Operations Research
Test Preparation
Course Introduction
Operations Research is a discipline that deals with the application of advanced analytical methods to help make better decisions. The course introduces students to modeling techniques, optimization methods, and quantitative tools used for solving problems in areas such as logistics, production, scheduling, transportation, and resource allocation. Key topics include linear programming, network flows, dynamic programming, queuing theory, and simulation. Through real-world examples and case studies, students learn to formulate problems, develop models, interpret solutions, and use computational tools, preparing them for decision-making roles in engineering, business, and public management.
Recommended Textbook
Statistics for Management and Economics 11th Edition by Gerald Keller
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Chapter 1: What Is Statistics
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Sample Questions
Q1) How do confidence levels compare to significance levels?
A)Confidence levels and significance levels are both typically small.
B)Confidence levels and significance levels are both typically large.
C)Confidence levels are typically small and significance levels are typically large.
D)Confidence levels are typically large and significance levels are typically small.
Answer: D
Q2) Which of the following represents a population,as opposed to a sample?
A)2,000 respondents to a magazine survey which has 600,000 subscribers.
B)The first 15 students in your class completing a final exam.
C)Every fourth student to arrive at the book store on your campus.
D)All registered voters in the state of West Virginia
Answer: D
Q3) What name do we give to a descriptive measure of a sample?
Answer: A statistic.
Q4) A descriptive measure of a population is called a parameter.
A)True
B)False
Answer: True
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Chapter 2: Graphical Descriptive Techniques 1
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Sample Questions
Q1) Interval data,such as heights,weights,incomes,and distances,are also referred to as quantitative or numerical data.
A)True
B)False
Answer: True
Q2) {Business School Graduates Narrative} How many graduates were surveyed?
Answer: 200; you get this by totaling the counts for each major.
Q3) Give an example of interval data that can also be treated as ordinal data and nominal data.
Answer: Example: Your actual age is interval data; your age group (1-17; 18-24; 25-30; etc.)is ordinal data; and whether or not you are over age 25 is nominal data.
Q4) Identify the type of data for which each of the following graphs is appropriate.a.Pie chartb.Bar chart
Answer: a. Nominal
b. Nominal
Q5) All calculations are permitted on interval data.
A)True
B)False
Answer: True
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Chapter 3: Graphical Descriptive Techniques 2
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Sample Questions
Q1) A(n)____________________ histogram is one with a long tail extending to either the right or the left.
Answer: skewed
Q2) {Home Care Narrative}Which graph do you think is the most appropriate display? Justify your answer.
Answer: Histogram 1 seems to give the fairest representation.It fills up the space,starts at 0,and goes by increments of 2.This histogram appears more neutral than the other two.
Q3) Which of the following statements illustrates graphical deception?
A)Absolute changes,rather than percentage changes are reported.
B)To reduce clutter,the scales of the axes are not shown.
C)The Y-axis is stretched or shrunk to show the data in their best possible light.
D)All of these choices are true.
Answer: D
Q4) In a histogram a(n)____________________ class is the one with the largest number of observations.
Answer: modal
Q5) A graph showing trends over time is called a(n)____________________ chart. Answer: line
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Chapter 4: Numerical Descriptive Techniques
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Sample Questions
Q1) The interquartile range will always exceed that of the range.
A)True
B)False
Q2) Consider the following population of measurements: 162,152,177,157,184,176,165,181,170,and 163.Label and compute the variance and standard deviation.
Q3) If two data sets have the same standard deviation,they must have the same coefficient of variation.
A)True
B)False
Q4) In a histogram,the proportion of the total area which must be to the right of the mean is exactly 0.50 if the distribution is symmetric and unimodal.
A)True
B)False
Q5) The advantage that the coefficient of correlation has over the covariance is that the former has a set lower and upper limit.
A)True
B)False
Q6) The ____________________ is the square root of the
6
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Chapter 5: Data Collection and Sampling
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Sample Questions
Q1) A researcher conducts a study where she divides subjects into two groups,gives each group a certain treatment, and records their responses.What type of data collection is being used here?
A)An experiment.
B)Direct observation.
C)A survey.
D)A census.
Q2) Give three important points to consider when designing a questionnaire.
Q3) A self-selected sample represents the sampled population but not the target population.
A)True
B)False
Q4) Excluding some members of the target population results in ____________________ bias.
