Business Modeling Final
1. If we plot a continuous probability distribution f(x), the total probability under the curve is a. -1. b. 0. c. 1. d. 100.
0.
1. The probability of an event and the probability of its complement always sum to a. 1. b. 0. c. any value between 0 and 1. d. any positive value.
0.
1. If A and B are any two events with P(A) = 0.8 and P(B|) = 0.7, then P(and B) is a. 0.56. b. 0.14. c. 0.24. d. none of these choices
0.24.
1. If A and B are any two events with P(A) = 0.8 and P(B|A) = 0.4, then the joint probability of A and B is: a. 0.80 b. 0.40 c. 0.32 d. 1.20
0.32
1. If events A and B are mutually exclusive, then the probability of both events occurring simultaneously is equal to a. 0.0. b. 0.5. c. 1.0. d. any value between 0.5 and 1.0.
0.5
1. If two events are collectively exhaustive, what is the probability that one or the other occurs? a. 0.25 b. 0.50 c. 1.00 d. This cannot be determined from the information given.
0.50
1. The standard normal distribution has a mean and a standard deviation respectively equal to a. 0 and 0. b. 1 and 1. c. 1 and 0. d. 0 and 1.
1 and 1.
1. The data below represents sales for a particular product. If you were to use the moving average method with a span of 3 periods, what would be your forecast for period 5? a. 90 b. 100 c. 105 d. 110
110
1. Suppose that a simple exponential smoothing model is used (with = 0.40) to forecast monthly sandwich sales at a local sandwich shop. The forecasted demand for September was 1560 and the actual demand was 1480 sandwiches. Given this information, what would be the forecast number of sandwiches for October? a. 1480 b. 1528 c. 1560 d. 1592
1528
11. The linear trend yt = 120 + 2t was estimated using a time series with 20 time periods. The forecasted value for time period 21 is
162.
1. The following are the values of a time series for the first four time periods: Using a four-period moving average, the forecasted value for time period 5 is a. 24.5. b. 25.5. c. 26.5. d. 27.5.
25.5.
1. If a manufacturing process takes 3 hours per unit of x and 5 hours per unit of y and a maximum of 100 hours of manufacturing process time are available, then an algebraic formulation of this constraint is
3x + 5y <= 100
1. The regression line Y = -3 + 2.5 has been fitted to the data points (28, 60), (20, 50), (10, 18), and (25, 55). The sum of the squared residuals will be a. 20.25. b. 16.00. c. 49.00. d. 94.25.
94.25.
1. What is a component of a time series?
All of these choices
1. In aggregate planning models, which of the following statements are correct? a. The number of workers available influences the possible production levels. b. We allow the workforce level to be modified each month through the hiring and firing of workers. c. We eventually allow demand to be backlogged; that is, demand need not be met on time. d. All of these choices are correct.
All of these choices are correct.
1. Which of these statements are true of multiple optimal solutions? a. All solutions have the same values for the decision variables. b. All solutions have the same value for the objective function. c. All solutions have the same shadow prices. d. All of these statements are true.
All solutions have the same value for the objective function.
1. Which equation shows the process of standardizing?
E(X) = np
1. The ANOVA table splits the total variation into two parts. They are the _____ variation. a. acceptable and unacceptable b. adequate and inadequate c. resolved and unresolved d. Explained and unexplained
Explained and unexplained
1. Which of the following does not represent a broad class of applications of linear programming models? a. Blending models b. Financial portfolio models c. Logistics models d. Forecasting models
