C) 4883.76 D) 4818.07 Answer: B Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Time Series with a Linear Trend LO1: Apply Holt-Winters forecasting models to time series with both trend and seasonality.

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Use the data shown below to answer the following question(s).

The table below is the data set of the Shiller Real Home Price Index for the years 1946-1956.

Year 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956

Real Home Price Index 106.5058955 109.3296707 101.2225795 100.0466076 105.8948393 103.8986687 103.9743275 114.7133093 114.199126 115.4621261 115.3166155

41) Setting k = 3, determine the simple moving average forecast for the year 1950.

Answer: Year 1950 forecast = (100.0466076 + 101.2225795 + 109.3296707)/3 = 103.5329526 ≈ 104.

Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Stationary Time Series LO1: Apply moving average and exponential smoothing models to stationary time series.

42) Setting k = 5, calculate the simple moving average forecast for the year 1951.

Answer: Year 1951 forecast = (106.5058955 + 109.3296707 + 101.2225795 + 100.0466076 + 105.8948393)/5 = 104.5999185 ≈ 105.

Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Stationary Time Series LO1: Apply moving average and exponential smoothing models to stationary time series.

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43) Setting k = 3, determine the value of mean absolute deviation.

Answer: Ft Year Real Home Price Index 1946 106.5058955 1947 109.3296707 1948 101.2225795 1949 100.0466076 105.6860486 1950 105.8948393 103.5329526 1951 103.8986687 102.3880088 1952 103.9743275 103.2800385 1953 114.7133093 104.5892785 1954 114.199126 107.5287685 1955 115.4621261 110.9622543 1956 115.3166155 114.7915205 SUM MAD =

=

At — Ft

|At — Ft|

(At — Ft)2

-5.63944 2.361887 1.51066 0.694289 10.12403 6.670358 4.499872 0.525095

5.639441 2.361887 1.51066 0.694289 10.12403 6.670358 4.499872 0.525095 32.02563

31.80329 5.578509 2.282093 0.482037 102.496 44.49367 20.24885 0.275725 207.6602

= 4.00

The mean absolute deviation is 4.00.

Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Stationary Time Series LO1: State three error metrics used for measuring forecast accuracy and explain the differences among them.

44) Setting k = 3, determine the value of root mean square of errors.

Answer: (At — Ft)2 At — Ft |At — Ft| Year Real Home Price Index Ft 1946 106.5058955 1947 109.3296707 1948 101.2225795 1949 100.0466076 105.6860486 -5.63944 5.639441 31.80329 1950 105.8948393 103.5329526 2.361887 2.361887 5.578509 1951 103.8986687 102.3880088 1.51066 1.51066 2.282093 1952 103.9743275 103.2800385 0.694289 0.694289 0.482037 1953 114.7133093 104.5892785 10.12403 10.12403 102.496 1954 114.199126 107.5287685 6.670358 6.670358 44.49367 1955 115.4621261 110.9622543 4.499872 4.499872 20.24885 1956 115.3166155 114.7915205 0.525095 0.525095 0.275725 SUM 32.02563 207.66 Copyright © 2020 Pearson Education, Inc.

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MSE =

=

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= 25.95752173

RMSE = √𝑀𝑆𝐸= 5.09 The value of root mean square errors is 5.09.

Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Stationary Time Series LO1: State three error metrics used for measuring forecast accuracy and explain the differences among them.

45) Setting k = 3, determine the value of mean absolute percentage of error.

Answer: At — Ft |At — Ft| Year Real Home Price Index Ft 1946 106.5058955 1947 109.3296707 1948 101.2225795 1949 100.0466076 105.6860486 -5.63944 5.639441 1950 105.8948393 103.5329526 2.361887 2.361887 1951 103.8986687 102.3880088 1.51066 1.51066 1952 103.9743275 103.2800385 0.694289 0.694289 1953 114.7133093 104.5892785 10.12403 10.12403 1954 114.199126 107.5287685 6.670358 6.670358 1955 115.4621261 110.9622543 4.499872 4.499872 1956 115.3166155 114.7915205 0.525095 0.525095 SUM 32.02563

MAPE =

× 100 =

0.056368 0.022304 0.01454 0.006678 0.088255 0.05841 0.038973 0.004554 0.290081

× 100 = 3.63

The value of mean absolute percentage of error is 3.63.

Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Forecasting Models for Stationary Time Series LO1: State three error metrics used for measuring forecast accuracy and explain the differences among them.

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46) Indicators are measures that are believed to influence the behavior of a variable an individual wishes to forecast.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Qualitative and Judgmental Forecasting LO1: Explain how judgmental approaches are used for forecasting.

47) The indexes in the forecasting indicators provide a complete forecast.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Qualitative and Judgmental Forecasting LO1: Explain how judgmental approaches are used for forecasting.

48) A cyclical effect is one that repeats at fixed intervals of time, typically a year, month, week, or day.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Statistical Forecasting Models LO1: Apply moving average and exponential smoothing models to stationary time series.

49) The Holt-Winters additive model applies to time series whose amplitude increases or decreases over time.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Forecasting Time Series with Seasonality LO1: Use Holt-Winters and regression models to forecast time series with seasonality.

50) If a time series has seasonality but no trend, the most appropriate model used for forecasting is the Holt-Winters multiplicative model.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Statistical Forecasting Models LO1: Use Holt-Winters and regression models to forecast time series with seasonality.

51) Write a short note on indicators and indexes used in forecasting.

Answer: Indicators are measures that are believed to influence the behavior of a variable an individual wishes to forecast. By monitoring changes in indicators, the individual expects to gain insight about the future behavior of the variable to help forecast the future.

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Indicators are often combined quantitatively into an index, a single measure that weights multiple indicators, thus providing a measure of overall expectation. For example, financial analysts use the Dow Jones Industrial Average as an index of general stock market performance.

Indexes do not provide a complete forecast, but rather a better picture of direction of change, and thus play an important role in judgmental forecasting.

Diff: 1 Blooms: Remember Topic: Qualitative and Judgmental Forecasting LO1: Explain how judgmental approaches are used for forecasting.

52) What is simple exponential smoothing?

Answer: A versatile, yet highly effective approach for short-range forecasting is simple exponential smoothing. The basic simple exponential smoothing model is: Ft+1 = (1 - α)Ft + aAt Ft+1 = Ft + α(At - Ft) where Ft+1 is the forecast for time period t + 1, Ft is the forecast for period t, At is the observed value in period t, and α is a constant between 0 and 1 called the smoothing constant.

Diff: 1 Blooms: Remember Topic: Forecasting Models for Stationary Time Series LO1: Apply moving average and exponential smoothing models to stationary time series.

53) Explain the significance of using double moving average and double exponential smoothing models.

Answer: For time series with a linear trend but no significant seasonal components, double moving average and double exponential smoothing models are more appropriate than using simple moving average or exponential smoothing models. Both methods are based on the linear trend equation: Ft+k = at + btk That is, the forecast for k periods into the future from period t is a function of a base value at, also known as the level, and a trend, or slope, bt. Double moving average and double exponential smoothing differ in how the data are used to arrive at appropriate values for at and bt.

In double exponential smoothing, the estimates of at and bt are obtained from the following equations: at = αFt + (1 - α)(at -1 + bt-1) bt = β(αt - at -1) + (1 - β)bt-1) Diff: 2 Blooms: Remember Topic: Forecasting Models for Time Series with a Linear Trend LO1: Apply double exponential smoothing models to time series with a linear trend.

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54) Explain the different types of Holt-Winters models used in forecasting.

Answer: Holt-Winters models are similar to exponential smoothing models in that smoothing constants are used to smooth out variations in the level and seasonal patterns over time. For time series with seasonality but no trend, XLMiner supports a Holt-Winters method but does not have the ability to optimize the parameters.

Many time series exhibit both trend and seasonality. Such might be the case for growing sales of a seasonal product. These models combine elements of both the trend and seasonal models. Two types of Holt-Winters smoothing models are often used.

The Holt-Winters additive model is based on the equation: Ft+1 = at + bt + St –s+1 and the Holt-Winters multiplicative model is: Ft+1 = (at + bt)St –s+1 The additive model applies to time series with relatively stable seasonality, while the multiplicative model applies to time series whose amplitude increases or decreases over time.

Therefore, a chart of the time series should be viewed first to identify the appropriate type of model to use. Three parameters, α, β , and γ, are used to smooth the level, trend, and seasonal factors in the time series. XLMiner supports both models.

Diff: 2 Blooms: Remember Topic: Forecasting Time Series with Seasonality LO1: Use Holt-Winters and regression models to forecast time series with seasonality. Apply Holt-Winters forecasting models to time series with both trend and seasonality.

55) Explain econometric models used in forecasting with examples.

Answer: Student examples may vary.

Explanatory/causal models, often called econometric models, seek to identify factors that explain statistically the patterns observed in the variable being forecast, usually with regression analysis.

For instance, a manufacturer of hospital equipment might include such variables as hospital capital spending and changes in the proportion of people over the age of 65 in building models to forecast future sales.

Diff: 1 Blooms: Remember Topic: Regression Forecasting with Causal Variables LO1: Explain how regression techniques can be used to forecast with explanatory or causal variables.

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Business Analytics, 3e (Evans) Chapter 10: Introduction to Data Mining 1) Which of the following is included in the data mining approach of Cluster Analysis?

A) analyzing data to predict how to classify a new data element B) identifying groups in which the elements of the groups are in some way similar C) creating rules for target marketing based on association of variables D) developing analytic models to describe the relationship between metrics Answer: B Diff: 1 Blooms: Remember Topic: The Scope of Data Mining LO1: Define data mining and some common approaches used in data mining.

2) Spam filtering for e-mails can be seen as an example of which of the following types of approaches of data mining?

A) reduction B) association C) cause-and-effect modeling D) classification Answer: D Diff: 1 Blooms: Remember Topic: The Scope of Data Mining LO1: Define data mining and some common approaches used in data mining.

3) U-botit.com is an electronic commerce company that sells music online. It keeps a tab of what genre of music their registered customers buy. If u-botit.com were to use the data mining approach of association, which of the following actions would it take?

A) send recommendations to customers based on their buying habits B) conduct surveys to customers to gauge customer satisfaction C) classify the customers based on the genre of music they listen to D) provide discounts to certain genre buyers where sales are less Answer: A Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: The Scope of Data Mining LO1: Describe association rule mining and its use in market basket analysis.

4) The data mining approach called ________ involves the developing of analytic models to describe the relationship between metrics that drive business performance like profitability, customer satisfaction, or employee satisfaction.

A) association Copyright © 2020 Pearson Education, Inc. 184

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B) reduction C) cause-and-effect modeling D) classification Answer: C Diff: 1 Blooms: Remember AACSB: Analytic Skills Topic: The Scope of Data Mining LO1: Define data mining and some common approaches used in data mining.

5) Sendstars is a package delivering company that recently made a study on its customer retention and service renewal metrics. They found that most customers defected from using Sendstars' services due to customer dissatisfaction stemming from delivery personnel being rude or ill-mannered. To curb this issue, Sendstars gave special training to its employees in customer service. Which of the following data mining approaches did Sendstars employ when they decided to train their employees in customer care based on the study?

A) association B) cause-and-effect modeling C) classification D) reduction Answer: B Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: The Scope of Data Mining LO1: Define data mining and some common approaches used in data mining.

6) ________ is a collection of techniques that seek to group or segment a collection of objects or observations into subsets, such that those within each subset are more closely related to one another than objects assigned to different subsets.

A) Association B) Discriminant analysis C) Cluster analysis D) Logistic regression Answer: C Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Cluster Analysis LO1: Explain how cluster analysis is used to explore and reduce data.

7) Which of the following is true of cluster analysis?

A) It is a cause-and-modeling type of analytic model.

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B) It does not provide a definitive answer from analyzing the data.

C) It is primarily a prescriptive analytical method.

D) It uses clustered data that are not affected by the specific method used.

Answer: B Diff: 2 Blooms: Understand Topic: Cluster Analysis LO1: Explain how cluster analysis is used to explore and reduce data.

8) Which of the following is true of hierarchical clustering?

A) All clusters must have the same number of data.

B) No single cluster can have all objects C) The data are not partitioned into a particular cluster in a single step.

D) All clusters must have more than one object in it.

Answer: C Diff: 1 Blooms: Remember Topic: Cluster Analysis LO1: Explain how cluster analysis is used to explore and reduce data.

9) Which of the following is the first stage of joining clusters in agglomerative hierarchical clustering?

A) by separating clusters into finer groups B) by joining two clusters farthest away from each other C) by joining two clusters that are not at a Euclidean distance D) by joining two clusters that are closest to each other Answer: D Diff: 1 Blooms: Remember Topic: Cluster Analysis LO1: Explain how cluster analysis is used to explore and reduce data.

10) Divisive clustering method is different from agglomerative clustering methods in that divisive clustering methods ________.

A) can only have a pair of subjects in each cluster B) separate objects into a particular cluster in one step C) separate n objects successively into finer groupings D) can only have a single subject in each cluster Answer: C Diff: 1 Blooms: Remember Topic: Cluster Analysis LO1: Explain how cluster analysis is used to explore and reduce data.

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11) If the Euclidean distance were to be represented in a right triangle, which of the following would be considered the distance between two objects of a cluster?

A) the hypotenuse B) the small leg C) the long leg D) the average of the sum of both the legs Answer: A Diff: 1 Blooms: Remember Topic: Cluster Analysis LO1: Explain how cluster analysis is used to explore and reduce data.

12) Which of the following formulas calculates the Euclidean distance between X and Y? A) B) C) D) Answer: C Diff: 1 Blooms: Remember Topic: Cluster Analysis LO1: Explain how cluster analysis is used to explore and reduce data.

13) In the ________ method, the distance between groups is defined as the distance between the closest pair of objects, where only pairs consisting of one object from each group are considered.

A) Ward's linkage clustering B) single linkage clustering C) divisive clustering D) average group linkage clustering Answer: B Diff: 1 Blooms: Remember Topic: Cluster Analysis LO1: Explain how cluster analysis is used to explore and reduce data.

14) Which of the following is a definition of distance between two clusters in a complete linkage clustering?

A) the average of distances between all pairs of objects, where each pair is made up of one object from each group B) the distance between the most distant pair of objects, one from each group C) the sum of squares of the distance between clusters D) the distance between the value of the shortest link between the clusters Copyright © 2020 Pearson Education, Inc.

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Answer: B Diff: 2 Blooms: Remember Topic: Cluster Analysis LO1: Explain how cluster analysis is used to explore and reduce data.

15) Which of the following uses the sum of squares between the objects in the cluster when measuring their distances?

A) divisive clustering B) average group linkage clustering C) Ward's hierarchical clustering D) single linkage clustering Answer: C Diff: 1 Blooms: Remember Topic: Cluster Analysis LO1: Explain how cluster analysis is used to explore and reduce data.

16) In classification, which of the following would be considered as a categorical variable of interest for a credit approval decision for a requester?

A) age of the requester B) income of the requester C) revolving balance of the requester D) reject or accept credit approval Answer: D Diff: 2 Blooms: Remember Topic: Classification LO1: Explain the purpose of classification methods and how to measure classification performance, and the use of training and validation data.

17) Which of the following features of classification, used in Excel, for a particular database will necessarily be coded to a certain value?

A) categorical variables B) non-numerical variables C) predictor variables D) numerical variables Answer: B Diff: 1 Blooms: Remember Topic: Classification LO1: Explain the purpose of classification methods and how to measure classification performance, and the use of training and validation data.

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18) The effectiveness of a classification rule can be judged making a probability of misclassification errors and summarizing the results in a ________.

A) classification matrix B) classification hierarchy C) dendogram D) classification algorithm Answer: A Diff: 1 Blooms: Remember Topic: Classification LO1: Explain the purpose of classification methods and how to measure classification performance, and the use of training and validation data.

19) The ________ algorithm is a classification scheme that attempts to find records in a database that are similar to one we wish to classify.

A) linear regression B) logistic regression C) k-Nearest Neighbors D) discriminant analysis Answer: C Diff: 1 Blooms: Understand Topic: Classification LO1: Explain the purpose of classification methods and how to measure classification performance, and the use of training and validation data.

20) In a k-Nearest Neighbors algorithm, similarity of records is based on the ________.

A) closeness of a record to numerical predictors in the other records B) sum of the squares of the distance between the numerical predictors C) set of linear functions of predictors called discriminant functions D) nearness of a record to its own observations Answer: A Diff: 1 Blooms: Understand Topic: Classification LO1: Explain the purpose of classification methods and how to measure classification performance, and the use of training and validation data.

21) Which of the following is true of the value of k in the k-Nearest Neighbors algorithm?

A) The value of k is always taken as a constant and is equal to 1.

B) If the value of k is large, it drastically increases variability.

C) If the value k is very large, it introduces biases into the classification decisions.

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D) If the value k is large, the classification of a record is very sensitive to the classification of the single record to which it is closest.

Answer: C Diff: 2 Blooms: Understand Topic: Classification LO1: Explain the purpose of classification methods and how to measure classification performance, and the use of training and validation data.

22) ________ is a data-mining technique used for classifying a set of observations into predefined classes.

A) Logistic regression B) k-Nearest Neighbors algorithm C) Discriminant analysis D) Linear regression Answer: C Diff: 1 Blooms: Remember Topic: Classification LO1: Explain the purpose of classification methods and how to measure classification performance, and the use of training and validation data.

23) Which of the following is true of logistic regression as a classifying method?

A) Its dependent variable is always categorical.

B) Its independent variable is always continuous or numerical.

C) It predicts the probability of output variables based on dependent variables.

D) It cannot be used when the depIIdent variable is binary.

Answer: A Diff: 1 Blooms: Remember Topic: Classification LO1: Explain the purpose of classification methods and how to measure classification performance, and the use of training and validation data.

24) When using logistic regression, where p being the probability that the dependent variable Y = 1, X1, X2 ..., Xk are the independent variables, and β0, β1, β2 ..., βk are unknown regression coefficients, ________ is called the odds of belonging to category 1(Y = 1).

A) p(β0 + β1X1 + β2X2 + ...+ βkXk) B) C)

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D) Answer: C Diff: 2 Blooms: Remember Topic: Classification LO1: Explain the purpose of classification methods and how to measure classification performance, and the use of training and validation data.

25) Which of the following is true of Association?

A) It develops analytic models to describe the relationship between metrics that drive business performance.

B) It identifies attributes that occur frequently together in a given data set.

C) It seeks to classify a categorical outcome into one of two or more categories.

D) It is a data reduction technique that reduces large information into smaller heterogeneous groups.

Answer: B Diff: 1 Blooms: Remember Topic: Association LO1: Describe association rule mining and its use in market basket analysis.

26) Which of the following types of data-mining methods provides probabilistic if-then statements?

A) association rule B) logistic regression C) reduction D) cause-and effect modeling Answer: A Diff: 1 Blooms: Remember Topic: Association LO1: Describe association rule mining and its use in market basket analysis.

27) Which of the following typically describes the support for the association rule?

A) the number of transactions that include all items that are in the antecedent parts of the rule B) the number of transactions that include all items in the antecedent and consequent parts of the rule C) the number of transactions that include half from the antecedent and half from the consequent D) the number of transactions that include all items that are in the consequent parts of the rule Answer: B Diff: 1

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Blooms: Understand Topic: Association LO1: Describe association rule mining and its use in market basket analysis.

28) ________ is the ratio of the number of transactions that include all items in the consequent as well as the antecedent to the number of transactions that include all items in the antecedent.

A) Lift B) Logit C) Support for the association rule D) Confidence of the association rule Answer: D Diff: 1 Blooms: Remember Topic: Association LO1: Describe association rule mining and its use in market basket analysis.

29) The strength of the association rule, known as lift, is calculated as the ratio of the ________.

A) sum of the antecedents and the consequents to the antecedents B) antecedents to the consequents C) support to the confidence level D) confidence to expected confidence Answer: D Diff: 1 Blooms: Remember Topic: Association LO1: Describe association rule mining and its use in market basket analysis.

30) Which of the following is true of the lift value in association rule?

A) Its strength is directly proportional to the strength of the association rule.

B) It cannot have a value that is more than 1 to be considered a good minimum.

C) It provides information on the increase of the antecedent given the consequent.

D) It does not require the expected confidence to be calculated.