Q5) In a(n)____________________ study,there is no attempt to control factors that might influence the variable of interest.
Q6) A sampling error can be reduced by taking a larger sample size.
A)True
B)False
Q7) Briefly describe three types of nonsampling errors.
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Chapter 6: Probability
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Sample Questions
Q1) {Financial Consultants Narrative} Find P(A and B).
Q2) Two events A and B are said to be independent if P(A|B)= P(B|A).
A)True
B)False
Q3) If A and B are independent events with P(A)= .40 and P(B)= .50,then P(A and B)= .20.
A)True
B)False
Q4) There are three approaches to determining the probability that an outcome will occur: classical,relative frequency,and subjective.For each situation that follows,determine which approach is most appropriate.
a.A Russian will win the French Open Tennis Tournament next year.
b.The probability of getting any single number on a balanced die is 1/6.
c.Based on the past,it's reasonable to assume the average book sales for a certain textbook is 6,500 copies per month.
Q5) The outcomes of a sample space must be ____________________ and ____________________.
Q6) {Hobby Shop Sales Narrative} Define the random experiment of interest to the store.
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Chapter 7: Random Variables and Discrete Probability
Distributions
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Q1) {Stress Narrative} Find P(2 X 4).
Q2) The number of days that a microcomputer goes without a breakdown is an example of a(n)____________________ random variable.
Q3) {Stress Narrative} Find the probability distribution of X.
Q4) {Returns on Investment Narrative} Find the mean of the return on a portfolio consisting of an equal investment in each of the two stocks.
Q5) {Number of Birds Narrative} Compute the mean and variance of Y.
Q6) {Elizabeth's Portfolio Narrative} Compute the standard deviation of the returns on the portfolio assuming that the two stocks' returns are perfectly positively correlated.
Q7) {Katie's Portfolio Narrative} If Katie is most interested in maximizing her returns,which stock should she choose?
Q8) {Number of Birds Narrative} Compute the coefficient of correlation between X and Y.Did you expect this result? Why?
Q9) {Number of Birds Narrative} Compute the mean and variance of X.
Q10) {Risky Undertaking Narrative} Find the expected value of the net profit from your investment of $2,000.
Q11) {Golfing Store Narrative} Calculate the expected values of X and Y. Page 9
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Chapter 8: Continuous Probability Distributions
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Sample Questions
Q1) The mean of an exponential random variable is ____________________ the median.
Q2) {Diet Narrative} What proportion of the dieters gained weight?
Q3) As the degrees of freedom approach infinity,the values of a Student t distribution approach those of a standard normal distribution.
A)True
B)False
Q4) Which of the following distributions is not skewed?
A)Student t
B) <sup>2</sup>
C)F
D)All of these distributions are skewed.
Q5) P(Z < 3.00)is approximately ____________________.
Q6) Which of the following statements is correct regarding the percentile points of the F distribution?
A)F<sub>0.10,10,20</sub> = 1/F<sub>0.90,10,20</sub>
B)F<sub>0.90,10,20</sub> = 1/F<sub>0.10,20,10</sub>
C)F<sub>0.90,10,20</sub> = 1/F<sub>0.90,20,10</sub>
D)F<sub>0.10,10,20</sub> = 1/F<sub>0.10,20,10</sub>
Page 11
Q7) If X has an exponential distribution with parameter ,then f(0)=
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Chapter 9: Sampling Distributions
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Q1) {CFO's Salary Narrative} Find the standard error of the sample mean difference.
Q2) The standard error of the mean for a sample of 100 is 25.In order to cut the standard error of the mean in half (to 12.5)we must:
A)increase the sample size to 200.
B)decrease the sample size to 50.
C)keep the sample size at 100 and change something else.
D)None of these choices.
Q3) What is the probability that you get more than 200 heads if you flip a coin 400 times?
Q4) Suppose the ages of students in your program follow a positively skewed distribution with mean of 24 years and a standard deviation of 4 years.If we randomly sampled 100 students,which of the following statements about the sampling distribution of the sample mean age is NOT true?
A)The mean of the sampling distribution of sample mean is equal to 24 years.
B)The standard deviation of the sampling distribution of sample mean is equal to 4 years.
C)The shape of the sampling distribution of sample mean is approximately normal.