Forecasting models
The appropriate hypothesis test for an ANOVA test is
H0: All B=0, Ha: at least one B not equal to 0
1. Which of the following is not one of the commonly used summary measures for forecast errors?
MFE (mean forecast error)
1. Which of the following is not a method for dealing with seasonality in data? a. Winter's exponential smoothing model b. Deseasonalizing the data, using any forecasting model, then reseasonalizing the data c. Multiple regression with lags for the seasons d. Multiple regression with dummy variables for the seasons
Multiple regression with lags for the seasons
1. In a minimum cost network flow model, the flow balance constraint for each demand node takes which form? a. Net Outflow > Capacity b. Net Inflow ≥ Demand c. Net Outflow ≤ Capacity d. Net Outflow ≤ Capacity
Net Inflow ≥ Demand
1. In a minimum cost network flow model, the flow balance constraint for each supply node takes which form? a. Net Inflow = Demand b. Net Inflow ≥ Demand c. Net Outflow > Capacity d. Net Outflow ≤ Capacity
Net Outflow ≤ Capacity
1. Which of the following best describes the concept of probability? a. It is a measure of the likelihood that a particular event will occur. b. It is a measure of the likelihood that a particular event will occur, given that another event has already occurred. c. It is a measure of the likelihood of the simultaneous occurrence of two or more events. d. None of these choices describe the concept of probability.
None of these choices describe the concept of probability.
1. Which of the following statements are false? a. Solver does not offer a sensitivity report for models with integer constraints. b. Solver's sensitivity report is not suited for questions about multiple input changes. c. Solver's sensitivity report is used primarily for questions about one-at-a time changes to input. d. None of these statements are false.
None of these statements are false.
1. Which of the following statements is true? a. Probabilities must be negative. b. Probabilities must be greater than 1. c. The sum of all probabilities for a random variable must be equal to 1. d. The sum of all probabilities for a random variable must be equal to 0.
Probabilities must be negative.
1. Which of the following is a type of constraint often required in blending problems? a. Integer constraint b. Binary constraint c. Quality constraint d. Nonlinear constraint
Quality constraint
_____ is/are especially helpful in identifying outliers. a. Linear regression b. Regression analysis c. Normal curves d. Scatterplots
Scatterplots
1. An efficient algorithm for finding the optimal solution in a linear programming model is the _____ method. a. spreadsheet b. solution mix c. complex d. Simplex
Simplex
1. Which of the following is not one of the assumptions of regression? a. There is a population regression line. b. The explanatory variable is normally distributed. c. The response variable is normally distributed. d. The errors are probabilistically independent.
The explanatory variable is normally distributed.
1. Given the least squares regression line, , which statement is true? a. The relationship between X and Y is positive. b. The relationship between X and Y is negative. c. As X increases, so does Y. d. As X decreases, so does Y.
The relationship between X and Y is negative.
1. To specify that must be at most 75% of the blend of, , and , we must have a constraint of the form
X1 <= 0.75(X1 + X2 + X3)
1. If refers to the number of hours that employee works in week, then to indicate that the number of working hours of four employees in week 3 should not exceed 160 hours, we must have a constraint of the form
X13 +X23+X33+X43 <= 160
1. In regression analysis, which of the following causal relationships are possible? a. X causes Y to vary. b. Y causes X to vary. c. Other variables cause both X and Y to vary. d. All of these options are possible.
Y causes X to vary.
1. In multiple regression, the coefficients reflect the expected change in _____ by one unit. a. Y when the associated X value increases b. X when the associated Y value increases c. Y when the associated X value decreases d. X when the associated Y value decreases
Y when the associated X value increases
1. The objective typically used in the tree types of equation-building procedures is to find the equation with a. a small se. b. a large R2. c. a small se and a large R2. d. the smallest F-ratio.
a small se and a large R2.
1. An important condition when interpreting the coefficient for a particular independent variable X in a multiple regression equation is that a. the dependent variable will remain constant. b. the dependent variable will be allowed to vary. c. all of the other independent variables remain constant. d. all of the other independent variables be allowed to vary.
all of the other independent variables remain constant.
1. All optimization problems have a. an objective function and decision variables. b. an objective function and constraints. c. decision variables and constraints. d. an objective function, decision variables and constraints.
an objective function, decision variables and constraints.
1. In a random series, successive observations are probabilistically independent of one another. If this property is violated, the observations are said to be
autocorrelated.
1. If A and B are mutually exclusive events with P(A) = 0.70, then P(B) a. can be any value between 0 and 1. b. can be any value between 0 and 0.70. c. cannot be larger than 0.30. d. can be any value between 0.30 and 0.70.
can be any value between 0.30 and 0.70.