Answer: A Diff: 1 Blooms: Understand Topic: Association LO1: Describe association rule mining and its use in market basket analysis.

31) In the cause-and-effect modeling, internal metrics, such as employee satisfaction, productivity, and turnover are considered to be ________ measures.

A) logit B) life

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C) leading D) lagging Answer: C Diff: 1 Blooms: Remember Topic: Cause-and-Effect Modeling LO1: Use correlation analysis for cause-and-effect modeling 32) Which of the following would be considered a lagging measure in a restaurant using the cause-and-modeling method of data mining?

A) a manager who is having trouble meeting the daily demands B) a waiter's behavior toward a customer C) an accurately billed meal D) a satisfied customer Answer: D Diff: 1 Blooms: Understand Topic: Cause-and-Effect Modeling LO1: Use correlation analysis for cause-and-effect modeling 33) A musical instruments retailer has 10,000 point-of-sale transactions out of which 1500 sales included both items of electric guitars and guitar cases, and out of which 750 had sales of new strings. If the electric guitars are considered A, the guitar cases are considered B, and the strings are considered C, then the associate rule for these sales become "If A and B are purchased, then C is also purchased." Calculate the confidence level, expected confidence level, and lift for this rule, given that total transactions for C is 3000.

Answer: Total sales = 10,000 Sales of A and B = 1,500 Sales of A, B, and C = 750 The association rule "If A and B are purchased, then C is also purchased" has a support of 750 out of 1500 sales. confidence = P (consequent | antecedent) = P(antecedent + consequent) / P(antecedent) Therefore the confidence level = Total support / Total sales = 750 / 1,500 = 50%.

The total number of transactions for C is given as 3000.

Expected confidence is the number of transactions that include the consequent divided by the total number of transactions.

Therefore the expected confidence level = 3,000 / 10,000 = 30%.

The lift is calculated as confidence / expected confidence = 50% / 30% = 1.67.

Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Association LO1: Describe association rule mining and its use in market basket analysis.

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34) In cluster analysis, the objects within clusters should exhibit a high amount of dissimilarity.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Cluster Analysis LO1: Explain how cluster analysis is used to explore and reduce data.

LO2: Identify different business uses for statistics and the major statistical tools businesses use 35) In the average linkage clustering, the distance between two clusters is defined as the average of distances between all pairs of objects, where each pair is made up of one object from each group.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Cluster Analysis LO1: Explain how cluster analysis is used to explore and reduce data.

36) Logistic regression cannot be employed when the dependent variable is binary.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Classification LO1: Explain the purpose of classification methods and how to measure classification performance, and the use of training and validation data.

37) In association analysis, the antecedent and consequent are sets of items that do not have any items in common.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Association LO1: Describe association rule mining and its use in market basket analysis.

38) Expected confidence assumes independence between the consequent and the antecedent.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Association LO1: Describe association rule mining and its use in market basket analysis.

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39) The market share of a business would be considered a lagging measure in the cause-andeffect modeling of data mining.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Cause-and-Effect Modeling LO1: Use correlation analysis for cause-and-effect modeling 40) Lagging and leading measures in cause-and-effect modeling are uncorrelated.

Answer: FALSE Diff: 1 Blooms: Understand Topic: Cause-and-Effect Modeling LO1: Use correlation analysis for cause-and-effect modeling 41) Briefly explain classification as a data-mining tool with an example.

Answer: Classification is the process of analyzing data to predict how to classify a new data element. An example of classification is spam filtering in an e-mail client. By examining textual characteristics of a message, the message is classified as junk or not. Classification methods can help predict whether a credit-card transaction may be fraudulent, whether a loan applicant is high risk, or whether a consumer will respond to an advertisement.

Diff: 1 Blooms: Remember Topic: The Scope of Data Mining LO1: Explain the purpose of classification methods and how to measure classification performance, and the use of training and validation data.

42) How are objects clustered in agglomerative hierarchical clustering?

Answer: An agglomerative hierarchical clustering procedure produces a series of partitions of the data, Pn, Pn-1, ..., P1 . Pn consists of n single-object clusters, and consists of a single group containing all n observations. At each particular stage, the method joins together the two clusters that are closest together. At the first stage, this consists of simply joining together the two objects that are closest together. The most commonly used measure of distance between objects is Euclidean distance. Some clustering methods use the squared Euclidean distance (that is, without the square root) because it speeds up the calculations.

Diff: 2 Blooms: Remember Topic: Cluster Analysis LO1: Explain how cluster analysis is used to explore and reduce data.

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43) Exemplify the k-Nearest Neighbor algorithm of classification.

Answer: Suppose we have a record X that we want to classify. If we use the k-Nearest Neighbor (k-NN) method, the nearest neighbor to that record in the training data set is the one that has the smallest distance from it. The 1-NN rule then classifies record X in the same category as its nearest neighbor. We can extend this idea to a k-NN rule by finding the k-Nearest Neighbors in the training data set to each record we want to classify and then assigning the classification as the classification of majority of the k-Nearest Neighbors. The choice of k is somewhat arbitrary. If k is too small, the classification of a record is very sensitive to the classification of the single record to which it is closest. A larger k reduces this variability, but making k too large introduces bias into the classification decisions. For example, if k is the count of the entire training dataset, all records will be classified the same way.

Diff: 2 Blooms: Remember Topic: Classification LO1: Explain the purpose of classification methods and how to measure classification performance, and the use of training and validation data.

44) How is the strength of an association measured?

Answer: To measure the strength of association, an association rule has two numbers that express the degree of uncertainty about the rule. The first number is called the support for the association rule. The support is simply the number of transactions that include all items in the antecedent and consequent parts of the rule. The second number is the confidence of the association rule. Confidence is the ratio of the number of transactions that include all items in the consequent as well as the antecedent to the number of transactions that include all items in the antecedent. Another measure of the strength of an association rule is lift, which is defined as the ratio of confidence to expected confidence. Expected confidence is the number of transactions that include the consequent divided by the total number of transactions. The higher the lift ratio, the stronger the association rule; a value greater than 1.0 is usually a good minimum.

Diff: 2 Blooms: Remember Topic: Association LO1: Describe association rule mining and its use in market basket analysis.

45) Explain how data-mining using lagging and leading measures of the cause-and-effect model can help managers make business decisions.

Answer: Managers are always interested in results, such as profit, customer satisfaction and retention, production yield, and so on. These results are divided as either lagging measures or leading measures. Customer satisfaction results in regard to sales or service transaction would be lagging measures; employee satisfaction, sales representative behavior, billing accuracy, and so on, would be examples of leading measures that might influence customer satisfaction. If employees are not satisfied, their behavior toward customers could be negatively affected, and customer satisfaction could be low. If this can be explained using business analytics, managers can take steps to improve employee satisfaction, leading to improved customer satisfaction.

Therefore, it is important to understand what controllable factors significantly influence key

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business performance measures that managers cannot directly control. Correlation analysis can help to identify these influences and lead to the development of cause-and-effect models that can help managers make better decisions today that will influence results tomorrow.

Diff: 2 Blooms: Remember Topic: Cause-and-Effect Modeling LO1: Use correlation analysis for cause-and-effect modeling

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Business Analytics, 3e (Evans) Chapter 11: Spreadsheet Modeling and Analysis 1) Troista Mobile Accessories sells mobile apps on their Web site. If a customer spends on average, $12 per visit and visits the Web site 20 times each year, what is the average nondiscounted gross profit during a customer's lifetime? Given that Troista makes a margin of 60 percent on the average bill, with 25 percent of customers not returning each year.

A) $30 B) $75 C) $360 D) $576 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Explain how to use logic, business principles, influence diagrams, and historical data to develop analytic decision models.

2) Which of the following is necessary to calculate the variable cost of production for the company to develop a profit model?

A) unit sale price B) quantity of item produced C) quantity of item sold D) fixed cost of production Answer: B Diff: 1 Blooms: Understand Topic: Model-Building Strategies LO1: Explain how to use logic, business principles, influence diagrams, and historical data to develop analytic decision models.

3) In which of the following ways does demand influence profit?

A) It predicts how many units will be sold.

B) It directly influences the fixed cost of production.

C) It helps in reducing the variable cost of production.

D) It reduces the unit cost of production.

Answer: A Diff: 1 Blooms: Understand Topic: Model-Building Strategies LO1: Explain how to use logic, business principles, influence diagrams, and historical data to develop analytic decision models.

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Using the spreadsheet below to answer the following question(s).

The spreadsheet below shows the net income model for a company that sells shoes.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

A Net Income Model

B

Data Sales $10,000,000 Cost of Goods Sold $ 6,400,000 Administrative Expenses $ 500,000 Selling Expenses $ 900,000 Depreciation Expenses $ 750,000 Interest Expenses $ 70,000 Taxes $ 620,000 Model Gross Profit Operating Expenses Net Operating Income Earnings Before Taxes

$ 3,600,000 $ 2,150,000 $ 1,450,000 $ 1,380,000

Net Income

4) Which of the following formulas would be used to calculate the net income value using only the data value?

A) =SUM(B5:B10)-B11 B) =SUM(B5:B11) C) =B5-SUM(B6:B11) D) =B5-SUM(B6:B10)+B11 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Implementing Models on Spreadsheets LO1: Apply principles of spreadsheet engineering to designing and implementing spreadsheet models.

5) Which of the following would be used to calculate the gross profit?

A) =SUM(B7:B11)-B6 B) =B5-B6 C) =B5-(B6-B11) D) =B5-B6+(B11-B10) Copyright © 2020 Pearson Education, Inc.

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Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Implementing Models on Spreadsheets LO1: Apply principles of spreadsheet engineering to designing and implementing spreadsheet models.

6) Which of the following formulas would be used to calculate the operating expenses?

A) =SUM(B7:B10) B) =SUM(B7:B9) C) =SUM(B7:B9)-B6 D) =SUM(B7:10)-B11 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Implementing Models on Spreadsheets LO1: Apply principles of spreadsheet engineering to designing and implementing spreadsheet models.

7) Which of the following formulas would be used to calculate the net operating income?

A) =B15-B5 B) =B15-B16 C) =SUM(B6:B10)-B11 D) =B15-B16+B6 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Implementing Models on Spreadsheets LO1: Apply principles of spreadsheet engineering to designing and implementing spreadsheet models.

8) Which of the following formulas would be used to calculate earnings before taxes?

A) =B15-B16+B6 B) =B15-B5 C) =B15-B16 D) =B17-B10 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills

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Topic: Implementing Models on Spreadsheets LO1: Apply principles of spreadsheet engineering to designing and implementing spreadsheet models.

9) Which of the following formulas would be used to calculate the net income value using only the information in the Model, and not in the Data section?

A) =B5-B17 B) =B6-B15 C) =B15-B16-B17+B18 D) =B18-B11 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Implementing Models on Spreadsheets LO1: Apply principles of spreadsheet engineering to designing and implementing spreadsheet models.

Use the table below to answer the following question(s).

Below is the profit model spreadsheet for the Lazarus Shoe Company producing their latest model of shoes for the month of January.

Profit Model for Lazarus Shoe Company for January (All cost in $) Unit Price 47 Unit Cost 22 Fixed Cost for Production 350,000 Demand 40,000 Model Unit Price Quantity Sold Revenue

47 38,000

Unit Cost Quantity Produced Variable Cost Fixed Cost

22 38,000 350,000

Profit Copyright © 2020 Pearson Education, Inc.

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10) Calculate the revenue for units sold.

A) $836,000 B) $1,136,000 C) $600,000 D) $1,786,000 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

11) Calculate the variable cost of production.

A) $1,786,000 B) $836,000 C) $600,000 D) $1,436,000 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

12) Calculate the total profit.

A) $600,000 B) $1,436,000 C) $836,000 D) $1,786,000 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

Use the table below to answer the following question(s).

Dresden Pharmaceuticals has decided to go ahead and start clinical trials on a potential new drug.

The total R&D costs are estimated to reach around $875,000,000 with clinical trials mounting to $145,000,000. The current market size is estimated to be around 3,000,000 and is expected to grow at 4 percent every year. The market share Dresden hopes to capture in the first year is 7 percent, and is projected to grow by 25 percent each year for the next 4 years. A monthly

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prescription is anticipated to generate revenue of $420 while incurring variable costs of $150. A discount rate of 8 percent is assumed.

Dresden Pharmaceuticals Data Market Size 3,000,000 Unit (monthly Rx) revenue ($) 420 Unit (monthly Rx) cost ($) 150 Discount Rate ( per cent) 8 Project Costs R&D ($) Clinical Trials ($)

875,000,000 145,000,000

13) Calculate the projected sales for the first year.

A) 273,000 B) 210,000 C) 378,000,000 D) 268,230 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

14) Calculate the market size for the second year.

A) 3,000,000 B) 273,000 C) 3,244,800 D) 3,120,000 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

15) Calculate the market share percentage in the third year.

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C) 11 percent D) 7 percent Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

16) Calculate the annual revenue for the fourth year.

A) $ 2,325,304,800 B) $830,466,000 C) $1,494,838,800 D) $1,149,876,000 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

17) Calculate the annual cost incurred for the second year.

A) $1,224,120,000 B) $884,520,000 C) $491,400,000 D) $638,820,000 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

18) Calculate the projected profit for the third year.

A) $31,315,200 B) $2,373,996,000 C) $1,149,876,000 D) $1,494,838,800 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies

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LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

19) Calculate cumulative net profit at the fourth year.

A) $1,073,538,462 B) $3,189,634,800 C) $1,312,041,240 D) $1,494,838,800 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

20) Calculate the net present value for Dresden's new drug.

A) $1,312,041,240 B) ($339,600,000) C) $3,702,463,939 D) ($932,028,690) Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

21) Which of the following years shows the first profit for Dresden's new drug?

A) first year B) second year C) third year D) fourth year Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

22) Which of the following is the root cause for the newsvendor problem?

A) uncertainty in supply B) uncertainty in demand C) high cost per unit sale

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D) high total production cost Answer: B Diff: 1 Blooms: Understand Topic: Descriptive Spreadsheet Models LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

23) Which of the following conditions is the optimal solution to the newsvendor problem, where Q is the quantity to be purchased, and D is demand?

A) Q > D B) Q = D C) D > Q D) Q / D = 0 Answer: B Diff: 1 Blooms: Understand Topic: Descriptive Spreadsheet Models LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

Use the table below to answer the following question(s).

Sujito Electronix makes headphones for $22 and sells them for $32. Sujito has sold at least 50 headphones on average per week in the past, though the actual demand is unknown. Sujito has also often run short of supply in the past. After three months of release, the headphones are sold at 40 percent discount. The spreadsheet below shows Sujito's sales and demand for the headphones. We take demand at 51, and quantity produced at 55.

Newsvendor model for Sujito's headphones Data Selling Price Cost Discount Price

$32 $22 $19.2

Model Demand Produced Quantity

51 55

Quantity Sold Surplus Quantity

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24) Which of the following is the value for quantity sold?

A) 51 B) 50 C) 4 D) 55 Answer: A Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

25) Calculate the net profit for the headphones.

A) $586.8 B) $498.8 C) $1653.8 D) $466.8 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

Use the table below to answer the following question(s).

Below is a room overbooking model spreadsheet for the Metza, a hotel chain. The hotel has 425 rooms priced at $180 per day each, and is usually fully booked. Reservations can be cancelled any time before 5:00 p.m. with no penalty. The hotel estimates an average overbooking cost of $150. Customer demand is set at 400 with an average cancellation of 20.

1 2 3 4 5 6 7 8 9 10

A B Hotel Overbooking Model for the Metza group of hotels Data Rooms Available Price per room Overbooking Cost

425 $180 $150

Model

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11 12 13 14 15 16

Reservation Limit Customer Demand Reservation Made Cancellations Customer Arrivals Overbooked Customers

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425 400 20

26) Calculate the customer arrivals at the Metza.

A) 425 B) 405 C) 400 D) 380 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

27) Which of the following is the excel formula used to estimate overbooked customers?

A) =MIN(0,B5-B15) B) =MAX(0,B15-B5) C) =MAX(B11,B12) D) =MIN(B11-B12,B11-B14) Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

28) Calculate the net revenue.

A) $72,900 B) $76,500 C) $64,650 D) $68,400 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

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Use the table below to answer the following question(s).

Sheila joined Simsin Tradings at the age of 36 with a starting salary of $75,000. She expects a salary increase of 5 percent every year. Her retirement plan requires her to pay 9 percent of her salary, while the company matches it at 32 percent. She expects an annual return of 7 percent on her retirement portfolio. Using a predictive model for Sheila's first five years, calculate the following, assuming that the salary increases at the same rate every year, and the return of interest does not change.

Retirement Plan Model for Sheila Data Retirement Contribution ( percent of salary) Employer Match Annual Salary Increase Annual Return on Investment

9 percent 32 percent 5 percent 7 percent

29) What will be Sheila's salary in her second year of work at Simsin?

A) $81,750 B) $82,688 C) $78,750 D) $ 75,000 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Explain how model validity can be assessed.

30) What will be the amount of employee contribution to retirement plan when Sheila has reached the age of 38?

A) $7,441.88 B) $7,813.97 C) $24,450 D) $2381.40 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Explain how model validity can be assessed.

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31) Calculate the employer contribution in Sheila's fourth year at Simsin.

A) $546.98 B) $703.26 C) $2,500.47 D) $2,160 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Explain how model validity can be assessed.

32) What's the total retirement balance when Sheila has reached the age of 40 while working with Simsin?

A) $108,374.54 B) $56,253.36 C) $53,627.87 D) $91,163 Answer: B Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Explain how model validity can be assessed.

Use the table below to answer the following question(s).

In the spreadsheet below, there is data on the price, cost, demand, and quantity produced for an item. There are also different "what if" values that can help a manager to calculate costs and revenue with variability in demand.

1 2 3 4 5 6 7 8 9 10

A Profit Model

B

Data Unit Price ($) Unit Cost ($) Fixed Cost ($) Demand Quantity Produced

50 25 550,000 60,000 55,000

C What-If Demand Values 20,000 40,000 55,000 60,000 65,000

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33) Calculate the total revenue when the quantity produced is 55,000 and demand is 60,000.

A) $1,375,000 B) ($1,320,000) C) $1,430,000 D) $2,750,000 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Analyzing Uncertainty and Model Assumptions LO1: Perform what-if analysis on spreadsheet models.

34) Calculate the variable cost when the demand is 60,000 units.

A) $1,430,000 B) $1,375,000 C) $2,750,000 D) $1,320,000 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Analyzing Uncertainty and Model Assumptions LO1: Perform what-if analysis on spreadsheet models.

35) From the “what if” values, calculate the revenue if the demand is 60,000 units.

A) $2,750,000 B) $825,000 C) $75,000 D) $1,375,000 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Analyzing Uncertainty and Model Assumptions LO1: Perform what-if analysis on spreadsheet models.

36) From the "what if" values, calculate the total cost when demand is 40,000.

A) “ 2,000,”00 B) $1,925,000 C) $1,100,000 D) $75,000 Answer: B Diff: 2

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Blooms: Apply AACSB: Analytic Skills Topic: Analyzing Uncertainty and Model Assumptions LO1: Perform what-if analysis on spreadsheet models.

37) From the "what if" values, calculate the total profit when the demand is 20,00“.

A) $8”5,000 B) $1,000,000 C) $1,100,000 D) ($925,000) Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Analyzing Uncertainty and Model Assumptions LO1: Perform what-if analysis on spreadsheet models.

38) From the "what if" values, calculate the net profit when the demand is 65,000.

A) $825,000 B) $1,650,000 C) $800,000 D) $925,000 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Analyzing Uncertainty and Model Assumptions LO1: Perform what-if analysis on spreadsheet models.

39) Calculate the economic value of a loyal customer for a company given that the customer purchases, on an average, worth $43 per visit and comes three times a year. The company's gross profit margin is 35 per cent with a customer defection rate of 0.4.

R F M Answer: The economic value of a loyal customer is, V, and it is calculated as V  , D where, R = revenue per purchase; F = purchase frequency per year; M = gross profit margin; D = defection rate.

From the data provided; R = $43; F = 3; M = 35/100 = 0.35;

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D = 0.4, Therefore V = (43 × 3 × 0.35)/0.4 = $112.88 Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Explain how to use logic, business principles, influence diagrams, and historical data to develop analytic decision models.