D)All of these choices are true.
Q5) {CFO's Salary Narrative} Find the expected value of the sample mean difference.
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Chapter 10: Introduction to Estimation
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Sample Questions
Q1) As the bound on the error of estimation decreases,the sample size
Q2) The letter in the formula for constructing a confidence interval estimate of the population mean is:
A)the level of confidence.
B)the probability that a particular confidence interval will contain the population mean.
C)the area in the lower tail of the sampling distribution of the sample mean.
D)None of these choices.
Q3) A financial consultant wanted to determine the mean annual return on Bond funds.A random sample of 60 returns shows a mean of 12%.If the population standard deviation is assumed to be 4%,estimate with 95% confidence the mean annual return on all Bond funds.
Q4) Suppose a sample size of 5 has mean 9.60.If the population variance is 5 and the population is normally distributed,the lower limit for a 92% confidence interval is 7.85.
A)True
B)False
Q5) The sample ____________________ is an unbiased estimator for the population mean.
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Chapter 11: Introduction to Hypothesis Testing
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Sample Questions
Q1) The probability of a Type II error is denoted by:
A)
B)
C)1
D)1
Q2) In a two-tail test for the population mean,the null hypothesis will be rejected at level of significance if the value of the standardized test statistic z is such that: A)z > z
B)z < z
C) z < z < z
D)| z | > z <sub> / 2</sub>
Q3) As the sample size increases,the operating characteristic curves drop down to zero at a(n)____________________ rate.
Q4) A two-tail test for the population mean produces a test-statistic z = 1.89.The p-value associated with the test is 0.0588. A)True B)False
Q5) {Toaster Oven Narrative} What is the parameter of interest in this situation?
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Chapter 12: Inference About a Population
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Sample Questions
Q1) {Single Mothers' Ages Narrative} What is the required condition of the techniques used in the previous questions? What graphical device can you use to check to see if that required condition is satisfied?
Q2) {Energy Drink Consumption Narrative} Formulate the null and alternative hypotheses.
Q3) {Applicants' Grades Narrative} Construct a 90% confidence interval estimate for the population variance.
Q4) {Healthy Foods Narrative} What is the point estimate of the proportion p of Spanish adults who classify themselves as concerned about eating healthy?
Q5) {Sinus Drug Narrative} Compute the p-value of the test.
Q6) The t-test for a population mean is ____________________,meaning that if the population is nonnormal,the results of the test and confidence interval are still valid as long as the nonnormality is not extreme.
Q7) Which of the following is an example illustrating the use of variance?
A)As a measure of risk.
B)As a judge of consistency.
C)To search for and reduce variability in a process.
D)All of these choices are true.
Page 15
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Chapter 13: Inference About Comparing Two Populations
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Sample Questions
Q1) Suppose we randomly selected 250 people,and on the basis of their responses to a survey we assigned them to one of two groups: high-risk group and low-risk group.We then recorded the blood pressure for the members of each group.Such data are called:
A)observational.
B)experimental.
C)matched.
D)None of these choices.
Q2) Which of the following statements is false for an F-distribution?
A)Variables that are F-distributed range from 0 to .
B)The exact shape of the distribution is determined by two numbers of degrees of freedom.
C)The degrees of freedom for the numerator can be larger than,smaller than,or equal to the degrees of freedom for the denominator.
D)All of these choices are true.
Q3) {Starting Salary Narrative} Estimate with 95% confidence the difference between the two population means.
Q4) {Profit Margin Narrative} Estimate with 95% confidence the ratio of the two population variances.
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Chapter 14: Analysis of Variance
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Sample Questions
Q1) When is the Tukey multiple comparison method used?
A)To test for normality.
B)To test for differences in pairwise means.
C)To test for equality of a group of population means.
D)To test equal variances.
Q2) {Keyboard Configuration and Size Narrative} Test at the 5% significance level to determine if time differences exist among the different keyboard configurations.
Q3) If you plan to compare all possible combinations of pairs of population means,the multiple comparison method to use is ____________________ method.
Q4) The F-statistic in a one-way ANOVA represents the variation within the treatments divided by the variation between the treatments.
A)True
B)False
Q5) In one-way ANOVA,the total variation SS(Total)is partitioned into two sources of variation: the sum of squares for treatments (SST)and the sum of squares for error (SSE).
