Operations Research
Chapter Exam Questions
Course Introduction
Operations Research is a discipline that applies advanced analytical methods to help make better decisions. The course introduces students to key concepts such as mathematical modeling, optimization, linear programming, network flows, queuing theory, decision analysis, and simulation. Through practical problem-solving and case studies, students learn how to formulate real-world business and engineering problems into structured models, analyze various solution strategies, and interpret results to inform operational and strategic decisions. Emphasis is placed on the use of computational tools to solve complex problems and enhance efficiency in a range of industries, including logistics, manufacturing, transportation, and healthcare.
Recommended Textbook
Statistical Techniques in Business and Economics 16th Edition by Douglas Lind
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Chapter 1: What Is Statistics
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Q1) The ordinal level of measurement is considered the "lowest" level of measurement.
A)True
B)False
Answer: False
Q2) The number of workers calling in sick during any particular week is considered to be _______________ data.
Answer: discrete
Q3) To infer something about a population, we usually take a sample from the population.
A)True
B)False
Answer: True
Q4) Your height and weight are examples of which level of measurement?
A) Nominal
B) Ordinal
C) Interval
D) Ratio
Answer: D
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Chapter 2: Describing Data: Frequency Tables, Frequency
Distributions, and Graphic Presentation
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Q1) When a class interval is expressed as 100 up to 200, _________________________.
A) Observations with values of 100 are excluded from the class
B) Observations with values of 200 are included in the class
C) Observations with values of 200 are excluded from the class
D) The class interval is 99
Answer: C
Q2) A table showing the number of observations that have been grouped into each of several classes is called a frequency ________________.
Answer: distribution
Q3) A frequency distribution for nominal data requires that the categories be ___________________ and _____________________.
Answer: exhaustive ; mutually exclusive
Q4) In a bar chart, the x-axis is labeled with the values of a qualitative variable. A)True
B)False
Answer: True
Q5) In a deck of cards, a class of all cards that are hearts and a class of all cards that are kings are NOT _____________.
Answer: mutually exclusive
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Chapter 3: Describing Data: Numerical Measures
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Q1) The mean, as a measure of central location, would be inappropriate for which one of the following?
A) Ages of adults at a senior citizen center
B) Incomes of lawyers
C) Number of pages in textbooks on statistics
D) Marital status of college students at a particular university
Answer: D
Q2) The Investment Research Institute reported in its Mutual Fund Fact Book that the number of mutual funds increased from 5725 in 1999 to 7977 in 2009. What is the geometric mean annual percent increase in the number of funds?
A) 1.034
B) 3.37
C) 39.34
D) 71.11
E) 633.5
Answer: B
Q3) The sum of the deviations of each value from the mean is ___.
Answer: zero
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Chapter 4: Describing Data: Displaying and Exploring Data
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Q1) A scatter diagram is used to illustrate a relationship between gender and the preference for Coke or Pepsi.
A)True
B)False
Q2) What is the common purpose of a scatter diagram and a contingency table?
Q3) A stem-and-leaf diagram shows the actual data values.
A)True
B)False
Q4) A dot plot is best applied when _____________________.
A) The mean, median, and mode are equal
B) The general shape of a distribution is symmetric
C) The relationship between two variables is summarized
D) A single variable is summarized
Q5) If a distribution is negatively skewed, the distribution is not symmetrical and the long tail is to the left.
A)True
B)False
Q6) A dot plot shows the symmetry of a distribution.
A)True
B)False
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Chapter 5: A Survey of Probability Concepts
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Q1) Giorgio offers the person who purchases an 8-ounce bottle of Allure two free gifts, chosen from the following: an umbrella, a 1-ounce bottle of Midnight, a feminine shaving kit, a raincoat, or a pair of rain boots. If you purchased Allure, what is the probability you randomly selected an umbrella and a shaving kit in that order?
A) 0.00
B) 1.00
C) 0.05
D) 0.20
Q2) When are two experimental outcomes mutually exclusive?
A) When they overlap on a Venn diagram.
B) If one outcome occurs, then the other cannot.
C) When the probability of one affects the probability of the other.
D) When the joint probability of the two outcomes is not equal to zero.
Q3) When the special rule of addition is used, the events must be _______________.
Q4) When are two outcomes independent? Explain in terms of the rules of probability.