40) Gruten Retailers sells Mother’s Day special greeting cards at their store at $6. They make the cards for a dollar apiece. Most of the cards are sold by Mother’s Day, but the actual demand is unknown. They have orders for 120 cards. In the past, they have had sales of at least 100 cards

by Mother’s Day. The remaining cards are sold at a 40 percent discount. Calculate the net profit, if demand, D, is set at 110 units.

Answer: Net profit is calculated as, (R × quantity sold + S × surplus quantity) - (C × Q), where, R = selling price, S, salvage value, C is the cost per unit, and Q, the quantity purchased.

From the data provided: R = $6 S = $6(1-0.4) = $3.6 C=1 Q = 120 Quantity sold will be the minimum value between demand and quantity purchased which is 110 units here and surplus quantity is 10.

Therefore, net profit = 6 × 110 + 3.6 × 10 - 1 × 120 = $576.

Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

41) Brenton joined the Kroos Corporation at a starting salary of $61,500. According to the company's retirement plan, Brenton has to make a retirement contribution of 6 percent of his salary. The company contributes 30 percent of this amount. Brenton is expected to receive a salary increment of 3.5 percent per year for the next three years. Brenton is also expected to receive an annual investment return of 8 percent on the plan. Assuming the same rate of salary increases and investment returns each year, calculate the total balance of the retirement plan in its second year.

Answer: Brenton joined the Kroos Corporation at $61,500. At an annual increment of 3.5 percent, Brenton's salary in the second year would be

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= 61,500 × (1 + 0.035) = $63,652.50. …. (1) Brenton's contribution to the retirement plan = (1) × 6 percent = 63,625.5 × 6/100 = $3,819.15. …. (2) The employer contribution is 30 percent of (2) Therefore, the employer contribution for the second year = 3,819.15 × 30/100 = 3,819.15 × 0.3 = $1,145.75. …. (3) In order to calculate the total balance for the second year, we must also calculate the retirement plan balance of the previous year.

Brenton's starting salary is $61,500.

Therefore, his contribution in the first year = 61,500 × 0.06 = $3,690. …. (4) The employer contribution for the first year = 3,690 × 0.3 = $1,107. …. (5) Therefore, the balance for the first year is calculated as (4) + (5) = 3,690 + 1,107 = $4,797. …. (6) From (6), we can now calculate the balance for the second year using the investment return on the retirement plan.

Therefore, total balance for the second year = (6) × (1 + 0.08) + (2) + (3) = (4,796 × 1.08) + 3,819.15 + 1,145.75 = $10,145.66.

Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

42) Blue Sunset Band is planning to record a new album. A major decision to be made is if the band can record the album on their own, or if they should hire a studio to record it with. The fixed cost for recording at the studio is $100,000, plus the manufacturing cost per CD, which is at $5. If they record the album in-house, the cost per CD is $10. They plan to produce 3000 copies of the album regardless of the place of recording. If the band wished to break even with the cost, how can they achieve this by using the Goal Seek feature in Excel?

A B 1 The Blue Sunset Band Album Recording Decision 2 3 Data 4 5 Recording at Studio 6 Fixed Cost $ 100,000 7 Unit CD Cost $ 5 8 Copyright © 2020 Pearson Education, Inc.

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9 Recording In-house 10 Unit CD Cost 11 12 Production Volume 13 14 Model 15 16 Total studio manufacturing cost 17 Total in-house manufacturing cost 18 19 Cost Difference 20 Recording Decision

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$

10

3000

$ 115,000 $ 30,000 $ 85,000 In-house

Answer: The break-even point is the value of demand volume for which total in-house manufacturing cost equals total manufacturing cost in studio, or, equivalently, for which the cost difference is zero.

Therefore, you seek to find the value of production volume in cell B12 that yields a value of zero in cell B19.

In the Goal Seek dialog, enter B19 that contains the formula for the Set cell, enter 0 in the To value box, and enter B12 in the By changing cell box.

The Goal Seek tool determines that the break-even volume is 20,000 and enters this value in cell B12 in the model.

A B 1 The Blue Sunset Band Album Recording Decision 2 3 Data 4 5 Recording at Studio 6 Fixed Cost 7 Unit CD Cost 8 9 Recording In-house 10 Unit CD Cost 11 12 Production Volume 13 14 Model 15 16 Total studio manufacturing cost 17 Total in-house manufacturing cost 18 19 Cost Difference 20 Recording Decision

$ 100,000 $ 5 $

10 20,000

$ 200,000 $ 200,000 $ 0 In-house

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Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Analyzing Uncertainty and Model Assumptions LO1: Apply the Excel Goal Seek tool for break-even analysis and other types of models.

43) Which of the following formulas is used to calculate the total studio recording cost?

A) =SUM(B6:B12)-B10 B) (B6+B7-B16)B12 C) B6+B7*B12 D) B6+B7*B12-B16 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Implementing Models on Spreadsheets LO1: Apply principles of spreadsheet engineering to designing and implementing spreadsheet models.

44) Which of the following formulas are used to calculate the In-house recording cost?

A) B10*B12 B) B10*B12-B17 C) B6+B10*B12 D) =SUM(B6:B12)-B7 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Implementing Models on Spreadsheets LO1: Apply principles of spreadsheet engineering to designing and implementing spreadsheet models.

45) Which of the following formula is used to make the recording decision in B20?

A) =IF(B19>0,"In-house","Studio") B) =IF(B19<=0,"Studio","In-house") C) =SUM(B19<=0,"Studio") D) =IF(B19>0,"Studio","In-house") Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Implementing Models on Spreadsheets LO1: Apply principles of spreadsheet engineering to designing and implementing spreadsheet models.

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46) The process of developing good, useful, and correct spreadsheet models is known as spreadsheet engineering.

Answer: TRUE Diff: 1 Blooms: Remember AACSB: Analytic Skills Topic: Implementing Models on Spreadsheets LO1: Use Excel features and spreadsheet engineering to ensure the quality of spreadsheet models.

47) In predictive modeling, validity refers to how well a model represents reality.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Model-Building Strategies LO1: Explain how model validity can be assessed.

48) Two-way data tables can evaluate only one output variable.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Analyzing Uncertainty and Model Assumptions LO1: Construct one- and two-way data tables using Excel.

49) Give an account of how the design and format of spreadsheets can be improved.

Answer: A logical design of the spreadsheet should be sketched after inputs, outputs, and key model relationships are well understood. For example, the spreadsheet should resemble a financial statement to make it easier for managers to read. It is good practice to separate the model inputs from the model itself and to reference the input cells in the model formulas; that way, any changes in the inputs will be automatically reflected in the model as shown in the text examples. Another useful approach is to break complex formulas into smaller pieces. This reduces typographical errors, makes it easier to check your results, and also makes the spreadsheet easier to read for the user. Finally, it is also important to set up the spreadsheet in a form that the end user, like a financial manager, can easily interpret and use.

Diff: 1 Blooms: Understand Topic: Implementing Models on Spreadsheets LO1: Use Excel features and spreadsheet engineering to ensure the quality of spreadsheet models.

50) Explain how the Data Validation feature in Excel helps in increasing spreadsheet quality.

Answer: The Data Validation feature allows you to define restrictions on what data can or

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should be entered in a cell. For example, it does not make sense to input a quantity produced that is not a whole number. You can prevent users from entering data that are not valid or allow users to enter invalid data but warn them when they try to type it in the cell. You can also provide messages to define what input you expect for the cell, and instructions to help users correct any errors. Data Validation can be found in the Data Tools group in the Data tab in the Excel ribbon.

Diff: 1 Blooms: Understand Topic: Implementing Models on Spreadsheets LO1: Use Excel features and spreadsheet engineering to ensure the quality of spreadsheet models.

51) Give an account of how data is used in predictive models.

Answer: Data used in models can come from subjective judgment based on past experience, existing databases and other data sources, analysis of historical data, or surveys, experiments, and other methods of data collection. For example, in the profit model, querying accounting records for values of the unit cost and fixed costs. Statistical methods are often used to estimate data required in predictive models. For example, historical data is used to compute the mean demand; quartiles or percentiles are used in the model to evaluate different scenarios. However, even if data are not available, using a good subjective estimate is better than sacrificing the completeness of a model that may be useful.

Diff: 1 Blooms: Remember Topic: Model-Building Strategies LO1: Explain how to use logic, business principles, influence diagrams, and historical data to develop analytic decision models.

52) Discuss how overbooking decisions are made by service businesses.

Answer: An important operations decision for service businesses such as hotels, airlines, and car-rental companies is the number of reservations to accept to effectively fill capacity knowing that some customers may not use their reservations or tell the business. If a hotel, for example, holds rooms for customers who do not show up, they lose revenue opportunities. A common practice in these industries is to overbook reservations. When more customers arrive than can be handled, the business usually incurs some cost to satisfy them. Therefore, the decision becomes how much to overbook to balance the costs of overbooking against the lost revenue for underuse.

Diff: 1 Blooms: Remember Topic: Descriptive Spreadsheet Models LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

53) How can managers judge the validity of a model?

Answer: Models cannot capture every detail of the real problem, and managers must understand the limitations of models and their underlying assumptions. Validity refers to how well a model represents reality. One approach for judging the validity of a model is to identify and examine

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the assumptions made in a model to see how they agree with our perception of the real world; the closer the agreement, the higher the validity. A “perfect” model corresponds to the real world in every respect; unfortunately, no such model has ever existed and never will exist in the future, because it is impossible to include every detail of real life in one model. To add more realism to a model generally requires more complexity and analysts have to know how to balance these.

Diff: 1 Blooms: Remember Topic: Model-Building Strategies LO1: Explain how model validity can be assessed.

54) Explain how a two-way data table is created.

Answer: To create a two-way data table, type a list of values for one input variable in a column and a list of input values for the second input variable in a row, starting one row above and one column to the right of the column list. In the cell in the upper left-hand corner immediately above the column list and to the left of the row list, enter the cell reference of the output variable you wish to evaluate. Select the range of cells that contain this cell reference and both the row and column of values. On the What-If Analysis menu, click Data Table. In the Row input cell of the dialog box, enter the reference for the input cell in the model that corresponds to the input values in the row. In the Column input cell box, enter the reference for the input cell in the model that corresponds to the input values in the column. Then click OK. Diff: 1 Blooms: Remember Topic: Analyzing Uncertainty and Model Assumptions LO1: Construct one- and two-way data tables using Excel.

55) The total cost of reaching consumers (C) depends upon the number of consumers (N), advertising costs (A), and transportation costs (T). The linear cost prediction model is represented as: C = c - nN + aA + tT where c, n, a, and t are constants and c estimates the total cost when the remaining variables are zero. Which of the following interpretations is true about this model?

A) Change in variables N, A, and T will cause n, a, and t to change.

B) As n decreases, c will increase.

C) When variables N, A, and T are zero, C = c - n + a + t.

D) Change in variables N, A, and T will not reflect any changes in c.

Answer: D Diff: 3 Blooms: Apply Topic: Predictive Spreadsheet Models LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

56) Which of the following is the mathematical model for deriving total cost of only manufacturing?

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A) TC = VC + (C × Q) B) TC = F + (C × Q) C) TC = F + C D) TC = F + (V × Q) Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Descriptive Spreadsheet Models LO1: Explain how to use logic, business principles, influence diagrams, and historical data to develop analytic decision models.

57) Which of the following is the mathematical model for deriving total cost of only outsourcing?

A) TC = Q x C B) TC = F + (C x Q) C) TC = (V + C) x Q D) TC = (VC + F) x Q Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Descriptive Spreadsheet Models LO1: Explain how to use logic, business principles, influence diagrams, and historical data to develop analytic decision models.

58) Which of the following is the mathematical model for deriving the break-even volume?

A) Q = (C - VC) + F B) Q = F / (C -V) C) Q = (V + C) / F D) Q = F / (VC - C) Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Descriptive Spreadsheet Models LO1: Explain how to use logic, business principles, influence diagrams, and historical data to develop analytic decision models.

59) When will a company use a predictive decision model?

A) when it wishes to determine the best product pricing to maximize revenue B) when it wishes to know how best to use advertising strategies to influence sales C) when it wishes to know sales patterns to plan inventory levels

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D) when it wishes to ensure that a specified level of customer service is achieved Answer: C Diff: 2 Blooms: Understand AACSB: Analytic Skills Topic: Predictive Spreadsheet Models LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

60) Which decision model incorporates the uncertainty element?

A) predictive B) normative C) prescriptive D) descriptive Answer: A Diff: 1 Blooms: Remember Topic: Predictive Spreadsheet Models LO1: Build spreadsheet models for descriptive, predictive, and prescriptive applications.

61) To meet consumer demand, Nib 'N' Ink must produce 800 gel-ink refills. Should the company produce them in-house or outsource them from the supplier? (Hint: Use the mathematical descriptive model).

Answer: Total Cost of Manufacturing (TC) = Fixed Cost (F) + Variable Cost (VC) VC = Unit Variable Cost (V) × Quantity Produced (Q) TC = F + VQ = 2,400 + 3 x 800 = 4,800 Total Cost of Outsourcing (TC) = Unit Cost (C) x Quantity Outsourced (Q) TC = CQ = 5 × 800 = 4,000 The gel-ink refills must be outsourced with the total cost of manufacturing the refills in-house being greater than outsourcing them.

Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Descriptive Spreadsheet Models LO1: Explain how to use logic, business principles, influence diagrams, and historical data to develop analytic decision models.

62) Find the range of volumes at which it is more economical for Nib 'N' Ink to produce the refills in-house or outsource them. (Hint: Use the break-even decision model).

Answer: Break-even volume can be arrived at by setting TC (manufacturing) = TC (outsourcing) and solving for Q.

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F+V×Q=C×Q Q = F / (C - V) = 2,400 / (5 - 3) = 1,200 Thus, if the anticipated production volume is greater than 1,200, it is more economical to manufacture the refills; if it is less than 1,200, then they should be outsourced.

Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Descriptive Spreadsheet Models LO1: Explain how to use logic, business principles, influence diagrams, and historical data to develop analytic decision models.

63) Profit is computed as the difference between total revenue from sales and total cost of production. Revenue depends on the market share captured by a company and the size of the target market. Various marketing decisions taken by managers are reflected upon the market share. The decisions also have an impact on marketing costs which in turn will affect the total cost of production. Construct an influence diagram that relates these variables.

Answer:

Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Model-Building Strategies LO1: Define and provide an example of an influence diagram.

Copyright © 2020 Pearson Education, Inc.

Business Analytics, 3e (Evans) Chapter 12: Simulation and Risk Analysis 1) Which of the following best defines Monte Carlo simulation?

A) It is a tool for building statistical models that characterize relationships among a dependent variable and one or more independent variables.

B) It is a collection of techniques that seeks to group or segment a collection of objects into subsets.

C) It is the process of selecting values of decision variables that minimizes or maximizes some quantity of interest.

D) It is the process of generating random values for uncertain inputs in a model and computing the output variables of interest.

Answer: D Diff: 1 Blooms: Remember Topic: Monte Carlo Simulation LO1: Explain the concept of Monte Carlo simulation and its importance of analyzing risk in business decisions.

2) Why is the ROUND function used in Excel?

A) to ensure that the values generated are whole numbers B) to ensure that the values generated are multiples of ten C) to ensure that the values generated are always positive D) to ensure that the values are even numbers Answer: A Diff: 1 Blooms: Remember Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

3) Which of the following statements is true of a triangular distribution?

A) We are required to know only the smallest and largest possible values that the variable might assume.

B) These distributions depend on multiple parameters that one can easily identify based on managerial knowledge and judgment.

C) The distribution has a limited range and can be skewed in either direction.

D) The distribution is very positively skewed, with no negative values.

Answer: C Diff: 1 Blooms: Remember Topic: Monte Carlo Simulation in Excel LO1: Generate random variates for common probability distributions using Excel functions..

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Use the information below to answer the following question(s).

Consider the following spreadsheet for an outsourcing decision model.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

A Outsourcing Decision Model

B

Data Manufactured in-house Fixed cost Unit variable cost

$ 60,000 $ 130

Purchased from supplier Unit cost

$ 165

Demand volume

1,000

Model Total manufacturing cost Total purchased cost Difference Decision

We assume that the production (demand) volume is normally distributed with a mean of 1,000 and a standard deviation of 100. For the unit cost, select the triangular distribution. It has a minimum value of $150, most likely value of $165, and a maximum value of $190. The number of trials per simulation is equal to 5,000 at a Sim. Random Seed of 1. Run the simulation and answer the following question(s) using the Analytic Solver Platform.

[Hint: choose the closest value.]

4) What is the value of mean obtained from the simulation results?

A) $18,385 B) $21,608 C) $14,894 D) $23,946 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

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5) What is the value of standard deviation obtained from the simulation results?

A) $9,175 B) $7,884 C) $3,860 D) $12,870 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

6) What is the value of mode obtained from the simulation results?

A) $28,435 B) $22,485 C) $27,198 D) $25,394 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

7) What is the value of mean absolute deviation obtained from the simulation results?

A) $10,893 B) $3,476 C) $7,443 D) $5,885 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

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8) What is the expected loss determined from the simulation results?

A) $(78) B) $(120) C) $(60) D) $(47) Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

9) What is the cost difference lower cutoff in thousands of dollars if the likelihood is 60%?

A) approximately 13.56 B) approximately 22.45 C) approximately 29.67 D) approximately 38.97 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

10) What is the cost difference upper cutoff in thousands of dollars if the likelihood is 75%?

A) approximately 46 B) approximately 28 C) approximately 32 D) approximately 59 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

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Use the information below to answer the following question(s).

Below is a spreadsheet for Trance Electronics.

A B 1 Trance Electronics 2 3 Data 4 5 Market size 20,000,000 6 Unit (monthly Rx) revenue $ 120.00 7 Unit (monthly Rx) cost $ 50.00 8 Discount rate 8% 9 10 Project costs 11 R&D $ 750,000,000 12 Clinical Trials $ 100,000,000 13 Total Project Costs 14 15 Model 16 17 Year 1 18 Market growth factor 19 Market size 20 Market share growth rate 21 Market share 7% 22 Sales 23 24 Annual revenue 25 Annual costs 26 Profit 27 Cumulative net profit 28 29 Net present value

C

D

E

F

2

3

4

5

4%

4%

4%

4%

18%

18%

18%

18%

Suppose that the project manager of Trance Electronics has identified the following uncertain variables in the model and the distributions and parameters that describe them, as follows: Market size: normal with mean of 20,000,000 units and standard deviation of 4,000,000 units.

R&D costs: uniform between $600,000,000 and $800,000,000.

Clinical trial costs: lognormal with mean of $150,000,000 and standard deviation $30,000,000.

Annual market growth factor: triangular with minimum = 2%, maximum = 6%, and most likely = 3%.

Annual market share growth rate: triangular with minimum = 15%, maximum = 25%, and most likely = 20%.

The number of trials per simulation is equal to 10,000 at a Sim. Random Seed of 2. Run the simulation and answer the following questions using the Analytic Solver Platform.

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[Hint: choose the closest value.]

11) What is the standard deviation obtained from the simulation results of the net present value?

A) $204,868,924 B) $162,135,408 C) $182,992,245 D) $138,134,040 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

12) What is the coefficient of variation obtained from the simulation results of the net present value?

A) 1.78392 B) -2.23958 C) -1.36659 D) 2.87645 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

13) What is the expected loss ratio obtained from the simulation results of the net present value?

A) 93.50% B) 72.45% C) 67.32% D) 86.32% Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

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14) What is the expected value margin obtained from the simulation results of the net present value?

A) 0.864 B) -0.726 C) 0.343 D) -0.467 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

15) What is the risk that the net present value over the 5 years will not be positive?

A) approximately 40% B) approximately 57% C) approximately 24% D) approximately 77% Answer: D Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

16) What are the chances that the product will show a cumulative net profit in the fourth year?

A) approximately 25% B) approximately 18% C) approximately 11% D) approximately 32% Answer: C Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

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17) What cumulative profit in the fifth year is likely to be realized with a probability of 0.50?

A) $78,244,098 B) $101,970,955 C) $144,058,696 D) $203,676,827 Answer: B Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

18) What is the correlation of the market size with the NPV with reference to the sensitivity chart?

A) 0.043 B) 0.888 C) -0.341 D) -0.026 Answer: B Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

19) What is the correlation of the R&D cost with the NPV with reference to the sensitivity chart?