1. In a transshipment problem, shipments a. can occur between any two nodes (suppliers, demanders, and transshipment locations). b. cannot occur between two supply locations. c. cannot occur between two demand locations. d. cannot occur between a transshipment location and a demand location.
can occur between any two nodes (suppliers, demanders, and transshipment locations).
1. The standard deviation of a probability distribution is a measure of a. variability of the distribution. b. central location. c. the shape of the distribution. d. skewness of the distribution.
central location.
1. If P(A) = P(A|B), then events A and B are said to be a. mutually exclusive. b. independent. c. dependent. d. complementary.
complementary.
1. In regression analysis, if there are several explanatory variables, it is called _____ regression. a. simple b. multiple c. compound d. Nonlinear
compound
1. Let A and B be the events of the FDA approving and rejecting a new drug to treat hypertension, respectively. The events A and B are a. independent. b. conditional. c. unilateral. d. mutually exclusive.
conditional.
1. A linear trend means that the time series variable changes by a _____ each time period. a. constant amount b. constant percentage c. positive amount d. negative amount
constant amount
1. In contrast to linear trend, an exponential trend is appropriate when the time series changes by a _____ each time period.
constant percentage
1. Conditions that must be satisfied in an optimization model are a. values of the objective function. b. constraints. c. shadow prices. d. intercepts.
constraints.
1. In an optimization model, there can only be one a. decision variable. b. constraint. c. objective function. d. shadow price.
decision variables cannot be less than zero.
1. The normal distribution is a a. discrete distribution with two parameters. b. binomial distribution with only one parameter. c. density function of a discrete random variable. d. continuous distribution with two parameters.
density function of a discrete random variable.
1. The primary reason for standardizing random variables is to measure variables with a. different means and standard deviations on a non-standard scale. b. different means and standard deviations on a single scale. c. dissimilar means and standard deviations in like terms. d. similar means and standard deviations on two scales.
different means and standard deviations on a non-standard scale.
1. Consider the following linear programming problem: Maximize Subject to:The above linear programming problem a. has only one optimal solution. b. has more than one optimal solution. c. exhibits infeasibility. d. exhibits unboundedness.
exhibits infeasibility.
1. In regression analysis, multicollinearity refers to the a. response variables being highly correlated. b. explanatory variables being highly correlated. c. response variable(s) and the explanatory variable(s) being highly correlated with one another. d. response variables being highly correlated over time.
explanatory variables being highly correlated.
1. When using the graphical solution method to solve linear programming problems, the set of points that satisfy all constraints is called the _____ region. a. optimal b. feasible c. constrained d. Logical
feasible
1. The decision variables in transportation problems are a. profits. b. costs. c. flows. d. capacities.
flows
1. The solution of a linear programming problem using Excel® typically involves the following three stages a. formulating the problem, invoking Solver, and sensitivity analysis. b. formulating the problem, graphing the problem, and sensitivity analysis. c. designing the decision variable cells, the target cells, and the constraints. d. designing the inputs, the decision variable cells, and the outputs.
formulating the problem, invoking Solver, and sensitivity analysis.
1. Many statistical packages have three types of equation-building procedures. They are a. forward, linear, and non-linear. b. forward, backward, and stepwise. c. simple, complex, and stepwise. d. inclusion, exclusion, and linear.
forward, backward, and stepwise.
1. A single variable X can explain a large percentage of the variation in some other variable Y when the two variables are a. mutually exclusive. b. inversely related. c. directly related. d. highly correlated.
highly correlated.
1. Regression analysis asks a. if there are differences between distinct populations. b. if the sample is representative of the population. c. how a single variable depends on other relevant variables. d. how several variables depend on each other.
how a single variable depends on other relevant variables.
1. Workforce scheduling problems are often integer programming models, which means that they have a. an integer objective function. b. integer decision variables. c. integer constraints. d. integer output.
integer decision variables.