A. In other words, the probability of A is unaffected by B.
Q5) The _________ approach to probability is based on a person's belief, opinion, or judgment.
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Chapter 6: Discrete Probability Distributions
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Q1) For the hypergeometric distribution there are ________________ possible outcomes.
Q2) A company is studying the number of daily debit card purchases. There were 20 purchases and the probability of a debit card purchase is 0.5. What is the standard deviation of the number of debit card purchases?
Q3) What kind of distributions are the binomial and Poisson probability distributions?
A) Discrete
B) Continuous
C) Both discrete and continuous
D) Neither discrete or continuous
Q4) When observing a checkout line at a food store, the average number of people served is 30 per hour. Using the Poisson distribution, what is the probability that no (zero) people check out in any given hour?
Q5) The probability of a particular outcome must always be between 0.0 and 1.0 inclusive.
A)True
B)False
Q6) The mean of a binomial distribution is calculated using ____.
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Chapter 7: Continuous Probability Distributions
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Q1) A normally distributed random variable has _________.
A) Any value between - and + .
B) Discrete values.
C) Any value between specified minimum and maximum values.
D) Only two values, success and failure.
Q2) Non-stop Airlines determined that the mean number of passengers per flight is 152 with a standard deviation of 10 passengers. Practically all flights have between 142 and 162 passengers.
A)True
B)False
Q3) If an average of 12 customers is served per hour, what is the probability that the next customer will arrive in 3 minutes or less?
A) 0.55
B) 0.30
C) 0.45
D) 0.39
Q4) After arriving at the university student medical clinic, the waiting times to receive service after checking-in follow an exponential distribution with a mean of 10 minutes. Calculate the probability a student waits more than 12 minutes.
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Chapter 8: Sampling Methods and the Central Limit
Theorem
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Q1) Auditors may select every 20<sup>th</sup> file starting with the 5<sup>th</sup> file in the top drawer. Then, file numbers 25, 45, 65, 85, . . . are selected. This type of sampling is called ___________.
Q2) The standard deviation of the sampling distribution of the sample means is called the ______________.
Q3) For the sampling distribution of sample means, sampling error will decrease as sample size increases.
A)True B)False
Q4) A university has 1,000 computers available for students to use. Each computer has a 250-gigabyte hard drive. The university wants to estimate the space occupied on the hard drives. A random sample of 100 computers showed a mean of 115 gigabytes used with a standard deviation of 20 gigabytes. What is the standard error of the mean?
Q5) A __________________ assumes that each item or individual in the population has an equal chance of being included.
Q6) What are the two population parameters that specify the location and dispersion for a normal distribution?
Q7) A population consists of 12 values. How many samples of size six are possible?
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Chapter 9: Estimation and Confidence Intervals
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Q1) A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selected nine students. Their mean age was 19.1 years, with a sample standard deviation of 1.5 years. What is the 95% confidence interval for the population mean?
A) [0.97, 3.27]
B) [15.64, 22.56]
C) [17.97, 20.23]
D) [17.95, 20.25]
Q2) A survey of 25 grocery stores revealed that the mean price of a gallon of milk was $2.98, with a standard error of $0.10. What is the 95% confidence interval to estimate the true cost of a gallon of milk?
A) $2.81 to $3.15
B) $2.94 to $3.02
C) $2.77 to $3.19
D) $2.95 to $3.01
Q3) When using the t distribution to calculate a confidence interval, we assume that the population of interest is normal or nearly normal.
A)True
B)False
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Chapter 10: One-Sample Tests of Hypothesis
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Q1) A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shelf life of the mix is 216 days. After a revised mix has been developed, a sample of nine boxes of cake mix had a mean of 217.222 days and a standard deviation of 1.2019 days. At the 0.025 significance level, what is the critical value?
Q2) The average cost of tuition plus room and board at small private liberal arts colleges is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let = 0.05. Based on the computed test statistic or p-value, what is our decision about the average cost?
A) Equal to $8,500
B) Greater than $8,500
C) Less than $8,500
D) Not equal to $8,500
Q3) A p-value is a probability.
A)True
B)False
Q4) A test statistic is computed using ________________ information.
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Chapter 11: Two-Sample Tests of Hypothesis
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Q1) When testing for a difference between the means of two dependent samples, n<sub>1</sub> and n<sub>2</sub> are ________________.