A) -0.404 B) 0.028 C) 0.908 D) -0.194 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

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20) Which year shows the highest mean net cumulative profit?

A) Year 1 B) Year 2 C) Year 4 D) Year 5 Answer: D Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

21) Which year shows the highest uncertainty in forecasting the future?

A) Year 1 B) Year 3 C) Year 4 D) Year 5 Answer: D Diff: 2 Blooms: Understand AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

Answer the following question(s) using the Analytic Solver Platform (5000 trials per simulation; use the Latin Hypercube sampling method).

[Hint: choose the closest value.]

Consider the spreadsheet for a Monte Carlo Simulation in Excel.

1 2 3 4 5 6 7 8 9 10 11

A Monte Carlo Simulation in Excel

B

Data Selling price Cost Discount price

$ 18.00 $ 12.00 $ 9.00

Model Demand

44

C

D Historical Candy Sales 50 45 40 46 43 43 46 42 44 43

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E $ 264.00 $ 264.00 $ 264.00 $ 228.00 $ 264.00 $ 255.00 $ 255.00 $ 264.00 $ 246.00 $ 264.00 $ 255.00

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12 13 14 15 16 17 18 19 20 21 22

Purchase Quantity

44

Business Analytics, 3e

47 41 41 45 51 43 45 42 44 48

Quantity Sold Surplus Quantity Profit

Average Profit

22) Which of the following cells is defined as the uncertain function cell?

A) B12 B) B14 C) B15 D) B17 Answer: D Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

23) What is the value of mean profit?

A) $255.90 B) $251.45 C) $245.98 D) $264.00 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

24) What is the value of standard deviation?

A) $12.50 B) $10.99 C) $15.86 D) $20.25 Answer: B Copyright © 2020 Pearson Education, Inc.

$ 264.00 $ 237.00 $ 237.00 $ 264.00 $ 264.00 $ 255.00 $ 264.00 $ 246.00 $ 264.00 $ 264.00

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Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

25) What is the value of mode?

A) $228 B) $245 C) $255 D) $264 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

26) What is the value of mean absolute deviation?

A) $8.91 B) $5.45 C) $12.35 D) $15.64 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Conduct Monte Carlo simulation using historical data and resampling techniques.

27) What is the purchase quantity lower cutoff if the likelihood is 75%?

A) 264 B) 255 C) 246 D) 228 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

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LO2: Analyze and interpret simulation results.

Use the information below to answer the following question(s).

Below is a spreadsheet for a hotel overbooking model.

A Hotel Monte Carlo Simulation in Excel

B

C

D

E

1 Demand Probability 2 290 0.03 3 Data 295 0.05 4 300 0.08 5 Rooms available 350 305 0.12 6 Price $ 120 310 0.15 7 Overbooking cost $ 100 315 0.20 8 320 0.15 9 Model 325 0.10 10 330 0.05 11 Reservation limit 350 335 0.04 12 Customer demand 320 340 0.02 13 Reservations made 345 0.01 14 Cancellations 15 15 Customer arrivals 16 17 Overbooked customers 18 Net revenue Assume that each reservation has a constant probability p = 0.04 of being cancelled. Answer the question(s) using the Analytic Solver Platform.

[Hint: choose the closest value.]

28) With respect to B12, what is the range for values given in the Parameters section in the Discrete dialog?

A) $E$2:$E$13 B) $D$2:$D$8 C) $D$2:$D$13 D) $E$2:$E$8 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

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29) With respect to B12, what is the range of weights given in the Parameters section in the Discrete dialog?

A) $E$2:$E$13 B) $D$2:$D$8 C) $D$2:$D$13 D) $E$2:$E$8 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

30) With respect to B14, what should the number of trials correspond to in the Parameters section of the Binomial dialog?

A) reservation limit B) customer demand C) reservations made D) customer arrivals Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

LO2: Analyze and interpret simulation results.

31) Which of the following cells is defined as an output cell?

A) B13 B) B14 C) B15 D) B17 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Monte Carlo Simulation in Excel LO1: Use data tables to conduct simple Monte Carlo simulations.

32) A normal distribution has a limited range and can be skewed in either direction.

Answer: FALSE Diff: 1

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Blooms: Remember Topic: Monte Carlo Simulation LO1: Generate random variates for common probability distributions using Excel functions.

33) Uniform or triangular distributions are used in the absence of data.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Monte Carlo Simulation LO1: Generate random variates for common probability distributions using Excel functions.

34) As Monte Carlo simulation is essentially statistical sampling, the larger the number of trials used, the more precise is the result.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Monte Carlo Simulation LO1: Generate random variates for common probability distributions using Excel functions.

35) What is Monte Carlo simulation?

Answer: Monte Carlo simulation is the process of generating random values for uncertain inputs in a model, computing the output variables of interest, and repeating this process for many trials in order to understand the distribution of the output results. It can easily be accomplished for the outsourcing model using a data table.

Diff: 1 Blooms: Remember Topic: Monte Carlo Simulation LO1: Generate random variates for common probability distributions using Excel functions.

Copyright © 2020 Pearson Education, Inc.

Business Analytics, 3e (Evans) Chapter 13: Linear Optimization 1) Which of the following best defines decision variables in an optimization model?

A) They are limitations, requirements, or other restrictions that are imposed on any solution.

B) They are the quantities that the model seeks to maximize or minimize.

C) They are quantities for which no feasible solutions exist.

D) They are unknown values that the model seeks to determine.

Answer: D Diff: 1 Blooms: Remember Topic: Developing Linear Optimization Models LO1: Apply the four-step process to show a mathematical model for an optimization problem.

2) Which of the following best defines objective functions?

A) They are limitations, requirements, or other restrictions that are imposed on any solution in an optimization model.

B) They are quantities that an optimization model seeks to maximize or minimize.

C) They are quantities for which no feasible solutions exist in an optimization model.

D) They are unknown values that an optimization model seeks to determine.

Answer: B Diff: 1 Blooms: Remember Topic: Developing Linear Optimization Models LO1: Apply the four-step process to show a mathematical model for an optimization problem.

3) Which of the following best defines constraints in an optimization problem?

A) They are limitations, requirements, or other restrictions that are imposed on any solution.

B) They are quantities that an optimization model seeks to maximize or minimize.

C) They are quantities for which no feasible solutions exist.

D) They are unknown values that the model seeks to determine.

Answer: A Diff: 1 Blooms: Remember Topic: Developing Linear Optimization Models LO1: Apply the four-step process to show a mathematical model for an optimization problem.

Use the following information to answer the following question(s), using the SUMPRODUCT function.

Stone Age Surfboards is a small manufacturer of two types of popular high-tide surfboards, the Rockwell and the Limestone models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 15 skilled workers, each of whom Copyright © 2020 Pearson Education, Inc. 237

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works 5 hours per day. The finishing department has 5 workers, who also work a 5-hour shift.

Each pair of Rockwell surfboards requires 3 labor hours in the fabrication department and 1.5 labor hours in finishing. The Limestone model requires 4.5 labor-hours in fabrication and 2 labor-hours in finishing. The company operates 6 days a week. It makes a per-unit profit of $60 on the Rockwell model and $75 on the Limestone model. Approximately 4.1 Rockwell models and 8.4 Limestone models are produced per day.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

A Stone Age Surfboards

B

C

D

Data Department Fabrication Finishing

Product Rockwell Limestone 3 4.5 1.5 2

Profit/Unit

$60.00

$75.00

Rockwell 4.1

Limestone 8.4

Limitation (hours) 75 25

Model Quantity Produced Fabrication Finishing

Hours Used

Excess Limestone Market Mixture Total Profit Profit Contribution

4) What is the total number of hours used for fabrication?

A) 42.58 B) 50.10 C) 35.64 D) 22.95 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Developing Linear Optimization Models LO1: Implement linear optimization models on spreadsheets.

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5) What is the total number of hours used for the finishing operation?

A) 42.58 B) 50.10 C) 35.64 D) 22.95 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Developing Linear Optimization Models LO1: Implement linear optimization models on spreadsheets.

6) What is the total profit generated?

A) $ 876.00 B) $ 675.50 C) $ 480.50 D) $ 965.00 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Developing Linear Optimization Models LO1: Implement linear optimization models on spreadsheets.

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), using the Standard Solver.

Stone Age Surfboards is a small manufacturer of two types of popular low-tide surfboards, the Graystone and the Lava models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 8 skilled workers, each of whom works 9.25 hours per day. The finishing department has 5 workers, each of whom works a 6-hour shift per day. Each pair of Graystone surfboards requires 2.5 labor hours in the fabrication department and 2 labor hours in finishing. The Lava model requires 4.2 labor-hours in fabrication and 3.6 labor-hours in finishing. The company operates 6 days a week. It makes a per unit profit of $40 on the Graystone model and $60 on the Lava model. The company anticipates selling at least twice as many Lava models as Graystone models.

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

A Stone Age Surfboards

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B

C

D

Data Department Fabrication Finishing

Product Graystone Lava 2.5 4.2 2 3.6

Profit/Unit

$40.00

$60.00

Graystone

Lava

Limitation (hours) 74 30

Model Quantity Produced Fabrication Finishing

Hours Used

Excess Lava Market Mixture Total Profit Profit Contribution

7) What is the total number of hours used for fabrication?

A) 54.5 B) 30.0 C) 35.5 D) 43.8 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Solving Linear Optimization Models LO1: Use the Solver add-in to solve linear optimization models in Excel.

8) What is the total number of hours used for the finishing operation?

A) 18.7 B) 30.0 C) 35.5 D) 24.2 Answer: B Copyright © 2020 Pearson Education, Inc.

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Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Solving Linear Optimization Models LO1: Use the Solver add-in to solve linear optimization models in Excel.

9) What is the total profit generated?

A) $ 675.68 B) $ 920.57 C) $ 521.74 D) $ 788.32 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Solving Linear Optimization Models LO1: Use the Solver add-in to solve linear optimization models in Excel.

10) What is the value of slack obtained from the answer report?

A) 46.78 B) 38.46 C) 59.24 D) 23.85 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Solving Linear Optimization Models LO1: Use the Solver add-in to solve linear optimization models in Excel.

11) What is the Allowable Increase for Lava surfboards produced?

A) 30 B) 24 C) 12 D) 18 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Solver Outcomes and Solution Messages LO1: Use the Solver add-in to solve linear optimization models in Excel.

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12) What is the Allowable Decrease for Graystone surfboards produced?

A) 30.74 B) 80.00 C) 12.33 D) 6.67 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Solver Outcomes and Solution Messages LO1: Use the Solver add-in to solve linear optimization models in Excel.

13) What is the shadow price for the finishing hours used?

A) 32.46 B) 17.39 C) 8.33 D) 6.67 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Visualization of Solver Reports LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

14) What is the Allowable Increase in the finishing hours used?

A) 32.46 B) 8.33 C) 26.84 D) 16.67 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Solver Outcomes and Solution Messages LO1: Use the Solver add-in to solve linear optimization models in Excel.

15) What is the Allowable Decrease in the fabrication hours used?

A) 26.84 B) 16.67 C) 8.33 D) 38.46 Answer: D

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Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Solver Outcomes and Solution Messages LO1: Use the Solver add-in to solve linear optimization models in Excel.

16) What will be the total profit contribution from Lava surfboards?

A) $ 391.30 B) $ 521.74 C) $ 130.43 D) $ 276.65 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Solver Outcomes and Solution Messages LO1: List the four possible outcomes when solving a linear optimization model and recognize them from Solver messages.

17) What will be the total profit contribution from Graystone surfboards?

A) $ 391.30 B) $ 521.74 C) $ 130.43 D) $ 276.65 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Solver Outcomes and Solution Messages LO1: List the four possible outcomes when solving a linear optimization model and recognize them from Solver messages.

18) Which of the following solving methods is selected in the Solver dialog for linear and linear integer optimization problems?

A) GRG Nonlinear B) Simplex LP C) SOCP Barrier Engine D) Evolutionary Answer: B Diff: 1 Blooms: Remember Topic: Solving Linear Optimization Models LO1: Use the Solver add-in to solve linear optimization models in Excel.

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Use the following information to answer the question(s) below.

Cerebro Manufacturing produces four types of structural support fittings-plugs, rails, rivets, and clips-which are machined on two CNC machining centers. The machining centers have a capacity of 250,000 minutes per year. The gross margin per unit and machining requirements are shown in the spreadsheet below.

A 1 2 3 4 5 6 7 8

B

C

D

E

F

Cerebro Manufacturing Model

Product Plugs Gross margin/unit $ 0.40 Minutes/unit 1 Gross margin/minute Maximum production Profit

Rails $ 1.20 2

Rivets $ 0.80 3

19) What is the gross margin per minute of plugs manufactured?

A) $ 0.60 B) $ 0.73 C) $ 0.40 D) $ 0.27 Answer: C Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: How Solver Works LO1: Explain how Solver works.

20) What is the gross margin per minute of rivets manufactured?

A) $ 0.60 B) $ 0.73 C) $ 0.40 D) $ 0.27 Answer: D Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: How Solver Works LO1: Explain how Solver works.

Copyright © 2020 Pearson Education, Inc.

Clips $ 1.10 1.5

Machine Capacity (mins./year) 250,000

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21) What is the maximum possible production of rails based on the machine capacity?

A) 250,000.00 B) 83,333.33 C) 166,666.67 D) 125,000.00 Answer: D Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: How Solver Works LO1: Explain how Solver works.

22) What is the maximum production of clips based on the machine capacity?

A) 250,000.00 B) 83,333.33 C) 166,666.67 D) 125,000.00 Answer: C Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: How Solver Works LO1: Explain how Solver works.

23) What is the total profit generated from the manufacture of only plugs?

A) $ 66,666.67 B) $ 100,000.00 C) $ 183,333.33 D) $ 150,000.00 Answer: B Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: How Solver Works LO1: Explain how Solver works.

24) What is the total profit generated from the manufacture of rivets?

A) $ 66,666.67 B) $ 100,000.00 C) $ 183,333.33 D) $ 150,000.00 Answer: A Diff: 1

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Blooms: Apply AACSB: Analytic Skills Topic: How Solver Works LO1: Explain how Solver works.

25) Which of the following options is used if Solver gives an error message that linearity is not satisfied?

A) Ignore Integer Constraints B) Show Iteration Results C) Use Automatic Scaling D) Use Multistart Answer: C Diff: 1 Blooms: Remember Topic: How Solver Works LO1: Explain how Solver works.

26) When a model has a unique optimal solution, it means that ________.

A) the objective is maximized or minimized by more than one combination of decision variables B) there is no solution that simultaneously satisfies all the constraints C) the Allowable Increase or Allowable Decrease values for changing cells are zero D) there is exactly one solution that will result in the maximum or minimum objective Answer: D Diff: 1 Blooms: Remember Topic: Solver Outcomes and Solution Messages LO1: List the four possible outcomes when solving a linear optimization model and recognize them from Solver messages.

27) If a model has alternative optimal solutions, ________.

A) the objective is maximized or minimized by more than one combination of decision variables B) there is no solution that simultaneously satisfies all the constraints C) the objective can be increased or decreased to infinity or negative infinity D) there is exactly one solution that will result in the maximum or minimum objective Answer: A Diff: 1 Blooms: Remember Topic: Solver Outcomes and Solution Messages LO1: List the four possible outcomes when solving a linear optimization model and recognize them from Solver messages.

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28) Alternate optimal solutions exist when the ________.

A) reduced cost is equal to the shadow price B) ratio of the objective coefficient to the constraint coefficient is one C) Allowable Increase values for changing cells are zero D) final value of the changing cells is greater than that of the constraints Answer: C Diff: 1 Blooms: Remember Topic: Solver Outcomes and Solution Messages LO1: List the four possible outcomes when solving a linear optimization model and recognize them from Solver messages.

29) An unbounded problem is one for which ________.

A) the objective is maximized or minimized by more than one combination of decision variables B) there is no solution that simultaneously satisfies all the constraints C) the objective can be increased or decreased to infinity or negative infinity while the solution remains feasible D) there is exactly one solution that will result in the maximum or minimum objective Answer: C Diff: 2 Blooms: Remember Topic: Solver Outcomes and Solution Messages LO1: List the four possible outcomes when solving a linear optimization model and recognize them from Solver messages.

30) An infeasible problem is one for which ________.

A) the objective is maximized or minimized by more than one combination of decision variables B) there is no solution that simultaneously satisfies all the constraints C) the objective can be increased or decreased to infinity or negative infinity D) there is exactly one solution that will result in the maximum or minimum objective Answer: B Diff: 1 Blooms: Remember AACSB: Analytic Skills Topic: Solver Outcomes and Solution Messages LO1: List the four possible outcomes when solving a linear optimization model and recognize them from Solver messages.

31) A constraint function is a function of the decision variables in the problem.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Developing Linear Optimization Models

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LO1: Apply the four-step process to show a mathematical model for an optimization problem.

32) Any solution that satisfies all constraints of a problem is called a feasible solution.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Solving Linear Optimization Models LO1: Implement linear optimization models on spreadsheets.

33) A binding constraint is one for which the Cell Value is greater than the right-hand side of the value of the constraint.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Solving Linear Optimization Models LO1: Use the Solver add-in to solve linear optimization models in Excel.

34) Infeasible problems can occur when the demand requirement is higher than the available capacity.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Solver Outcomes and Solution Messages LO1: List the four possible outcomes when solving a linear optimization model and recognize them from Solver messages.

35) What are the two basic properties of a linear optimization model?

Answer: A linear optimization model has two basic properties: (1) The objective function and all constraints are linear functions of the decision variables. This means that each function is simply a sum of terms, each of which is some constant multiplied by a decision variable. (2) All variables are continuous, meaning that they may assume any real value. This assumption may not be realistic for a practical business problem, but it simplifies the solution method.

Diff: 1 Blooms: Remember Topic: Optimization Models LO1: State the properties that characterize linear optimization models.

36) What are the Excel functions to avoid in linear optimization?

Answer: Several common functions in Excel can cause difficulties when attempting to solve linear programs using Solver because they are discontinuous and no longer satisfy the conditions of a linear model. Common Excel functions to avoid are ABS, MIN, MAX, INT, ROUND, IF,

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and COUNT. Diff: 1 Blooms: Remember Topic: Developing Linear Optimization Models LO1: Implement linear optimization models on spreadsheets.

37) Explain the simplex method used by Solver.

Answer: Solver uses a mathematical algorithm called the simplex method. It characterizes feasible solutions algebraically by solving systems of linear equations. It moves systematically from one corner point to another to improve the objective function until an optimal solution is found. Because of the linearity of the constraints and objective function, the simplex method is guaranteed to find an optimal solution if one exists and usually does so quickly and efficiently.

Diff: 1 Blooms: Remember Topic: How Solver Works LO1: Explain how Solver works.

38) What are the four possible outcomes that can be obtained by solving a linear optimization model?

Answer: • When a model has a unique optimal solution, it means that there is exactly one solution that will result in the maximum (or minimum) objective.

• If a model has alternative optimal solutions, the objective is maximized (or minimized) by more than one combination of decision variables.

• An unbounded problem is one for which the objective can be increased or decreased without bound.

• An infeasible problem is one for which no feasible solution exists.

Diff: 1 Blooms: Remember Topic: Solver Outcomes and Solution Messages LO1: List the four possible outcomes when solving a linear optimization model and recognize them from Solver messages.

39) Which of the following is an example of a simple bounds constraint?

A) confirming that production does not go beyond a certain unit value B) reducing production due to scarcity of resources C) meeting targets for a specific sales job D) equaling production in September with the resources available at the end of August Answer: A Diff: 1 Blooms: Understand Topic: Developing Linear Optimization Models LO1: Recognize different types of constraints in problem statements.

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40) Problem statements such as production must be sufficient to meet promised customer orders would be categorized as a ________ constraint.

A) limitations B) requirements C) proportional relationships D) balance Answer: B Diff: 1 Blooms: Remember Topic: Developing Linear Optimization Models LO1: Recognize different types of constraints in problem statements.

41) ________ constraints essentially state that input = output and ensure that the flow of material or money is accounted for at locations or between time periods.

A) Requirements B) Proportional relationships C) Balance D) Limitations Answer: C Diff: 1 Blooms: Remember Topic: Developing Linear Optimization Models LO1: Recognize different types of constraints in problem statements.