1. Rounding the solution of a linear programming problem to the nearest integer values provides a(n): a. integer solution that is optimal. b. integer solution that may be neither feasible nor optimal. c. feasible solution that is not necessarily optimal. d. infeasible solution.
integer solution that may be neither feasible nor optimal.
1. When determining whether to include or exclude a variable in regression analysis, if the p-value associated with the variable's t-value is above some accepted significance value, such as 0.05, then the variable a. is a candidate for inclusion. b. is a candidate for exclusion. c. is redundant. d. does not fit the guidelines of parsimony.
is a candidate for exclusion.
1. A discrete probability distribution a. is a set of possible values and a corresponding set of probabilities that sum to 1. b. is a modeling tool that can be used to incorporate uncertainty into models. c. can be estimated from long-run proportions. d. is the distribution of a single random variable.
is a modeling tool that can be used to incorporate uncertainty into models.
1. In multiple regression, the constant a. is the expected value of the dependent variable Y when all of the independent variables have the value zero. b. is necessary to fit the multiple regression line to set of points. c. must be adjusted for the number of independent variables d. is all of these options.
is the expected value of the dependent variable Y when all of the independent variables have the value zero.
1. Forecasting models can be divided into three groups. They are _____ methods.
judgmental, extrapolation, and econometric
1. Residuals separated by one period that are autocorrelated indicate _____ autocorrelation. a. simple b. redundant c. time 1 d. lag 1
lag 1
1. The most common form of autocorrelation is positive autocorrelation, in which
large observations tend to follow large observations and small observations tend to follow small observations.
1. Linear programming is a subset of a larger class of models called _____ models. a. mathematical programming b. mathematical optimality c. linear regression d. linear simplex
mathematical programming
1. When there is a problem with Solver being able to find a solution, many times it is an indication of a(n) a. older version of Excel®. b. nonlinear programming problem. c. problem that cannot be solved using linear programming. d. mistake in the formulation of the problem.
mistake in the formulation of the problem.
1. Perhaps the simplest and one of the most frequently used extrapolation methods is the
moving average.
1. The t-value for testing H0: Bi - 0 is calculated using which of the following equations? a. n - k - 1 b. E (xi/Yi) c. B/si d. Bi/sq
n - k - 1
1. A scatterplot that appears as a shapeless mass of data points indicates _____ relationship among the variables. a. a curved b. a linear c. a nonlinear d. no
no
1. The idea behind the runs test is that a random number series should have a number of runs that is
not large or small.
1. The value k in the number of degrees of freedom, n-k-1, for the sampling distribution of the regression coefficients represents the a. sample size. b. population size. c. number of coefficients in the regression equation, including the constant. d. number of independent variables included in the equation.
number of independent variables included in the equation.
1. A knapsack problem is any integer program involving 0 - 1 variable with _____ constraints. a. three b. two c. one d. zero
one
1. An error term represents the vertical distance from any point to the a. estimated regression line. b. population regression line. c. value of the Y's. d. mean value of the X's.
population regression line.
1. Models such as moving averages, exponential smoothing, and linear trend use only
previous values of Y to forecast future values of Y.
1. Linear programming models have three important properties a. optimality, additivity, and sensitivity. b. optimality, linearity, and divisibility. c. divisibility, linearity, and nonnegativity. d. proportionality, additivity, and divisibility.
proportionality, additivity, and divisibility.
1. When using exponential smoothing, a smoothing constant must be used. The value for a. ranges between 0 and 1. b. ranges between -1 and +1. c. equals the largest observed value in the series. d. represents the strength of the association between the forecasted and observed values.
ranges between 0 and 1.
1. There are a variety of deseasonalizing methods, but they are typically variations of a. ratio-to-seasonality methods. b. ratio-to-exponential-smoothing methods. c. ratio-to-moving-average methods. d. linear trend.
ratio-to-moving-average methods.
1. There are two types of random variables, they are a. discrete and continuous. b. exhaustive and mutually exclusive. c. complementary and cumulative. d. real and unreal.
real and unreal.