Q2) If a hypothesis states that one population mean is greater than another population mean, then the test is _______________.
Q3) A statistics professor wants to compare grades in two different classes of the same course. This is an example of a paired sample.
A)True
B)False
Q4) When independent samples with unknown but equal standard deviations are used to test for differences in the means, we pool the sample _________________.
Q5) If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations, the variances are pooled to compute the best estimated variance.
A)True
B)False
Q6) If the null hypothesis states that there is no difference between the two population means, then the test is ______________.
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Chapter 12: Analysis of Variance
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Q1) A preliminary study of hourly wages paid to unskilled employees in three metropolitan areas was conducted. Seven employees were included from Area A, 9 from Area B, and 12 from Area C. The test statistic was computed to be 4.91. What can we conclude at the 0.05 level?
A) The mean hourly wages of unskilled employees of all areas are equal.
B) The mean hourly wages in at least two metropolitan areas are different.
C) More degrees of freedom are needed.
D) None of these is correct.
Q2) The F distribution is a ______________ distribution.
Q3) In a study of protein breakfast bars, five bars from each of three brands were tested to see if the mean amount of protein per bar differs among the brands. If the brand sum of squares is 0.07 and the error sum of squares is 0.09, the calculated value of F is
Q4) In a study of protein breakfast bars, five bars from each of three brands were tested to see if the mean amount of protein per bar differs among the brands. To select a critical F-statistic, the number of degrees of freedom for the numerator is _____.
Q5) The shape of the F distribution is _____________________.
Q6) ANOVA requires that the populations should be ______, ______, and have _____.
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Q7) The minimum and maximum of values of an F statistic are _______ and ______.
Chapter 13: Correlation and Linear Regression
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Q1) Which of the following are true assumptions underlying linear regression? (1) For each value of X, there is a group of Y values that is normally distributed.
(2) The means of these normal distributions of Y values all lie on the regression line.
(3) The standard deviations of these normal distributions are equal.
A) Only (1)
B) Only (2)
C) Only (3)
D) All of them
Q2) The regression equation is used to estimate a value of the dependent variable Y based on a selected value of the independent variable X.
A)True
B)False
Q3) The minimum and maximum values of the coefficient of determination are ________.
Q4) Because the coefficient of determination is expressed as a percent, its value is between 0% and 100%.
A)True
B)False
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Chapter 14: Multiple Regression Analysis
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Q1) A variable that can assume only one of two possible outcomes that take on the values of either 0 or 1, and is used to incorporate the effect of qualitative variables in a regression model is referred to as ________.
A) a dummy variable
B) a constant endogenous variable
C) an interaction
D) a constant
Q2) A multiple regression model includes the term (X<sub>1</sub>)(X<sub>2</sub>). If the hypothesis is that the term's regression coefficient is NOT rejected, what is a valid conclusion?
A) The independent variables are correlated.
B) There is only one independent variable in the regression model.
C) The effect of X<sub>1</sub> on the dependent variable is independent of the value of X<sub>2</sub>.
D) The effect of X<sub>1</sub> on the dependent variable depends on the value of X<sub>2</sub>.
Q3) In multiple regression analysis, the ________ scale is used to measure a dummy variable.
Q4) In multiple regression, the form of the global hypothesis test is ____________.
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Chapter 15: Nonparametric Methods: Nominal Level
Hypothesis Tests
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Q1) If we wanted to see if tossing a die (a cube with the sides numbered one through six) had an equal chance of showing each side or number, what statistical test should be applied?
Q2) Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the alternate hypothesis?
A) H<sub>1</sub>: = 0.36
B) H<sub>1</sub>: = 0.41
C) H<sub>1</sub>: 0.41
D) H<sub>1</sub>: µ 0.41
Q3) In the goodness-of-fit test, the chi-square distribution is used to determine how well an observed distribution of observations "fits" an expected distribution of observations.
A)True
B)False
Q4) To verify that a frequency distribution for sample data is normally distributed, the expected frequencies are computed using probabilities from a _____________ distribution.
Q5) The shape of the chi-square distribution is _________________.