42) Which of the following would be considered as an example of a proportional relationships constraint?

A) making certain that only a certain amount of units are produced B) guaranteeing that a certain amount of workforce will be available for a certain month C) balancing the input to the output during production D) ensuring that the budget allocated to marketing is thrice that of research and development Answer: D Diff: 1 Blooms: Understand Topic: Developing Linear Optimization Models LO1: Recognize different types of constraints in problem statements.

43) Problem statements such as the amount of material used in production cannot exceed the amount available in inventory would be categorized as a ________ constraint.

A) proportional relationships B) limitations C) requirements D) simple bounds Answer: B

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Diff: 1 Blooms: Understand Topic: Developing Linear Optimization Models LO1: Recognize different types of constraints in problem statements.

Use the table below to answer the following question(s).

Qualis Investments is a private limited business that manages personal financial portfolios. The company manages six mutual funds and has a client that has acquired $750,000 from an inheritance. Characteristics of the funds are given in the table below.

Qualis Mutual Fund Data 1 2 3 4 5 6

Qualis Low-priced Stock Fund Qualis Multinational Fund Qualis Mid-cap Stock Fund Qualis Mortgage Fund Qualis Income Equity Fund Qualis Balanced Fund

Expected Annual Return Risk Measure 7.23% 11.87 8.42% 12.62 6.66% 13.72 2.72% 3.37 8.89% 8.4 3.50% 6.91

The company recommends that no more than $300,000 be invested in any individual fund, and that at least $80,000 be invested in each of the mid-cap stock and mortgage fund. The total amount invested in the low-priced and multinational funds are at least 35% of the total investment. The client would like an average return of at least 6%. Assume that X1- X6 represent the dollar amounts invested in funds 1 through 6, respectively.

44) Which of the following is the objective function minimize total risk?

A) 11.87 X1 + 12.62 X2 + 13.72 .X3 + 3.37 X4 + 8.4 X5 + 6.91 X6 B) 7.23 X1 + 8.42 X2 + 6.66 .X3 + 2.72 X4 + 8.89 X5 + 3.5 X6 C) 11.87 X1 + 12.62 X2 + 13.72 .X3 + 3.37 X4 + 8.4 X5 + 6.91 X6 / 750,000 D) 7.23 X1 + 8.42 X2 + 6.66 .X3 + 2.72 X4 + 8.89 X5 + 3.5 X6 ≥ 6% Answer: C Diff: 2 Blooms: Apply Topic: Applications of Linear Optimization LO1: Formulate and solve linear optimization models for a variety of applications in business.

45) Which of the following is the constraint for the weighted return?

A) X1 + X2 + X3 + X4 + X5 + X6 = 750,000 B) 7.23 X1 + 8.42 X2 + 6.66 .X3 + 2.72 X4 + 8.89 X5 + 3.5 X6 ≥ 6.00 C) 7.23 X1 + 8.42 X2 + 6.66 .X3 + 2.72 X4 + 8.89 X5 + 3.5 X6 / 750,000 ≥ 6.00 D) 7.23 X1 + 8.42 X2 + 6.66 .X3 + 2.72 X4 + 8.89 X5 + 3.5 X6 / 750,000 Copyright © 2020 Pearson Education, Inc.

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Answer: C Diff: 2 Blooms: Apply Topic: Applications of Linear Optimization LO1: Formulate and solve linear optimization models for a variety of applications in business.

46) Which of the following is the constraint for investment in low-priced and multinational funds?

A) X1 + X2 ≥ 0.35(750,000) B)

≥ 0.35(750,000)

C) X1 + X2 + X3 + X4 + X5 + X6 ≥ 0.35(750,000) D)

≥ 0.35

Answer: A Diff: 2 Blooms: Apply Topic: Applications of Linear Optimization LO1: Formulate and solve linear optimization models for a variety of applications in business.

47) Which of the following describes the constraint on the mid-cap fund?

A) X3 ≥ 0.35(750,000) B) X3 ≥ 80,000 C) X3 ≥ 0.35(80,000) D) X3 ≤ 670,000 Answer: B Diff: 2 Blooms: Apply Topic: Applications of Linear Optimization LO1: Formulate and solve linear optimization models for a variety of applications in business.

Use the table below to answer the following question(s).

The Riviera Transport Company (RTC) produces car accessories at two plants: Dallas and Atlanta. They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis. The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands. RTC's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost, not exceed available capacity, and meet customer demand.

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Assume Xij = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on.

Transportation Model Data Plant Dallas Atlanta Demand

Distribution Center Houston 13.00 10.75 175

San Jose 15.25 15.16 325

Jacksonville 10.99 9.65 480

Memphis 18.48 18.50 950

Capacity 1250 750

Answer the following question(s) using a linear optimization model.

48) Which of the following is the objective function for cost minimization?

A) minimize cost = 13 X11 +15.25 X12 +10.99 X13 +18.48 X14 / 10.75 X21 +15.16 X22 +9.65 X23 +18.5 X24 B) minimize cost = 13 X11 +15.25 X12 +10.99 X13 +18.48 X14 + 10.75 X21 +15.16 X22 +9.65 X23 +18.5 X24 C) minimize cost = 13 X11 +15.25 X12 +10.99 X13 +18.48 X14 - 10.75 X21 +15.16 X22 +9.65 X23 +18.5 X24 D) minimize cost = (13 X11 +15.25 X12 +10.99 X13 +18.48 X14 - 10.75 X21 +15.16 X22 +9.65 X23 +18.5 X24 )(1,250 / 750) Answer: B Diff: 2 Blooms: Apply Topic: Applications of Linear Optimization LO1: Formulate and solve linear optimization models for a variety of applications in business.

49) Which of the following is the constraint for total amount shipped from Dallas?

A) X11 + X12 + X13 + X14 ≤ 1,250 B) X21 + X22 + X23 + X24 ≤ 1,250 C) X21 + X22 + X23 + X24 ≤ 750 D) X11 + X12 + X13 + X14 - X21 + X22 + X23 + X24 ≤ 850 Answer: A Diff: 2 Blooms: Apply Topic: Applications of Linear Optimization LO1: Formulate and solve linear optimization models for a variety of applications in business.

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50) Which of the following is the constraint for total amount shipped from Atlanta?

A) X11 + X12 + X13 + X14 - X21 + X22 + X23 + X24 ≤ 850 B) X21 + X22 + X23 + X24 ≤ 750 C) X21 + X22 + X23 + X24 ≤ 1250 D) X11 + X12 + X13 + X14 ≤ 1250 Answer: B Diff: 2 Blooms: Apply Topic: Applications of Linear Optimization LO1: Formulate and solve linear optimization models for a variety of applications in business.

51) Which of the following gives the constraint for the demand met at a distribution center?

A) X11 + X21 = 1,250 B) X13 + X23 ≥ 210 C) X13 + X23 = 770 D) X13 + X23 = 480 Answer: D Diff: 2 Blooms: Apply Topic: Applications of Linear Optimization LO1: Formulate and solve linear optimization models for a variety of applications in business.

52) Which of the following is the constraint of nonnegativity for all values of i and j?

A) 13 X11 +15.25 X12 +10.99 X13 +18.48 X14 / 10.75 X21 +15.16 X22 + 9.65 X23 +18.5 X24 ≤ 0 B) Xij ≥ 0, for all i and j C) Xij ≤ 0, for all i and j D) Answer: B Diff: 1 Blooms: Apply Topic: Applications of Linear Optimization LO1: Formulate and solve linear optimization models for a variety of applications in business.

53) Keychain Publishing is planning to release two books, simultaneously, by the same author.

One is a fictional book, while the other is the author's autobiography. The details of its cost, production, and demand are given in the table below.

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Keychain Publishing Data Cost/book Price/book

Fictional $1.75 $11.49

Base demand 50,000 Increase/$1 Adv. 25 Min. percent requirement 35% Max. percent limitation 70% Total Budget

Autobiography $1.50 $9.86 65,000 35

$150,000

Keychain Publishing has $150,000 available to bind books and advertise them with an objective of maximizing profit contribution. Provide the objective function for maximizing profits, along with its constraints.

Answer: To formulate this model, let F = number of the fictional copies produced B = number of the autobiographical copies produced Af = dollar amount spent on the fictional copies Ab = dollar amount spent on the autobiographical copies The objective is to maximize the profits, which is, revenue minus costs. = (11.49F + 9.86B) - (1.75F + 1.5B + Af + Ab) = 9.74F + 8.36B -Af - Ab The constraints are defined as follows: 1. Budget cannot be exceeded: 1.75F + 1.5B + Af + Ab ≤ $150,000 2. Contractual requirements must be met: .35 ≤ F / (F + B) ≤ 0.7 3. Production must not exceed demand: F ≤ 50,000 + 25Af B ≤ 65,000 + 35Ab

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4. Nonnegativity: All variables F, B, Af, Ab ≥ 0 Diff: 3 Blooms: Apply Topic: A Production/Marketing Allocation Model LO1: Build linear optimization models for a variety of applications.

54) The mathematical form Y ≤ 450 would be considered as representing a simple bounds constraint.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Developing Linear Optimization Models LO1: Recognize different types of constraints in problem statements.

55) Linear optimization cannot be used on problems having multiple time periods.

Answer: FALSE Diff: 1 Blooms: Understand Topic: Applications of Linear Optimization LO1: Formulate and solve linear optimization models for a variety of applications in business.

56) List out the different types of constraints that help model formulation.

Answer: The most challenging aspect of model formulation is identifying constraints.

Understanding the different types of constraints can help in proper identification and modeling.

Constraints generally fall into one of the following categories: • Simple Bounds • Limitations • Requirements • Proportional Relationships • Balance Constraints Diff: 1 Blooms: Remember Topic: Developing Linear Optimization Models LO1: Recognize different types of constraints in problem statements.

Use the table below to answer the following question(s).

Letherin Hides is a company that makes boots specifically targeting college students. Forecasts of sales for the next year are 200 in the summer, 450 in the autumn, and 500 in the winter.

Accessories that are used on the boots are purchased from a supplier for $31.66. The cost of capital is estimated to be 24% per year (or 6% per quarter); thus, the holding cost per item is

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0.06($31.66) = $1.9 per quarter (rounded figure). Letherin Hides hires freelance art designers at part-time to craft designs during the summer, and they earn $6 per hour. In the autumn, labor is more difficult to keep, and the owner must pay $6.5 per hour to retain qualified help. Because of the high demand for part-time help during the winter holiday season, labor rates are higher in the winter, and workers earn $7.75 per hour. Each boot design takes 2 hours to complete. How should production be planned over the three quarters to minimize the combined production and inventory holding costs?

The table below provides information on Letherin Hides boot design cost and production.

Letherin Hides Data Summer Unit Production Cost 12 Unit Inventory Holding Cost 1.9 Demand 200

Autumn Winter 13

15.5

1.9 450

1.9 500

Use a linear optimization model based on the data to answer the following questions.

57) According to the linear optimization model, what is the total amount to be produced in summer?

A) 200 B) 100 C) 550 D) 0 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Applications of Linear Optimization LO1: Formulate and solve linear optimization models for a variety of applications in business.

58) According to the linear optimization model, what is the inventory held at the end of summer?

A) 450 B) 0 C) 200 D) 550 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Copyright © 2020 Pearson Education, Inc.

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Topic: Applications of Linear Optimization LO1: Formulate and solve linear optimization models for a variety of applications in business.

59) According to the linear optimization model, what is the inventory held at the end of autumn?

A) 0 B) 200 C) 950 D) 500 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Applications of Linear Optimization LO1: Formulate and solve linear optimization models for a variety of applications in business.

60) According to the linear optimization model, what is the net production for autumn?

A) 200 B) 500 C) 450 D) 50 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Applications of Linear Optimization LO1: Formulate and solve linear optimization models for a variety of applications in business.

61) According to the linear optimization model, what is the net production for winter?

A) 0 B) 950 C) 200 D) 500 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Applications of Linear Optimization LO1: Formulate and solve linear optimization models for a variety of applications in business.

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62) According to the linear optimization model, what is the total cost incurred by Letherin Hides for the combined seasons?

A) $17,885 B) $15,605 C) $15,700 D) $18,700 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Applications of Linear Optimization LO1: Formulate and solve linear optimization models for a variety of applications in business.

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Business Analytics, 3e (Evans) Chapter 14: Integer and Nonlinear Optimization Models 1) ________ is the parameter that specifies when the Solver algorithm will terminate an optimization process with integer constraints.

A) Mutation Rate B) Population Size C) Integer Tolerance D) Convergence Answer: C Diff: 1 Blooms: Remember Topic: Integer Linear Optimization Models LO1: Incorporate integer variables into Solver models.

2) What should be the value of Integer Tolerance in order to find the guaranteed optimal integer solution?

A) -1 B) 0 C) 0.5 D) 1 Answer: B Diff: 1 Blooms: Remember Topic: Integer Linear Optimization Models LO1: Incorporate integer variables into Solver models.

Stone Age Surfboards is a small manufacturer of two types of popular low-tide surfboards, the Graystone and the Lava models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 8 skilled workers, each of whom works 9.25 hours per day. The finishing department has 5 workers, each of whom works a 6-hour shift per day. Each pair of Graystone surfboards requires 2.5 labor hours in the fabrication department and 2 labor hours in finishing. The Lava model requires 4.2 labor-hours in fabrication and 3.6 labor-hours in finishing. The company operates 6 days a week. It makes a per unit profit of $40 on the Graystone model and $60 on the Lava model. The company anticipates selling at least twice as many Lava models as Graystone models.

Use the spreadsheet below for Stone Age Surfboards to answer the following question(s) using integer constraints on variables in the optimization models using the standard Solver.

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

A Stone Age Surfboards

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B

C

D

Data Department Fabrication Finishing

Product Graystone Lava 2.5 4.2 2 3.6

Profit/Unit

$40.00

$60.00

Graystone

Lava

Limitations (hours) 74 30

Model Quantity Produced Fabrication Finishing

Hours Used

Excess Lava Market Mixture Total Profit Profit Contribution

3) Which of the following constraints does Solver use?

A) $B$14:$C$14 = integer B) $D$15 > = $D$6 C) $D$16 > = $D$7 D) $D$19 < = 0 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Integer Linear Optimization Models LO1: Incorporate integer variables into Solver models.

4) What is the quantity of Graystone surfboards produced?

A) 2 B) 5 C) 7

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D) 10 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Integer Linear Optimization Models LO1: Incorporate integer variables into Solver models.

5) What is the quantity of Lava surfboards produced?

A) 2 B) 5 C) 7 D) 10 Answer: C Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Integer Linear Optimization Models LO1: Incorporate integer variables into Solver models.

6) What is the total number of hours used for fabrication?

A) 39.6 B) 34.4 C) 29.2 D) 24.8 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Integer Linear Optimization Models LO1: Incorporate integer variables into Solver models.

7) What is the total number of hours used for the finishing operation?

A) 39.6 B) 34.4 C) 29.2 D) 24.8 Answer: C Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Integer Linear Optimization Models LO1: Incorporate integer variables into Solver models.

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8) What is the total profit generated?

A) $ 748.28 B) $ 687.46 C) $ 385.65 D) $ 500.00 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Integer Linear Optimization Models LO1: Incorporate integer variables into Solver models.

Use the table below to answer the following question(s) using the standard Solver.

A company makes standard 130-inch-wide rolls of thin sheet metal and slits them into smaller rolls to meet customer orders for widths of 10, 14, and 25 inches. Suppose that the company has proposed the following cutting patterns: A Cutting-Stock Problem

B

C

D

E

Pattern 1 2 3 4 5 6

10-in rolls 0 0 3 10 3 8

14 in. rolls 8 2 0 0 2 2

25-in. rolls 0 3 3 0 2 0

Scrap 10 10 4 10 4 4

1 2 3 Data 4 5 6 7 8 9 10

Demands for the coming week are 950 10-inch rolls, 725 14-inch roles, and 640 25-inch rolls.

Develop a model using the Analytic Solver Platform that will determine how many 130-inch rolls to cut into each of the six patterns in order to meet demand and minimize scrap.

9) What is the total number of 10-inch rolls produced?

A) 940 B) 946 C) 950 D) 960 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills

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Topic: Integer Linear Optimization Models LO1: Incorporate integer variables into Solver models.

10) What is the total number of 14-inch rolls produced?

A) 721 B) 725 C) 728 D) 740 Answer: C Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Integer Linear Optimization Models LO1: Incorporate integer variables into Solver models.

11) What is the total number of 25-inch rolls produced?

A) 630 B) 635 C) 640 D) 645 Answer: C Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Integer Linear Optimization Models LO1: Incorporate integer variables into Solver models.

12) What is the total scrap produced?

A) 1,389 B) 1,390 C) 1,427 D) 1,445 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Integer Linear Optimization Models LO1: Incorporate integer variables into Solver models.

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Use the table below to answer the following question(s) using the standard Solver.

Coppell Services contracts with outsourcing partners to handle various customer service functions. Based on a study of call volumes provided by one of the firm's partners, the minimum number of staff needed for each hour of the day is as follows: Hour 8-9 9-10 10-11 11-noon noon-1 1-2 2-3 3-4 4-5

Minimum Staff Required 6 10 12 10 8 16 15 20 15

Mr. Coppell hires 6 permanent employees and wants to staff the remaining requirements using part-time employees who work 4-hour shifts (four consecutive hours starting as early as 8 A.M. or as late as 1 P.M.).

13) How many part-time employees are present in the 8-9 time slot?

A) 4 B) 6 C) 9 D) 14 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Integer Linear Optimization Models LO1: Develop integer optimization models for practical applications such as workforce scheduling and location.

14) How many excess employees are present in the noon-1 time slot?

A) 2 B) 4 C) 5 D) 6 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Integer Linear Optimization Models

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LO1: Develop integer optimization models for practical applications such as workforce scheduling and location.

15) How many part-time employees are present in the 3-4 time slot?

A) 16 B) 14 C) 9 D) 7 Answer: B Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Integer Linear Optimization Models LO1: Develop integer optimization models for practical applications such as workforce scheduling and location.

16) How many excess employees are present in the 4-5 time slot?

A) 0 B) 2 C) 4 D) 6 Answer: A Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Integer Linear Optimization Models LO1: Develop integer optimization models for practical applications such as workforce scheduling and location.

17) What is the minimum number of total part-time employees needed across all the 4-hour shifts to ensure meeting the staffing requirements?

A) 16 B) 28 C) 24 D) 20 Answer: D Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Integer Linear Optimization Models LO1: Develop integer optimization models for practical applications such as workforce scheduling and location.

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18) Which of the following best defines a binary variable?

A) It is a general integer variable that is restricted to being between -1 and 1.

B) It is a general integer variable that is restricted to being a multiple of 2.

C) It is a general integer variable that is restricted to being between 0 and 1.

D) It is a general integer variable that is restricted to being greater than 2.

Answer: C Diff: 1 Blooms: Remember Topic: Integer Linear Optimization Models LO1: Formulate and solve optimization models with binary variables and logical constraints.

Use the table below to answer the following question(s) by invoking the binary constraints on the variables using the standard Solver.

Below is the spreadsheet for a project selection model:

1 2 3

A B Project Selection Model

6

D

E

F

G

Project 2

Project 3

Project 4

Project 5

Available Resources

Data

4 5

C

Project 1

Expected Return (NPV) $160,000 $200,000 $125,000 Cash requirements $45,000 $70,000 $28,000 Personnel requirements 7 4 2

7 8 9 Model 10 Project selection 11 decisions 12 Cash Used 13 Personnel Used 14 Return

$150,000 $225,000 $52,000

$65,000

$175,000

6

4

10

19) Which of the following cells is set as the objective cell in Solver?

A) $G$12 B) $F$14 C) $G$14 D) $B$12 Answer: C Diff: 2 Copyright © 2020 Pearson Education, Inc.

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Blooms: Apply AACSB: Analytic Skills Topic: Models with Binary Variables LO1: Formulate and solve optimization models with binary variables and logical constraints.

20) What is the amount of cash used for Project 2?

A) $ 105,000 B) $ 25,000 C) $ 115,000 D) $ 70,000 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Models with Binary Variables LO1: Formulate and solve optimization models with binary variables and logical constraints.

21) What is the amount of cash used for Project 5?