1. In linear regression, we fit the least squares line to a set of values (or points on a scatterplot). The distance from the line to a point is called the a. fitted value. b. residual. c. correlation. d. covariance.
residual
1. The percentage of variation () can be interpreted as the fraction (or percent) of variation of the a. explanatory variable explained by the independent variable. b. explanatory variable explained by the regression line. c. response variable explained by the regression line. d. error explained by the regression line.
response variable explained by the regression line.
P(A) = 1 =P(A) is the a. addition rule. b. commutative rule. c. rule of complements. d. rule of opposites.
rule of complements.
1. A function that associates a numerical value with each possible outcome of an uncertain event is called a _____ variable. a. conditional b. random c. population d. sample
sample
1. Extrapolation methods attempt to
search for patterns in the data and then use those to predict future values.
1. As related to sensitivity analysis in linear programming, when the profit increases with a unit increase in labor, this change in profit is referred to as the a. add-in price. b. sensitivity price. c. shadow price. d. additional profit.
shadow price.
1. In choosing the "best-fitting" line through a set of points in linear regression, we choose the one with the a. smallest sum of squared residuals. b. largest sum of squared residuals. c. smallest number of outliers. d. largest number of points on the line.
smallest sum of squared residuals.
1. The standard error of the estimate () is essentially the a. mean of the residuals. b. standard deviation of the residuals. c. mean of the explanatory variable. d. standard deviation of the explanatory variable.
standard deviation of the residuals.
1. Many organizations must determine how to schedule employees to provide adequate service. If we assume that an organization faces the same situation each week, this is referred to as a(n) _____ scheduling problem. a. static b. dynamic c. transportation d. Organization
static
1. Which of the following is not one of the techniques that can be used to identify whether a time series is truly random?
the autocorrelations (or a correlogram)
1. The adjusted R2 adjusts R2 for a. non-linearity. b. outliers. c. low correlation. d. the number of explanatory variables in a multiple regression model.
the number of explanatory variables in a multiple regression model.
1. Correlation is a summary measure that indicates a. a curved relationship among the variables. b. the rate of change in Y for a one unit change in X. c. the strength of the linear relationship between pairs of variables. d. the magnitude of difference between two variables.
the strength of the linear relationship between pairs of variables.
1. In regression analysis, the ANOVA table analyzes a. the variation of the response variable Y. b. the variation of the explanatory variable X. c. the total variation of all variables. d. some of the variation in the explanatory variable and some of the variation in the response variable.
the variation of the response variable Y.
1. When the error variance is nonconstant, it is common to see the variation increases as the explanatory variable increases (you will see a "fan shape" in the scatterplot). There are two ways you can deal with this phenomenon. These are a. the weighted least squares and a logarithmic transformation. b. the partial F and a logarithmic transformation. c. the weighted least squares and the partial F. d. stepwise regression and the partial F.
the weighted least squares and a logarithmic transformation.
1. The term autocorrelation refers to a. the analyzed data refers to itself. b. the sample is related too closely to the population. c. the data are in a loop (values repeat themselves). d. time series variables are usually related to their own past values.
time series variables are usually related to their own past values.
1. A problem that deals with the direct distribution of products from supply locations to demand locations is called a(n) _____ problem. a. transportation b. assignment c. network d. Transshipment
transportation
1. Holt's model differs from simple exponential smoothing in that it includes a term for a. seasonality. b. trend. c. residuals. d. cyclical fluctuations.
trend.
1. A linear programming problem with _____decision variable(s) can be solved by a graphical solution method. a. two b. three c. four d. Five
two
1. A "fan" shape in a scatterplot indicates a. unequal variance. b. a nonlinear relationship. c. the absence of outliers. d. sampling error.
unequal variance.
1. In using Excel® to solve linear programming problems, the objective cell represents the a. value of the objective function. b. constraints. c. decision variables. d. total cost of the model.
value of the objective function.
1. Suppose a firm must at least meet minimum expected demands of 60 for product x and 80 of product y. An algebraic formulation of these constraints is
x>= 60, y >=80
1. What is the equation of the line representing this constraint?
y <= - 2x +100