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Chapter 16: Nonparametric Methods: Analysis of Ordinal
Data
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Q1) Fifty-five voters from a sample of 80 indicated that they favored casino gambling in their city. The city council is interested in finding out whether or not there is a significant difference between the proportions of those favoring and not favoring casino gambling in their community. The test statistic is ______.
A) 0.50
B) 3.71
C) 80
D) 3.24
Q2) When testing H<sub>0</sub>: Median equals $12.40 and the alternate hypothesis: Median does not equal $12.40, what is the critical value of z at the 10% level of significance?
A) ±1.96
B) ±1.65
C) ±2.33
D) ±0.10
Q3) The _____________ of the differences between "before and after" measurements is evaluated in a Wilcoxon signed-rank test.
Q4) In the Kruskal-Wallis method, testing for differences among populations is based on the sum of the ________.
Page 18
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Chapter 17: Index Numbers
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Q1) The purpose of an index is to _____________________________________.
Q2) Suppose your annual 2005 salary was $95,000 and your 2010 salary was $125,000. Assume the annual CPI rose from 177.1 to 215.9 during this period of time. What was your real income in 2005?
Q3) Another name for the unweighted method of computing an index is the _________________.
Q4) What does a typical market basket of goods and services include?
A) Bread
B) Beer
C) Milk
D) All of these
Q5) Suppose your annual 2001 salary was $40,000 and your 2006 salary was $52,000. Assume the annual CPI rose from 177.1 to 202.9 during this period of time. What was the purchasing power of the dollar in 2006?
Q6) Cost-of-living adjustments are based on the _______________________.
Q7) Suppose your annual 2005 salary was $95,000 and your 2010 salary was $125,000. Assume the annual CPI rose from 177.1 to 215.9 during this period of time. What was your real income in 2010?
Q8) Another term for real income is _______________.
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Chapter 18: Time Series and Forecasting
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Q1) The forecast for the third quarter is 1,000 units; the seasonal index for the quarter is 0.85. What are the seasonally adjusted sales for the quarter?
A) 1,085
B) 850
C) 985
D) 1,015
Q2) Why are long-range predictions considered essential to managing a firm?
A) To develop plans for possible new plants
B) To have raw materials available for future demand
C) To develop plans for future financing
D) All of these
Q3) If the exports (in $millions) for the period 2006 through 2010 were $878, $892, $864, $870, and $912, respectively, what are these values called?
A) Moving average
B) Linear trend equation
C) Logarithmic trend equation
D) Time series data
Q4) A graph of a deseasonalized time series does NOT show ________.
Q5) Autocorrelation in a time series can be tested using the ___________.
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Chapter 19: Statistical Process Control and Quality Management
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Q1) A major distributor buys shoes from a supplier. The distributor randomly samples the shoes to inspect for quality. The distributor's specifications state that a delivery of 100 pairs of shoes will be accepted only if the number of defective pairs of shoes in a sample of 10 pairs is two or less. Based on the sampling plan, what is the probability of accepting the delivery of 100 pairs of shoes if the actual percent defective is 0.05?
Q2) In a control chart, expected variation is defined by the:
A) standard deviation.
B) standard error of the distribution.
C) upper control limits only.
D) upper and lower control limits.
Q3) Control charts can be developed for both variables and attributes.
A)True
B)False
Q4) The cause-and-effect chart is an example of a: A) range chart.
B) Pareto chart.
C) control chart.
D) fishbone diagram.
Q5) Another name for the p-bar chart is the ______________.
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Chapter 20: An Introduction to Decision Theory
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Q1) The maximin strategy is a __________ strategy for decision making.
Q2) The manager of Paul's fruit and vegetable store is considering the purchase of a new seedless watermelon from a wholesale distributor. Since this seedless watermelon costs $4, will sell for $7, and is highly perishable, he only expects to sell between six and nine of them. Based on a maximin decision strategy, what alternative is selected?
A) Order 6
B) Order 7
C) Order 8
D) Order 9
Q3) Statistical decision theory is defined as the collection of techniques a decision maker can apply to choose the best alternative action.
A)True
B)False
Q4) The maximax strategy is an ________ strategy for decision making.
Q5) Optimists advocate a maximin strategy.
A)True
B)False
Q6) In a payoff table, another name for alternatives is _______.
Q7) In decision theory, a payoff is expressed as a profit or a ______.
Page 22
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