A) $ 65,000 B) $ 117,000 C) $ 13,000 D) $ 110,000 Answer: A Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Models with Binary Variables LO1: Formulate and solve optimization models with binary variables and logical constraints.

22) What is the total amount of cash used for all five projects?

A) $ 175,000 B) $ 163,000 C) $ 215,000 D) $ 260,000 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Models with Binary Variables LO1: Formulate and solve optimization models with binary variables and logical constraints.

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23) What is the amount of personnel used for Project 2?

A) 3 B) 4 C) 6 D) 11 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Models with Binary Variables LO1: Formulate and solve optimization models with binary variables and logical constraints.

24) What is the total amount of personnel used for all five projects?

A) 23 B) 17 C) 10 D) 4 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Models with Binary Variables LO1: Formulate and solve optimization models with binary variables and logical constraints.

25) What is the return obtained from Project 3?

A) $ 200,000 B) $ 125,000 C) $ 275,000 D) $ 225,000 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Models with Binary Variables LO1: Formulate and solve optimization models with binary variables and logical constraints.

26) What is the return obtained from Project 5?

A) $ 200,000 B) $ 125,000 C) $ 275,000 D) $ 225,000 Answer: D Diff: 2

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Blooms: Apply AACSB: Analytic Skills Topic: Models with Binary Variables LO1: Formulate and solve optimization models with binary variables and logical constraints.

27) What is the total return obtained from all five projects?

A) $ 860,000 B) $ 550,000 C) $ 700,000 D) $ 395,000 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Models with Binary Variables LO1: Formulate and solve optimization models with binary variables and logical constraints.

28) Decision variables that are forced to be integers are called general integer variables.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Integer Linear Optimization Models LO1: Recognize when to use integer variables in optimization models.

29) If the Integer Tolerance is set to 0.01, the Solver will stop if it finds an integer solution that is within 10% of the optimal solution.

Answer: FALSE Diff: 1 Blooms: Understand Topic: Integer Linear Optimization Models LO1: Incorporate integer variables into Solver models.

30) Mathematically, a binary variable x can be represented as x > 2 and integer.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Integer Linear Optimization Models LO1: Formulate and solve optimization models with binary variables and logical constraints.

31) To invoke the binary constraints on the variables, the option bin is chosen from the dropdown box in the Add Constraint dialog.

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Answer: TRUE Diff: 1 Blooms: Remember Topic: Models with Binary Variables LO1: Formulate and solve optimization models with binary variables and logical constraints.

32) Explain the method of Integer Linear Optimization Models.

Answer: Decision variables that are forced to be integers are called general integer variables. If the linear optimization model is solved without the integer restrictions and the optimal solution happens to have all integer values, then it clearly would have solved the integer model. However, this is generally not the case. The algorithm used to solve integer optimization models begins by solving the LP relaxation and proceeds to enforce the integer restrictions using a systematic research process that involves solving a series of modified linear optimization problems.

Diff: 1 Blooms: Remember Topic: Integer Linear Optimization Models LO1: Recognize when to use integer variables in optimization models.

33) What is the importance of Integer Tolerance in Solver?

Answer: When using Solver, it is important to set a parameter called the Integer Tolerance. This value specifies when the Solver algorithm will terminate. By default, the Integer Tolerance is set to 0.05 within Solver. This means that Solver will stop if it finds an integer solution that is within 5% of the optimal solution. To find the guaranteed optimal integer solution, Integer Tolerance must be set to 0. To do this, click the Options button in the Solver Parameters dialog and change the value of Integer Optimality (%) to 0.

Diff: 1 Blooms: Remember Topic: Integer Linear Optimization Models LO1: Incorporate integer variables into Solver models.

34) What is the importance of binary variables in integer optimization models?

Answer: Many optimization models require binary variables, which are variables that are restricted to being either 0 or 1. Binary variables are used to model logical decisions in optimization models. They can be used to model whether to place (x=1) or not to place (x=0) a facility at a certain location, whether or not to run a production line, or whether or not to invest in a certain stock.

Diff: 1 Blooms: Remember Topic: Models with Binary Variables LO1: Formulate and solve optimization models with binary variables and logical constraints.

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35) Explain the implementation of a project-selection model.

Answer: 1 2 3 4 5 6 7 8 9 10 11 12 13 14

A B Project Selection Model

C

D

E

F

G

Project 4

Project 5

Available

$150,000 $225,000

Resources

$52,000

$65,000

$175,000

6

4

10

Data Project 1 Project 2 Project 3 Expected Return (NPV) $160,000 $200,000 $125,000 Cash requirements $45,000 $70,000 $28,000 Personnel requirements 7 4 2 Model Project selection decisions Cash Used Personnel Used Return

B6*B11

C6*C11

D6*D11

E6*E11

F6*F11

SUM(B12:F12)

B7*B11 B5*B11

C7*C11 C5*C11

D7*D11 D5*D11

E7*E11 E5*E11

F7*F11 F5*F11

SUM(B13:F13) SUM(B14:F14)

The decision variables are defined in cells B11:F11. By multiplying these values by the data for each project in rows 5-7, the total return, cash used, and personnel used for the projects that are selected, can be computed in rows 12-14. The objective function is computed in cell G14 as the sum of the returns for the selected projects. Similarly, the amounts of cash and personnel used are also summed for the projects selected, representing the constraint functions in cells G12 and G13. The binary constraints are invoked in the Solver.

Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Models with Binary Variables LO1: Formulate and solve optimization models with binary variables and logical constraints.

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Use the table below to answer the following question(s).

Bolton Computer's Laptop Pricing Decision Inputs Price Model Sales

-3.85 × price + 1150.9

Outputs Total revenue

sales × price

36) Bolton Computers are planning to release a new line of low-end laptops. Using Excel's Solver, develop a nonlinear model to calculate the optimal price for the laptops, given that sales = -3.85 × price + 1150.9.

A) 342.40 B) 380.90 C) 719.70 D) 149.47 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

37) According to the nonlinear model, which of the following is the expected sales figure based on the computed price?

A) 149.47 B) 719.7 C) 575.45 D) 500 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

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38) According to the nonlinear model, which of the following is the total revenue expected from the sales?

A) 22,340.91 B) 86,011.09 C) 107,571.78 D) 74,733.77 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

Use the table below to create a nonlinear model based on the table to answer the following question(s).

The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues. They have three classes of tickets: Classic, Silver, and Gold. The table below provides information on the average ticket sales, revenue and price elasticity on demand. They have a total seating capacity of 300. The table also provides the price range within which they plan to reduce their ticket rates.

Atlas Movie Theater Ticketing Data Ticket Class

Current Average Elasticity Total Rate Daily Seating Sold Capacity

Classic Silver Gold

$8.45 $13.25 $17.50

150 80 30

-1.5 -2 -1

300

Price Range

$6.50 $11.50 $15.50

$7.50 $12.50 $16.50

39) According to the nonlinear model, what is the new price for Classic tickets?

A) $7.50 B) $12.45 C) $6.50 D) $8.20 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Copyright © 2020 Pearson Education, Inc.

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Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

40) According to the nonlinear model, what is the new price for Silver tickets?

A) $7.40 B) $12.17 C) $11.50 D) $12.50 Answer: B Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

41) According to the nonlinear model, what is the new price for Gold tickets?

A) $16.50 B) $15.50 C) $16 D) $16.11 Answer: A Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

42) According to the nonlinear model, which of the following is the projected sales figure for Classic tickets at the new price?

A) 32 B) 90 C) 175 D) 202 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

43) According to the nonlinear model, which of the following is the projected sales figure for Silver tickets at the new price?

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A) 93 B) 178 C) 202 D) 101 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

44) According to the nonlinear model, which of the following is the projected sales figure for Gold tickets at the new price?

A) 32 B) 90 C) 33 D) 178 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

45) According to the nonlinear model, which of the following is the projected revenue figure for Classic tickets based on its new price?

A) $1,314.72 B) $1,116.03 C) $521.68 D) $1,312.52 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

46) According to the nonlinear model, which of the following is the projected revenue figure for Silver tickets based on its new price?

A) $1,163.02 B) $1,132.08 C) $1,224.63 D) $1,316.92

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Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

47) According to the nonlinear model, which of the following is the projected revenue figure for Gold tickets based on its new price?

A) $432.93 B) $1,316.92 C) $1,116.03 D) $523.29 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

48) According to the nonlinear model, which of the following is the total projected revenue for the new sales figures?

A) $1,637.72 B) $2,970.09 C) $1,316.92 D) $2,865.89 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

49) Which of the following is true of the nonlinear model created for the Atlas movie ticket repricing scenario?

A) The projected revenue for the Gold class is infeasible within the price range provided.

B) The projected value for most tickets sold is for the Silver class.

C) The total projected tickets sold exceed the total seating capacity.

D) The projected revenue is lowest for the Gold tickets.

Answer: D Diff: 3 Blooms: Understand AACSB: Analytic Skills

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Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

50) Which of the following is the rectilinear distance between the points A(13,15) and B(10,12)?

A) 4 B) 25 C) 6 D) 10 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

Use the table below to answer the following question(s).

Shirley Templeton is a real estate agent for Paralol Realty. Shirley is given the responsibility to manage potential customers for 5 of the Realty’s bungalows. These 5 bungalows are situated in close proximity. In order to make traveling easier, Shirley decides to move to a location closer to the 5 bungalows. The table below gives the location (X and Y coordinates) of the 5 bungalows along with the number of trips she would have to make to each bungalow. Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley’s accommodation and the 5 bungalows.

Bungalow Location Data Location Bungalow 1 Bungalow 2 Bungalow 3 Bungalow 4 Bungalow 5

X-coordinate 0 25 20 90 60

Y-coordinate 0 100 75 80 100

Trips/Month 6 30 15 28 10

51) According to the model, what is the X-coordinate for the location of Shirley’s new accommodation?

A) 54.62 B) 36.53 C) 25 D) 23.12 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Copyright © 2020 Pearson Education, Inc.

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Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

52) According to the model, what is the Y-coordinate for the location of Shirley's new accommodation?

A) 91.16 ’) 25.08 C) 98.21 D) 54.62 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

53) According to the model, what is the distance between Shirley's new accommodation and Bungalow 1?

A) 36.53 B) 14.53 C) 98.21 D) 23.12 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

54) According to the model, what is the distance between Shirley's new accommodation and Bungalow 2?

A) 91.16 B) 23.12 C) 98.21 D) 14.53 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

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55) According to the model, what is the distance between Shirley's new accommodation and Bungalow 3?

A) 54.62 B) 25.08 C) 36.53 D) 23.12 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

56) According to the model, what is the distance between Shirley’s new accommodation and Bungalow 4?

A) 14.53 B) 250.78 C) 54.62 D) 98.21 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

57) According to the model, what is the distance between Shirley's new accommodation and Bungalow 5?

A) 54.62 B) 25.08 C) 14.53 D) 91.16 Answer:’ B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

58) According to the model, what is the weighted distance between Shirley’s new accommodation and Bungalow 1?

A) 589.25 B) 435.89

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C) 346.77 D) 3152.08 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Non-Smooth Optimization LO1: Develop and solve nonlinear optimization models for different applications.

59) According to the model, what is the weighted distance between Shirley's new accommodation and Bungalow 2?

A) 435.89 B) 250.78 C) 1529.39 D) 589.25 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Non-Smooth Optimization LO1: Develop and solve nonlinear optimization models for different applications.

60) According to the model, what is the weighted distance between Shirley's new accommodation and Bungalow 3?

A) 3152.08 B) 1529.39 C) 346.77 D) 250.78 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Non-Smooth Optimization LO1: Develop and solve nonlinear optimization models for different applications.

61) According to the model, what is the weighted distance between Shirley's new accommodation and Bungalow 4?

A) 589.25 B) 346.77 C) 1529.39 D) 3152.08 Answer: C Diff: 2

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Blooms: Apply AACSB: Analytic Skills Topic: Non-Smooth Optimization LO1: Develop and solve nonlinear optimization models for different applications.

62) According to the model, what is the weighted distance between Shirley's new accommodation and Bungalow 5?

A) 435.89 B) 1529.39 C) 589.25 D) 250.78 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Non-Smooth Optimization LO1: Develop and solve nonlinear optimization models for different applications.

63) According to the model, what is the total weighted distance that Shirley would travel between the bungalows?

A) 4151.29 B) 1529.39 C) 3152.08 D) 4305.30 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Non-Smooth Optimization LO1: Develop and solve nonlinear optimization models for different applications.

64) According to the model, which of the following bungalows is Shirley's new accommodation closest to?

A) Bungalow 1 B) Bungalow 5 C) Bungalow 2 D) Bungalow 4 Answer: C Diff: 2 Blooms: Understand AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

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65) Given that Q = order quantity, D = annual demand, C = unit cost of the item, C0 = cost per order placed, i = inventory carrying charge per unit, which of the following represents the holding cost per unit?

A) D/Q B) iC C) (D/Q)C0 D) iCQ/2 Answer: B Diff: 2 Blooms: Remember Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

66) Which of the following is the ideal next step if you get the message "Solver has converged to the current solution./All constraints are satisfied," when using Solver for nonlinear optimization models?

A) Accept the values, but run Solver again from the current solution.

B) Do not accept the Solver values and re-run Solver with the starting values.

C) Accept the values and run simulations with different values.

D) Accept the values, and then tweak the values, and re-run Solver on tweaked values.

Answer: A Diff: 2 Blooms: Understand Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

Use the table below to answer the following question(s).

Jonathan Reese is considering three stocks in which to invest with a fixed budget. The table below provides information on Jonathan's expected returns for each stock. The table also provides information, collected from market researchers, on the variance-covariance matrix of the individual stocks. He expects a total return of at least 10%.

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Reese's Stock Investment Plan Data

Stock 1 Stock 2 Stock 3 Target Return

Expected Return 10% 11% 9%

Stock 1 Stock 2 Stock 3

Variance-Covariance Matrix Stock 1 Stock 2 Stock 3 0.021 0.018 -0.003 0.018 0.070 0.006 -0.003 0.006 0.003

10%

Develop a Nonlinear Optimization Models model to find the optimal allocation of the budget to each stock, and variance calculations for squared terms and cross-products based on the variance-covariance matrix.

67) According to the model, what percentage of the budget should be allocated to Stock 1?

A) 10% B) 25% C) 50% D) 40% Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

68) According to the model, what percentage of the budget should be allocated to Stock 2?

A) 90% B) 25% C) 50% D) 75% Answer: B Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

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69) According to the model, what percentage of the budget should be allocated to Stock 3?

A) 40% B) 20% C) 25% D) 75% Answer: C Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

70) According to the model, what is the squared term value for Stock 1 variance?

A) 0.00065 B) 0.00535 C) 0.01132 D) 0.00283 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

71) According to the model, what is the squared term value for Stock 2 variance?

A) 0.00236 B) -0.00031 C) 0.00080 D) 0.00430 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

72) According to the model, what is the squared term value for Stock 3 variance?

A) 0.00018 B) 0.00080 C) 0.00096 D) 0.00194 Answer: A Diff: 2

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73) According to the model, what is the cross-product value for Stock 1 variance?

A) 0.00176 B) 0.00450 C) -0.00047 D) 0.00194 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

74) According to the model, what is the cross-product value for Stock 2 variance?

A) 0.00080 B) -0.00080 C) -0.00075 D) 0.01132 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

75) According to the model, what is the cross-product value for Stock 3 variance?

A) 0.00049 B) 0.00283 C) -0.00047 D) 0.00074 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

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76) According to the model, what is the expected total return on all stocks?

A) 18% B) 10% C) 11% D) 12% Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

77) According to the model, what is the expected variance of the resulting portfolio?

A) 0.014 B) 0.010 C) 0.009 D) 0.012 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

Use the table below to answer the following question(s).

Pickson Luthiers Corporation is studying where to locate a phone charging point on the factory floor. The locations of five production cells are expressed as X- and Y-coordinates on a rectangular grid of the factory layout. The daily demand for the charging point (measured as the number of trips to the charging point) at each production cell is also known. Because of the nature of the equipment layout in the factory and for safety reasons, workers must travel along marked horizontal and vertical aisles to access the charger. Thus, the distance from a cell to the charger is measured as rectilinear distance.

The table below provides the relevant information.

Pickson Luthiers Corporation

Phone Recharging Points

Data Cell Measurements Paint Electricals

X-coordinate 2 1 4

Y-coordinate 5 3 2

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Demand 27 12 25

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Testing Packaging

3.5 3

5 3

Maximum

4

5

5 7

The optimal location should minimize the total weighted distance between the charging point and all production cells, where the weights are the daily number of trips to the phone charging point.

Create a nonsmooth optimization model, based on the data, to answer the following questions.

(Hint: Choose the closest answers.)

78) According to the model, which of the following is the X-coordinate for the phone charger location?

A) 2.00 B) 3.00 C) 3.50 D) 4.00 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Non-Smooth Optimization LO1: Develop and solve nonlinear optimization models for different applications.

79) According to the model, which of the following is the Y-coordinate for the phone charger location?

A) 1.50 B) 1.00 C) 3.00 D) 5.00 Answer: C Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Non-Smooth Optimization LO1: Develop and solve nonlinear optimization models for different applications.

80) According to the model, which of the following is the weighted distance between the phone charger and Measurements cell?

A) 12.00 B) 75.00 C) 7.00 D) 54.00

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Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Non-Smooth Optimization LO1: Develop and solve nonlinear optimization models for different applications.

81) According to the model, which of the following is the weighted distance between the phone charger and Paint cell?

A) 36.00 B) 12.00 C) 24.00 D) 0 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Non-Smooth Optimization LO1: Develop and solve nonlinear optimization models for different applications.

82) According to the model, which of the following is the weighted distance between the phone charger and Electricals cell?

A) 75.00 B) 125.00 C) 100.00 D) 112.50 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Non-Smooth Optimization LO1: Develop and solve nonlinear optimization models for different applications.

83) According to the model, which of the following is the weighted distance between the phone charger and Testing cell?

A) 7.00 B) 17.50 C) 22.50 D) 27.50 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills

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Topic: Non-Smooth Optimization LO1: Develop and solve nonlinear optimization models for different applications.

84) According to the model, which of the following is the weighted distance between the phone charger and Packaging cell?

A) 10.50 B) 0 C) 7.00 D) 14.00 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Non-Smooth Optimization LO1: Develop and solve nonlinear optimization models for different applications.

85) According to the model, what is the total weighted distance between the 5 production cells and the phone charger?

A) 253.50 B) 113.00 C) 172.50 D) 165.50 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Non-Smooth Optimization LO1: Develop and solve nonlinear optimization models for different applications.

86) According to the model, which of the following production cells covers the most distance according to its demand when using the phone charger?

A) Measurements B) Paint C) Electricals D) Testing Answer: C Diff: 2 Blooms: Understand AACSB: Analytic Skills Topic: Non-Smooth Optimization LO1: Develop and solve nonlinear optimization models for different applications.

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87) Jonathan Reese is considering three stocks in which to invest with a fixed budget. The table below provides information on Jonathan's expected returns for each stock. The table also provides information, collected from market researchers, on the variance-covariance matrix of the individual stocks. He expects a total return of at least 10%.

Reese's Stock Investment Plan Data Expected Return 10% 11% 9%

Stock 1 Stock 2 Stock 3 Target Return

Stock 1 Stock 2 Stock 3

Variance-Covariance Matrix Stock 1 Stock 2 Stock 3 0.021 0.018 -0.003 0.018 0.070 0.006 -0.003 0.006 0.003

10%

Using the table above, provide the objective function for minimal variance, and the constraints for creating an optimization model.

Answer: The model here is a Nonlinear Optimization Models model that seeks to minimize the risk of a portfolio of stocks subject to a constraint on the portfolio's expected return.

From the above data, the objective function for minimal variance = 0.0212

+ 0.070

+ 0.003

+ 2(0.018)x1x2 + 2(-0.003)x1x3 + 2(0.006)x2x3

where x1, x2, x3 are stock variables or the fractions of the portfolio to invest in stocks 1, 2, 3 respectively.

The constraints must first ensure that we invest 100% of our budget. Because the variables are defined as fractions, we must have x1 + x2 + x3 = 1 Second, the portfolio must have an expected return of at least 10%. The return on a portfolio is simply the weighted sum of the returns of the stocks in the portfolio. This results in the constraint 10x1 + 11x2 + 9x3 ≥ 10 Finally, we cannot invest negative amounts: x1, x2, x3 ≥ 0 Therefore, the complete model is 0.0212

+ 0.070

+ 0.003

+ 2(0.018)x1x2 + 2(-0.003)x1x3 + 2(0.006)x2x3

x1 + x2 + x3 = 1 10x1 + 11x2 + 9x3 ≥ 10 x1, x2,, x3 ≥ 0

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Diff: 2 Blooms: Understand Topic: Nonlinear Optimization Models LO1: Recognize a Nonlinear Optimization Models model.

88) Pickson Luthiers Corporation is studying where to locate a phone charging point on the factory floor. The locations of five production cells are expressed as X- and Y-coordinates on a rectangular grid of the factory layout. The daily demand for the charging point (measured as the number of trips to the charging point) at each production cell is also known. Because of the nature of the equipment layout in the factory and for safety reasons, workers must travel along marked horizontal and vertical aisles to access the charger. Thus, the distance from a cell to the charger is measured as rectilinear distance.

The table below provides the relevant information.

Pickson Luthiers Corporation

Phone Recharging Points

Data Cell Measurements Paint Electricals Testing Packaging

X-coordinate 2 1 4 3.5 3

Y-coordinate 5 3 2 5 3

Maximum

4

5

Demand 27 12 25 5 7

The optimal location should minimize the total weighted distance between the charging point and all production cells, where the weights are the daily number of trips to the phone charging point.

From the above table, provide the objective function for the best location of the charging point.

What kind of solution technique from Solver can be used to make the optimization model based on the data?

Answer: To formulate an optimization model for the best location, define (X, Y) as the location coordinates of the charging point. The weighted distance between the charging point and each cell is expressed by the objective function minimize 27(|X-2|+|Y-5|) + 12(|X-1|+|Y-3|) + 25(|X4|+|Y-2|) + 5(|X-3.5|+|Y-5|) + 7(|X-3|+|Y-3|) The absolute value functions used in this objective function create a non-smooth model. Thus, Evolutionary Solver is the appropriate solution technique.

Diff: 1 Blooms: Knowledge Topic: Non-smooth optimization LO1: Identify non-smooth optimization models and when to use Evolutionary Solver.

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89) Rectilinear distance is the measure of distance as a straight line between two points.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Non-smooth optimization LO1: Identify non-smooth optimization models and when to use Evolutionary Solver.

90) The economic order quantity is the amount to order that minimizes the total cost of ordering and holding.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Nonlinear Optimization Models LO1: Develop and solve nonlinear optimization models for different applications.

91) All Nonlinear Optimization Models models have nonlinear constraints.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Nonlinear Optimization Models LO1: Recognize a Nonlinear Optimization Models model.

92) Absolute value functions, in optimization models, result in non-smooth functions.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Non-smooth optimization LO1: Identify non-smooth optimization models and when to use Evolutionary Solver.

93) Explain how the Markowitz portfolio model is a Nonlinear Optimization Models model.

Answer: The Markowitz portfolio model is a classic Nonlinear Optimization Models model in finance that seeks to minimize the risk of a portfolio of stocks subject to a constraint on the portfolio's expected return. The decision variables are the percent of each stock to allocate to the portfolio. In the Markowitz model, the objective function is to minimize the risk of the portfolio as measured by its variance. Because stock prices are correlated with one another, the variance of the portfolio must reflect not only variances of the stocks in the portfolio but also the covariance between stocks.

Define xj to be the fraction of the portfolio to invest in stock j. The variance of a portfolio is the weighted sum of the variances and covariances: variance of portfolio =

+

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where = the sample variance in the return of stock i sy = the sample covariance between stocks i and j.

Diff: 1 Blooms: Remember Topic: Nonlinear Optimization Models LO1: Recognize when to use nonlinear optimization models.

94) What is a job-sequencing problem? How can we find an optimal solution for such problems?

Answer: Job-sequencing problems involve finding an optimal sequence, or order, by which to process a set of jobs. For any job sequence, we may compute the completion time for each job by successively adding the processing times of that job and all that were completed before it. We may then compare the completion times with the requested due dates to determine if the job is either completed early or late. Lateness (Li) is the difference between the completion time (Ci) and the due date (Di), which can either be positive or negative. Tardiness (Ti) is the amount of time by which the completion time exceeds the due date; thus, tardiness is zero if a job is completed early). Hence, for job i, Li = Ci - Di Ti = max {0, Li} Researchers have shown that sequencing jobs in order of shortest processing time (SPT) first will minimize the average completion time for all jobs. Sequencing by earliest due date (EDD) first will minimize the maximum number of tardy jobs.

Diff: 3 Blooms: Understand Topic: Non-smooth optimization LO1: Identify non-smooth optimization models and when to use Evolutionary Solver.

95) Explain the travelling salesperson problem with examples.

Answer: The traveling salesperson problem (TSP) can be described as follows. A salesperson needs to visit each of n different cities and return home in the minimum total distance. A route that visits each city exactly once and returns to the start is called a tour. Many practical problems can be formulated as a TSP. For example, drivers for FedEx and UPS must deliver packages to customers and return to their central location. Soft-drink vendors must collect money and replenish bottles for a set of retail locations and then return to the warehouse. Other examples are programming drilling machines to drill holes in circuit boards and picking orders within a warehouse. In all these applications, the goal is to perform the task in minimum total time or distance.

Diff: 1 Blooms: Understand Topic: Non-smooth optimization LO1: Identify non-smooth optimization models and when to use Evolutionary Solver.

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Business Analytics, 3e (Evans) Chapter 15: Optimization Analytics Use the table below to answer the following question(s).

Qualis Investments is a private limited business that manages personal financial portfolios. The company manages six mutual funds and has a client that has acquired $750,000 from an inheritance. Characteristics of the funds are given in the table below.

Qualis Mutual Fund Data 1 2 3 4 5 6

Qualis Low-priced Stock Fund Qualis Multinational Fund Qualis Mid-cap Stock Fund Qualis Mortgage Fund Qualis Income Equity Fund Qualis Balanced Fund

Expected Annual Return Risk Measure 7.23% 11.87 8.42% 12.62 6.66% 13.72 2.72% 3.37 8.89% 8.4 3.50% 6.91

The company recommends that no more than $300,000 be invested in any individual fund, and that at least $80,000 be invested in each of the mid-cap stock and mortgage fund. The total amount invested in the low-priced and multinational funds are at least 35% of the total investment. The client would like an average return of at least 6%. Assume that X1- X6 represent the dollar amounts invested in funds 1 through 6, respectively.

1) If the unit profit on Graystone surfboards is increased by $10, what is the total profit generated?

A) $ 489.13 B) $ 521.74 C) $ 423.91 D) $ 554.35 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Visualization of Solver Reports LO1: Conduct what-if analysis for optimization models.

2) If the unit profit on Graystone surfboards is increased by $10, what is the Allowable Increase for Lava surfboards?

A) 30.00 B) 85.00 C) 16.67 D) 58.75 Answer: A Copyright © 2020 Pearson Education, Inc. 295

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Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Visualization of Solver Reports LO1: Conduct what-if analysis for optimization models.

3) If the unit profit on Graystone surfboards is increased by $10, what is the Allowable Decrease for Lava surfboards?

A) 30.00 B) 85.00 C) 16.67 D) 58.75 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Visualization of Solver Reports LO1: Conduct what-if analysis for optimization models.

4) If the unit profit on Graystone surfboards is increased by $10, what is the shadow price for the finishing hours used?

A) $ 18.48 B) $ 17.39 C) $ 15.42 D) $ 14.15 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Visualization of Solver Reports LO1: Conduct what-if analysis for optimization models.

5) If the unit profit on both Graystone and Lava surfboards is increased by $10, what is the total profit generated?

A) $ 521.74 B) $ 505.43 C) $ 423.91 D) $ 619.57 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Visualization of Solver Reports

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LO1: Conduct what-if analysis for optimization models.

6) If the unit profit on both Graystone and Lava surfboards is increased by $10, what is the Allowable Decrease for Lava surfboards?

A) 95.00 B) 38.46 C) 20.00 D) 11.11 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Visualization of Solver Reports LO1: Conduct what-if analysis for optimization models.

7) If the unit profit on both Graystone and Lava surfboards is increased by $10, what is the shadow price for the finishing hours used?

A) -4.35 B) 8.33 C) 20.65 D) 32.46 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Visualization of Solver Reports LO1: Conduct what-if analysis for optimization models.

8) Due to decreasing profits, if the production of Graystone surfboards is stopped, compute the total profit the firm can earn.

A) $ 521.74 B) $ 489.13 C) $ 423.91 D) $ 500.00 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Visualization of Solver Reports LO1: Conduct what-if analysis for optimization models.

9) The ________ indicates how much the value of the objective function will change as the righthand side of a constraint is increased by 1.

A) objective coefficient

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B) shadow price C) binding constraint D) reduced cost Answer: B Diff: 1 Blooms: Remember Topic: What-If Analysis for Optimization Models LO1: Interpret the Solver Sensitivity Report for both linear and nonlinear optimization models.

10) Whenever a constraint has positive slack, the shadow price is equal to one.

Answer: FALSE Diff: 1 Blooms: Remember Topic: What-If Analysis for Optimization Models LO1: Interpret the Solver Sensitivity Report for both linear and nonlinear optimization models.

11) What is the importance of Shadow Price in the Sensitivity Report?

Answer: The Constraints section of the Sensitivity Report lists the final value of the constraint function (the left-hand side), a number called the shadow price, the original right-hand side value of the constraint, and an Allowable Increase and Allowable Decrease. The Shadow Price tells how much the value of the objective function will change as the right-hand side of a constraint is increased by 1. Whenever a constraint has positive slack, the shadow price is zero. When a constraint involves a limited resource, the shadow price represents the economic value of having an additional unit of that resource.

Diff: 1 Blooms: Remember Topic: What-If Analysis for Optimization Models LO1: Interpret the Solver Sensitivity Report for both linear and nonlinear optimization models.

Use the table below to answer the following question(s).

Remington Textiles has a mill that produces three types of fabrics on a make-to-order basis. The mill operates on a 24/7 basis. The key decision facing the plant manager is about the type of loom needed to process each fabric during the coming 12 weeks to meet demands for the three fabrics and not exceed the capacity of the looms in the mill. Two types of looms are used: Jaquard and Northrop. Jaquard looms can be used to make all fabrics and are the only looms that can weave certain fabrics, such as plaids. Demands, variable costs for each fabric, and production rates on the looms are given in the table below. The mill has 10 Northrop looms and 2 Jaquard looms. Any fabrics that cannot be woven in the mill because of limited capacity will be purchased from an external supplier, finished at the mill, and sold at the selling price. In addition to determining which looms to use to process the fabrics, the manager also needs to determine which fabrics to buy externally.

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Remington Textiles Data Fabric 1 2 3

Demand (yards) 50,000 62,000 35,000

Jaquard Capacity (yards/hour) 5.6 5.2 4.8

Northrop Capacity (yards/hour) 0 4.8 4.5

Mill Cost ($/yard) 0.53 0.6 0.71

Outsourcing Cost ($/yard) 0.81 0.85 0.84

Answer the following questions using a linear optimization model.

12) According to the model, what is the total amount of Fabric 1 to be produced on Jaquard?

A) 50,000 B) 0 C) 27,420.8 D) 22,579.2 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Visualization of Solver Reports LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

13) According to the model, what is the total amount of Fabric 1 to be purchased?

A) 27,420.8 B) 50,000 C) 22,579.2 D) 32,595 Answer: A Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Visualization of Solver Reports LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

14) According to the model, what is the total amount of Fabric 2 to be produced with Northrop?

A) 0 B) 62,000 C) 20,160 D) 32,595 Copyright © 2020 Pearson Education, Inc.

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Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Visualization of Solver Reports LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

15) According to the model, what is the total amount of Fabric 2 to be purchased?

A) 50,000 B) 62,000 C) 0 D) 2,405 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Visualization of Solver Reports LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

16) According to the model, what is the total amount of Fabric 3 to be produced with Northrop?

A) 0 B) 35,000 C) 2,405 D) 32,595 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Visualization of Solver Reports LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

17) According to the model, what is the total amount of Fabric 3 to be purchased?

A) 2,405 B) 0 C) 32,595 D) 35,000 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills

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Topic: Visualization of Solver Reports LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

18) According to the model, what is the total cost incurred by Remington for producing the three fabrics?

A) $96,540.47 B) $149,240.47 C) $96,227.82 D) $88,862.65 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Visualization of Solver Reports LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

19) From the Sensitivity Report, what cost reduction ($/hour) would make it feasible to purchase some amount of Fabric 2 from the external supplier rather than just produce it?

A) $0.6 B) $0.25 C) $0.128 D) $1.1 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Visualization of Solver Reports LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

20) From the Sensitivity Report, which of the following would reduce the total cost by $1.568 for each additional hour of capacity for the Jaquard looms?

A) decreasing the Northrop loom cost per hour by $0.58 B) decreasing the Northrop loom capacity down by 534.4 C) increasing the Jaquard loom capacity up by 4896.5 hours D) increasing the Jaquard loom capacity up by 4032 hours Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Visualization of Solver Reports

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LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

Use the table below to answer the following question(s).

The Riviera Transport Company (RTC) produces car accessories at two plants: Dallas and Atlanta. They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis. The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands. RTC's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost, not exceed available capacity, and meet customer demand.

Assume Xij = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on.

Transportation Model Data Plant Dallas Atlanta Demand

Distribution Center Houston 13.00 10.75 175

San Jose 15.25 15.16 325

Jacksonville 10.99 9.65 480

Memphis 18.48 18.50 950

Capacity 1250 750

Answer the following question(s) using a linear optimization model.

21) According to the transportation model, which of the following is the amount shipped from Dallas to Houston?

A) 0 B) 175 C) 1,180 D) 750 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Visualization of Solver Reports LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

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22) According to the transportation model, which of the following is the amount shipped from Dallas to San Jose?

A) 0 B) 95 C) 230 D) 325 Answer: C Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Applications of Linear Optimization LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

23) According to the transportation model, what is the amount shipped from Atlanta to Jacksonville?

A) 950 B) 480 C) 0 D) 95 Answer: B Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Applications of Linear Optimization LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

24) According to the transportation model, what is the amount shipped from Atlanta to Memphis?

A) 480 B) 0 C) 230 D) 950 Answer: B Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Applications of Linear Optimization LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

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25) According to the transportation model, what is the total shipment from Dallas?

A) 750 B) 1,180 C) 430 D) 950 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Applications of Linear Optimization LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

26) According to the transportation model, what is the total cost incurred by Riviera Transport Company?

A) $29,016.95 B) $26,698.95 C) $20,331.35 D) $41,978.75 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Applications of Linear Optimization LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

27) According to the Sensitivity report on the model, by what price should the unit cost of shipment reduce to make shipment from Dallas to Houston feasible?

A) $8.68 B) $2.16 C) $10.84 D) $3.41 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Applications of Linear Optimization LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

28) From the Sensitivity Report on the model, to which of the following cities can Atlanta not ship to without reducing unit cost of production?

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A) Houston B) San Jose C) Jacksonville D) Memphis Answer: D Diff: 3 Blooms: Apply AACSB: Analytic Skills Topic: Applications of Linear Optimization LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

29) Based on the Sensitivity Report on the model, which of the following is the savings on a reduction of demand of 2 units at Jacksonville?

A) $2.5 B) $1.25 C) $19.48 D) $16.98 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Applications of Linear Optimization LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

30) According to the Sensitivity Report, which of the following is true if the capacity at Atlanta is increased by 230 units?

A) the total cost can be reduced by $.09 per unit B) the total cost at Atlanta increases by $9 C) the total cost per unit will reduce by $.09 to Memphis D) the shadow price at Atlanta will increase to $0.09 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Applications of Linear Optimization LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

31) Degeneracy does not impact the interpretation of sensitivity analysis information.

Answer: FALSE Diff: 1

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Blooms: Remember Topic: What-If Analysis for Optimization Models LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

32) When interpreting sensitivity analysis information for changes in model parameters, all other model parameters are held constant.

Answer: TRUE Diff: 1 Blooms: Remember Topic: What-If Analysis for Optimization Models LO1: Ensure that assumptions underlying the use of sensitivity information hold when interpreting Solver reports.

33) In a sensitivity report, a solution is considered a(n) ________ solution if the right-hand-side value of any constraint has a zero Allowable Increase or Allowable Decrease.

A) algorithmic B) unbounded C) infeasible D) degenerate Answer: D Diff: 1 Blooms: Remember Topic: What-If Analysis for Optimization Models LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

Use the table below to answer the following question(s).

Pickson Luthiers Corporation makes four models of electric guitars, ScarCT, Dela Mort, Warax, and Invazen. Each guitar must flow through five departments, assembly, painting, sound testing, inspection, and packaging. The table below shows the relevant data. Production rates are shown in units/hour. (ScarCT is assembled elsewhere). Pickson wants to determine how many guitars to make to maximize monthly profit.

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Pickson Luthiers Corporation Data Guitar Model ScarCT Dela Mort Warax Invazen

Selling price/Unit 750.00 788.00 800.00 850.00

Production rates (units/hour) ScarCT Assembly Painting 35 Sound Testing 20 Inspection 10 Packaging 9

Variable cost/Unit 660.00 680.00 700.00 800.00

Min Sales 0 0 100 80

Max Sales 2500 2000 1000 500

Dela Mort 35 20 10 12 10

Warax 25 15 20 8 5

Invazen 20 10 18 5 8

Hours Available 220 220 220 220 220

Use a linear optimization model based on the data to answer the following question.

34) According to the linear optimization model, what would be the total time spent on inspecting the Dela Mort models?

A) 158.33 B) 12.5 C) 85 D) 48 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Models with Bounded Variables LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

35) According to the linear optimization model, what would be the total time spent for sound testing the Warax model?

A) 5 B) 4 C) 6 D) 10.5 Answer: A Diff: 1 Blooms: Apply Copyright © 2020 Pearson Education, Inc.

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AACSB: Analytic Skills Topic: Models with Bounded Variables LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

36) According to the linear optimization model, what would be the total time spent for assembling the Invazen models?

A) 8 B) 4 C) 16 D) 10 Answer: B Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Models with Bounded Variables LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

37) According to the linear optimization model, what would be the total time spent for packaging the Invazen models?

A) 8 B) 16 C) 20 D) 10 Answer: D Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Models with Bounded Variables LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

38) According to the linear optimization model, what is the total hours spent for painting all the models?

A) 220 B) 94.94 C) 109.67 D) 199.44 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills

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Topic: Models with Bounded Variables LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

39) According to the linear optimization model, which of the following departments uses all the time that it is allocated to finish its job?

A) assembly B) painting C) inspection D) packaging Answer: D Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Models with Bounded Variables LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

40) According to the linear optimization model, what is the total number of ScarCTs produced?

A) 2500 B) 750 C) 0 D) 100 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Models with Bounded Variables LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

41) According to the linear optimization model, what is the net profit per unit on Dela Mort?

A) $205,200 B) $108 C) $680 D) $90 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Models with Bounded Variables LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

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42) According to the linear optimization model, what is the total profit contribution by the Invazen model?

A) $205,200 B) $20,000 C) $10,000 D) $4,000 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Models with Bounded Variables LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

43) According to the linear optimization model, what is the total profit for the Pickson Luthiers Corporation?

A) $10,000 B) $199,880 C) $205,200 D) $219,200 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Models with Bounded Variables LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

44) According to the Sensitivity Report, by how much should the unit profit on ScarCT be increased in order for its production to be feasible?

A) $30 B) $90 C) $60 D) $120 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Models with Bounded Variables LO1: Understand and interpret the Solver Sensitivity Report for models that have bounded variables.

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45) What is degeneracy in linear optimization? Give an example.

Answer: Linear optimization solutions can exhibit degeneracy. A solution is a degenerate solution if the right-hand-side value of any constraint has a zero Allowable Increase or Allowable Decrease. For example, reduced costs and shadow prices may not be unique, and objective function coefficients may have to be changed beyond their allowable increases or decreases before the optimal solution will change.

Diff: 1 Blooms: Remember Topic: What-If Analysis for Optimization Models LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

46) How does Solver handle simple lower bounds and upper bounds compared to ordinary constraints?

Answer: Solver handles simple lower bounds (e.g., C ≥500) and upper bounds (e.g., D≤1,000) quite differently from ordinary constraints in the Sensitivity report. In Solver, lower and upper bounds are treated in a manner similar to nonnegativity constraints, which also do not appear explicitly as constraints in the model. Solver does this to increase the efficiency of the solution procedure used; for large models this can represent significant savings in computer-processing time.

Diff: 1 Blooms: Remember Topic: Models with Bounded Variables LO1: Understand and interpret the Solver Sensitivity Report for models that have bounded variables.

47) How does Excel's Solver help interpret reduced cost as shadow price for bounded variables?

Answer: Interpreting reduced costs as shadow prices for bounded variables can be confusing.

Excel's Solver has a unique feature to make this easier. In the spreadsheet model, define auxiliary variables–a new set of cells for any decision variables that have upper- or lower-bound constraints by referencing, not copying, the original changing cells. Then in the Solver model, use these auxiliary variable cells–not the changing variable cells as defined–to define the bound constraints.

Diff: 1 Blooms: Remember Topic: Models with Bounded Variables LO1: Use auxiliary variables to model bound constraints and obtain more complete sensitivity information.

48) Give an account of balance constraints with some examples of verbal clues.

Answer: Balance constraints essentially state that input = output and ensure that the flow of material or money is accounted for at locations or between time periods. Examples include production in June plus any available inventory must equal June's demand plus inventory held to

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July, the total amount shipped to a distribution center from all plants must equal the amount shipped from the distribution center to all customers, or the total amount of money invested or saved in March must equal the amount of money available at the end of February.

Diff: 1 Blooms: Remember Topic: Developing Linear Optimization Models LO1: Recognize different types of constraints in problem statements.

49) For nonlinear models, the Lagrange multipliers are only approximate indicators of shadow prices.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Visualization of Solver Reports LO1: Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.

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Business Analytics, 3e (Evans) Chapter 16: Decision Analysis 1) A(n) ________ is a matrix whose rows correspond to decisions and whose columns correspond to events.

A) decision tree model B) payoff table C) utility function table D) scoring model Answer: B Diff: 1 Blooms: Remember Topic: Formulating Decision Problems LO1: Construct a payoff table for a decision situation.

Use the information below to answer the following question(s).

Below is a payoff table that lists four mortgage options:

Decision 1-year ARM 3-year ARM 5-year ARM 30-year fixed

Rates Rise $66,645 $62,857 $55,895 $52,276

Outcome Rates Stable $43,650 $47,698 $50,894 $52,276

Rates Fall $38,560 $42,726 $48,134 $52,276

2) What is the average payoff for the 3-year ARM? A) $ 52,792 B) $ 45,212 C) $ 51,094 D) $ 55,278 Answer: C Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Decision Strategies with Outcome Probabilities LO1: Apply average, aggressive, conservative, and opportunity-loss decision strategies for problems involving minimization and maximization objectives.

3) What is the average payoff for the 5-year ARM? A) $ 49,514 B) $ 52,015 C) $ 53,395 Copyright © 2020 Pearson Education, Inc. 313

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D) $ 51,641 Answer: D Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Decision Strategies with Outcome Probabilities LO1: Apply average, aggressive, conservative, and opportunity-loss decision strategies for problems involving minimization and maximization objectives.

4) Which of the following decisions has the best average payoff?

A) 1-year ARM B) 3-year ARM C) 5-year ARM D) 30-year fixed Answer: A Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Decision Strategies with Outcome Probabilities LO1: Apply average, aggressive, conservative, and opportunity-loss decision strategies for problems involving minimization and maximization objectives.

5) What is the best payoff rate for the 1-year ARM? A) $ 49,618 B) $ 43,650 C) $ 38,560 D) $ 66,645 Answer: C Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Decision Strategies Without Outcome Probabilities LO1: Apply average, aggressive, conservative, and opportunity-loss decision strategies for problems involving minimization and maximization objectives.

6) What is the worst payoff rate for the 5-year ARM? A) $ 50,894 B) $ 48,134 C) $ 51,641 D) $ 55,895 Answer: D Diff: 1 Blooms: Apply

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AACSB: Analytic Skills Topic: Decision Strategies Without Outcome Probabilities LO1: Apply average, aggressive, conservative, and opportunity-loss decision strategies for problems involving minimization and maximization objectives.

7) A(n) ________ is also called a minimax regret strategy.

A) opportunity-loss strategy B) aggressive strategy C) conservative strategy D) average payoff strategy Answer: A Diff: 1 Blooms: Remember Topic: Decision Strategies Without Outcome Probabilities LO1: Apply average, aggressive, conservative, and opportunity-loss decision strategies for problems involving minimization and maximization objectives.

Use the information given below to answer the following question(s).

Below is a payoff table that lists three mortgage options:

Decision 2-year ARM 5-year ARM 25-year fixed

Rates Rise $66,645 $62,857 $52,276

Outcome Rates Stable $43,650 $47,698 $52,276

Rates Fall $38,560 $42,726 $52,276

8) What is the maximum opportunity loss incurred for the 2-year ARM? A) $ 8,626 B) $ 13,716 C) $ 14,369 D) $ 10,581 Answer: C Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Decision Strategies Without Outcome Probabilities LO1: Apply average, aggressive, conservative, and opportunity-loss decision strategies for problems involving minimization and maximization objectives.

9) What is the maximum opportunity loss incurred for the 5-year ARM? A) $ 8,626 B) $ 13,716 Copyright © 2020 Pearson Education, Inc.

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C) $ 14,369 D) $ 10,581 Answer: D Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Decision Strategies Without Outcome Probabilities LO1: Apply average, aggressive, conservative, and opportunity-loss decision strategies for problems involving minimization and maximization objectives.

10) What is the maximum opportunity loss incurred for the 25-year fixed decision?

A) $ 8,626 B) $ 13,716 C) $ 14,369 D) $ 10,581 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Decision Strategies Without Outcome Probabilities LO1: Apply average, aggressive, conservative, and opportunity-loss decision strategies for problems involving minimization and maximization objectives.

Use the information below to answer the following question(s).

The payoff table given below lists four mortgage options:

Probability Decision 1-year ARM 3-year ARM 5-year ARM 30-year fixed

0.6 Rates Rise $66,645 $62,857 $55,895 $52,276

Outcome 0.3 Rates Stable $43,650 $47,698 $50,894 $52,276

0.1 Rates Fall $38,560 $42,726 $48,134 $52,276

The probability of rates rising is 0.6, rates stable is 0.3, and rates falling is 0.1.

11) What is the expected payoff for the 1-year ARM? A) $ 53,082.00 B) $ 16,951.00 C) $ 56,938.00 D) $ 18,979.30 Answer: C

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Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Decision Strategies Without Outcome Probabilities LO1: Apply expected values to a decision problem when probabilities of events are known.

12) What is the expected payoff of the 5-year ARM? A) $ 17,872.90 B) $ 53,618.60 C) $ 48,805.20 D) $ 20,081.80 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Decision Strategies Without Outcome Probabilities LO1: Apply expected values to a decision problem when probabilities of events are known.

13) Which of the following decisions has the largest expected payoff?

A) 1-year ARM B) 3-year ARM C) 5-year ARM D) 30-year fixed Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Decision Strategies Without Outcome Probabilities LO1: Apply expected values to a decision problem when probabilities of events are known.

14) Which of the following is considered the best expected value decision?

A) 1-year ARM B) 3-year ARM C) 5-year ARM D) 30-year fixed Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Decision Strategies Without Outcome Probabilities LO1: Apply expected values to a decision problem when probabilities of events are known.

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Use the information below to answer the following question(s).

Below is a payoff table that lists four mortgage options:

Probability Decision 1-year ARM 3-year ARM 5-year ARM 30-year fixed

0.6 Rates Rise $68,246 $64,897 $57,240 $59,720

Outcome 0.3 Rates Stable $47,487 $49,356 $52,988 $59,720

0.1 Rates Fall $36,450 $44,898 $50,642 $59,720

The probability of rates rising is 0.6, rates stable is 0.3, and rates falling is 0.1. Answer the following questions by creating a decision tree.

15) Which of the following is considered the best expected value decision?

A) 1-year ARM B) 3-year ARM C) 5-year ARM D) 30-year fixed Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Decision Trees LO1: Use Risk Solver Platform to construct decision trees.

16) Which of the following is considered the worst expected value decision?

A) 1-year ARM B) 3-year ARM C) 5-year ARM D) 30-year fixed Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Decision Trees LO1: Use Risk Solver Platform to construct decision trees.

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Use the information below to answer the following question(s).

Below is a decision tree illustrating the R&D process for a new drug.

Let us assume that if market is large, payoff is lognormally distributed with a mean of $4,900 million and a standard deviation of $1,000 million; if market is medium, payoff is lognormally distributed with a mean of $2,500 million and a standard deviation of $500 million; and if market is small, payoff is normally distributed with a mean of $1,800 million and standard deviation of $200 million. Let us also assume that the cost of clinical trials is uncertain and estimates are modeled with a triangular distribution with a minimum of -$700 million, a most likely value of $550 million, and a maximum of -$500 million. Use 10,000 trials and a random seed of 1.

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17) What is the value of mean obtained from the simulation results? [Hint: Choose the approximate value.]

A) $ 119.0 B) $ 116.1 C) $ 106.2 D) $ 94.4 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Decision Trees LO1: Incorporate Monte Carlo simulation in decision trees.

18) What is the value of standard deviation obtained from the simulation results? [Hint: Choose the approximate value.]

A) $ 119.1 B) $ 116.1 C) $ 105.7 D) $ 94.4 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Decision Trees LO1: Incorporate Monte Carlo simulation in decision trees.

19) What is the value of mode obtained from the simulation results? [Hint: Choose the approximate value.]

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C) $ 105.7 D) $ 94.1 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Decision Trees LO1: Incorporate Monte Carlo simulation in decision trees.

20) What is the mean absolute deviation obtained from the simulation results? [Hint: Choose the approximate value.]

A) $ 119.0 B) $ 116.1 C) $ 105.7 D) $ 94.0 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Decision Trees LO1: Incorporate Monte Carlo simulation in decision trees.

21) What is the coefficiIIt of variation obtained from the simulation results? [Hint: Choose the approximate value.]

A) 1.587 B) 1.122 C) 2.015 D) 1.890 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Decision Trees LO1: Incorporate Monte Carlo simulation in decision trees.

22) What is the probability that the drug will not reach the market? [Hint: Choose the approximate value.]

A) 0.95 B) 0.89 C) 0.77 D) 0.82 Answer: D Diff: 1

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Blooms: Apply AACSB: Analytic Skills Topic: Decision Trees LO1: Incorporate Monte Carlo simulation in decision trees.

Use the information below to answer the following question(s).

Below is a decision tree for the airline revenue management.

Create a one-way table and answer the following questions.

23) What is the expected value of the ticket when a discount is offered on the full fare? [Hint: Choose the approximate value.]

A) $ 442.50 B) $ 472.00 C) $ 410.00 D) $ 501.50 Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Decision Trees LO1: Incorporate Monte Carlo simulation in decision trees.

24) If the probability of selling the full-fare ticket is 0.80, what is the expected value of the ticket?

A) $ 442.50 B) $ 472.00 C) $ 501.50 D) $ 531.00 Copyright © 2020 Pearson Education, Inc.

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Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: Decision Trees LO1: Incorporate Monte Carlo simulation in decision trees.

25) The expected value of perfect information (EVPI) is equal to the ________.

A) Expected Monetary Value (EMV) with perfect information minus the EMV without any information B) EMV with perfect information divided by the EMV without any information C) sum of the EMV with information and the EMV without any information D) EMV without any information minus the EMV with perfect information Answer: A Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: The Value of Information LO1: Compute the expected value of perfect information.

Use the below information to answer the following question(s).

Below is a payoff table with three mortgage options:

Probability Decision 1-year ARM 3-year ARM 30-year fixed

0.6 Rates Rise $66,645 $62,857 $52,276

Outcome 0.3 Rates Stable $43,650 $47,698 $52,276

0.1 Rates Fall $38,560 $42,726 $52,276

26) What is the expected opportunity loss for the 1-year ARM? A) $ 7,979.60 B) $ 3,959.40 C) $ 6,853.50 D) $ 8,621.40 Answer: D Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: The Value of Information LO1: Compute the expected value of perfect information.

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27) What is the expected opportunity loss for the 3-year ARM? A) $ 7,979.60 B) $ 3,959.40 C) $ 6,853.50 D) $ 8,621.40 Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: The Value of Information LO1: Compute the expected value of perfect information.

28) What is the expected opportunity loss for the 30-year fixed decision?

A) $ 7,979.60 B) $ 3,959.40 C) $ 6,853.50 D) $ 8,621.40 Answer: B Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: The Value of Information LO1: Compute the expected value of perfect information.

29) The expected value of sample information (EVSI) is equal to the ________.

A) Expected Monetary Value (EMV) without sample information divided by the EMV with sample information B) EMV without sample information minus the EMV with sample information C) sum of the EMV with sample information and the EMV without sample information D) EMV with sample information minus the EMV without sample information Answer: D Diff: 1 Blooms: Remember Topic: The Value of Information LO1: Compute the expected value of perfect information.

Use the information below to answer the following question(s) Misty Inc. launches a new range of perfumes for men and women. The probability of high consumer demand for the product is 0.6 and low consumer demand is 0.4. The probability of a favorable survey response given high consumer demand is 0.9 and the probability of a favorable survey response given low consumer demand is 0.2.

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30) What is the likelihood for high demand knowing that the market report is favorable?

A) 84% B) 90% C) 87% D) 80% Answer: C Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: The Value of Information LO1: Incorporate sample information in decision trees and apply Bayes's rule to compute conditional probabilities.

31) If the marketing report is u’favorable, what is the probability of low demand?

A) 84% B) 90% C) 87% D) 80% Answer: A Diff: 2 Blooms: Apply AACSB: Analytic Skills Topic: The Value of Information LO1: Incorporate sample information in decision trees and apply Bayes's rule to compute conditional probabilities.

32) A children's welfare fundrai’er involves selling one thousand $70 tickets to win a $20,000’grand prize. If the probability of winning is only 0.005, what is the expected payoff?

A) -$40 B) -$50 C) $30 D) $60 Answer: C Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Utility and Decision Making LO1: Construct a utility function and use it to make a decision.

33) Greg is indifferent between receiving $2,000, and taking a chance at $2,500 with probability 0.7 and losing $1200 with probability 0.5. What is the expected value of this gamble?

A) $ 1,150 B) $ 1,800

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C) $ 1,460 D) $ 2,045 Answer: A Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Utility and Decision Making LO1: Construct a utility function and use it to make a decision.

Use the information below to answer the following question(s).

Below are four options for an investment decision.

Decision/Event Bank CD Bond fund Index fund Growth fund

Rates Rise 0.80 -0.75 0.00 -0.30

Rates Stable 0.80 0.86 0.90 0.70

Rates Fall 0.80 1.50 1.20 1.40

34) Which of the following is the average utility for the bond fund decision?

A) 1.18 B) 0.38 C) 0.54 D) 0.43 Answer: C Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Utility and Decision Making LO1: Construct a utility function and use it to make a decision.

35) Which of the following is the average utility for the index fund decision?

A) 1.05 B) 0.70 C) 0.60 D) 0.45 Answer: B Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Utility and Decision Making LO1: Construct a utility function and use it to make a decision.

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36) Identify the average utility for the growth fund decision.

A) 1.05 B) 0.70 C) 0.20 D) 0.60 Answer: D Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Utility and Decision Making LO1: Construct a utility function and use it to make a decision.

37) Based on the average utility, which of the following is considered the best decision?

A) Bank CD B) Bond fund C) Index fund D) Growth fund Answer: A Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Utility and Decision Making LO1: Construct a utility function and use it to make a decision.

38) Based on the average utility, which of the following is considered the worst decision?

A) Bank CD B) Bond fund C) Index fund D) Growth fund Answer: B Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Utility and Decision Making LO1: Construct a utility function and use it to make a decision.

39) Which of the following formulas is used to determine the exponential utility function?

A) U(x) = 1 + e—x/R B) U(x) = 1× ex/R C) U(x) = 1/ exR D) U(x) = 1 — e—x/R Answer: D Diff: 1 Copyright © 2020 Pearson Education, Inc.

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Blooms: Remember Topic: Utility and Decision Making LO1: Construct a utility function and use it to make a decision.

40) If the payoff is $2200 and R is equal to $500, what is the utility function?

A) 0.9877 B) 0.6819 C) 0.7645 D) 0.4502 Answer: A Diff: 1 Blooms: Apply AACSB: Analytic Skills Topic: Utility and Decision Making LO1: Construct a utility function and use it to make a decision.

41) A payoff table is a matrix whose rows correspond to events and whose columns correspond to decisions.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Formulating Decision Problems LO1: Construct a payoff table for a decision situation.

42) For the average payoff strategy, the decision with the best average payoff is chosen.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Decision Strategies with Outcome Probabilities.

LO1: Construct a payoff table for a decision situation.

43) In a minimin strategy, the decision which minimizes the minimum payoff is chosen.

Answer: TRUE Diff: 1 Blooms: Remember Topic: Decision Strategies without Outcome Probabilities.

LO1: Apply average, aggressive, conservative, and opportunity-loss decision strategies for problems involving minimization and maximization objectives.

44) The average payoff strategy weights the likelihood that the actual outcomes can occur.

Answer: FALSE

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Diff: 1 Blooms: Remember Topic: Making Decisions with Uncertain Information LO1: Apply average, aggressive, conservative, and opportunity-loss decision strategies for problems involving minimization and maximization objectives.

45) An outcome over which the decision maker has complete control is called an event node.

Answer: FALSE Diff: 1 Blooms: Remember Topic: Decision Trees LO1: Use Risk Solver Platform to construct decision trees.

46) What are the three elements required to characterize decisions with uncertain consequences?

Answer: Many decisions involve a choice from among a small set of alternatives with uncertain consequences. Such decisions can be characterized by defining three things: (1) the decision alternatives (2) the outcomes that may occur once a decision is made (3) the payoff associated with each decision and outcome Diff: 1 Blooms: Remember Topic: Formulating Decision Problems LO1: List the three elements needed to characterize decisions with uncertain consequences.

47) What are the differences between an aggressive strategy and a conservative strategy?

Answer: An aggressive decision maker might seek the option that holds the promise of minimizing the potential loss. For a minimization objective, this strategy is also often called a minimin strategy, that is, the decision that minimizes the minimum payoff is chosen. Aggressive decision makers are often called speculators, particularly in financial arenas because they increase their exposure to risk in hopes of increasing their return. A conservative decision maker, on the other hand, might take a more pessimistic attitude. Such a strategy is also known as a minimax strategy because we seek the decision that corresponds to the minimum value of the largest cost. Conservative decision makers are often called risk averse and are willing to forgo potential returns in order to reduce their exposure to risk.

Diff: 2 Blooms: Remember Topic: Decision Strategies Without Outcome Probabilities LO1: Apply average, aggressive, conservative, and opportunity-loss decision strategies for problems involving minimization and maximization objectives.

48) Describe the steps involved in the construction of a decision tree.

Answer: A useful approach to structuring a decision problem involving uncertainty is to use a

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graphical model called a decision tree. Decision trees consist of a set of nodes and branches.

Nodes are points in time at which events take place. The event can be a selection of a decision from among several alternatives, represented by a decision node, or an outcome over which the decision maker has no control, an event node.

Diff: 1 Blooms: Remember Topic: Decision Trees LO1: Use Risk Solver Platform to construct decision trees.

49) What is the expected value of perfect information?

Answer: The expected value of perfect information (EVPI) is the Expected Monetary Value (EMV) with perfect information minus the EMV without any information. It represents the most a person is willing to pay for perfect information. Perfect information states with certainty what outcome will occur.

Diff: 1 Blooms: Remember Topic: The Value of Information LO1: Compute the expected value of perfect information.

50) What is the expected value of sample information?

Answer: The expected value of sample information (EVSI) is the EMV with sample information minus the EMV without sample information. It represents the most a person is willing to pay for the sample information. Sample information is the result of conducting some type of experiment, such as market research study.

Diff: 1 Blooms: Remember Topic: The Value of Information LO1: Compute the expected value of perfect information.

Copyright © 2020 Pearson Education, Inc.