A)True
B)False
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Chapter 15: Chi-Squared Tests
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Sample Questions
Q1) If we want to conduct a one-tail test of a population proportion,we can employ:
A)z-test of a population proportion.
B)the chi-squared test of a binomial experiment since z<sup>2</sup> = <sup>2</sup>.
C)the chi-squared test of a contingency table.
D)Both a and b
Q2) The alternative hypothesis in a chi-squared test of a contingency table is that the two nominal variables are ____________________.
Q3) If we square the value of z (the test statistic in the test of a proportion)we produce the ____________________ statistic.
Q4) In testing the difference between two proportions using the normal distribution,we may use either a one-tailed or two-tailed test.
A)True
B)False
Q5) The number of degrees of freedom associated with a chi-squared test of a contingency table is ____________________.
Q6) {Seat Belts Narrative} Prepare the table of expected values.
Q7) The values of a chi-squared distribution are always ____________________ zero.
Page 18
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Chapter 16: Simple Linear Regression and Correlation
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Q1) {Game Show Winnings & Education Narrative} Conduct a test of the population coefficient of correlation to determine at the 5% significance level whether a negative linear relationship exists between years of education and TV game shows' winnings.
Q2) {Trivia Games & Education Narrative} Estimate the game winnings for a contestant with 15 years of education.
Q3) {Rock Concert Revenues Narrative} Determine the coefficient of determination and discuss what its value tells you about the two variables.
Q4) {Grateful Dead Concert Narrative} Do the and <sub>1</sub> tests in the previous two questions provide the same results? Explain.
Q5) The coefficient of determination is equal to the coefficient of correlation squared. A)True B)False
Q6) The vertical spread of the data points about the regression line is measured by the y-intercept.
A)True
B)False
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Chapter 17: Multiple Regression
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Sample Questions
Q1) {Life Expectancy Narrative} Is there enough evidence at the 5% significance level to infer that the model is useful in predicting length of life?
Q2) In multiple regression analysis,the ratio MSR/MSE yields the:
A)t-test statistic for testing each individual regression coefficient.
B)F-test statistic for testing the validity of the regression equation.
C)coefficient of determination.
D)adjusted coefficient of determination.
Q3) Multicollinearity is present when there is a high degree of correlation between the dependent variable and any of the independent variables.
A)True
B)False
Q4) For a multiple regression model the following statistics are given: Total variation in y = 250,SSE = 50,k = 4,and n = 20.Then,the coefficient of determination adjusted for the degrees of freedom is:
A)0.800
B)0.747
C)0.840
D)0.775
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Chapter 18: Model Building
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Sample Questions
Q1) In order to represent a nominal variable with m categories,we must create m 1 indicator variables.
A)True
B)False
Q2) Regression analysis allows the statistics practitioner to use mathematical models to realistically describe relationships between the dependent variable and independent variables.
A)True
B)False
Q3) In order to represent 3 categories of a nominal variable,we need to create _______________ indicator variables.
Q4) {Motorcycle Fatalities Narrative} What is the multiple coefficient of determination? What does this statistic tell you about the model?
Q5) The last category represented by I<sub>1</sub> = I<sub>2</sub> = .....Im <sub>1</sub> = 0 is called the omitted category.
A)True
B)False
Q6) A second-order polynomial model is shaped like a(n)____________________.
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Chapter 19: Nonparametric Statistics
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Q1) The population Spearman correlation coefficient is labeled ____________________ and the sample statistic used to estimate its value is labeled ____________________.
Q2) A two-sample t-test is the parametric counterpart of the Wilcoxon signed rank sum test for matched pairs.
A)True
B)False
Q3) {Movie Scripts Narrative} What is the p-value of this test?
Q4) {Assessments of TV Shows Narrative} Can we infer at the 5% significance level that differences exist among the show's evaluations?
Q5) When the relationship between two variables is very strong and decreasing in a linear way,the Spearman rank-correlation coefficient will be close to:
A)0
B) 1 C) D)
Q6) When the Kruskal-Wallis test is used to test for a difference between two populations,it will produce the same outcome as the two-tail Wilcoxon ____________________ test.
Page 22
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Chapter 20: Time-Series Analytics and Forecasting
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Sample Questions
Q1) One measure of the accuracy of a forecasting model is the:
A)deseasonalized time series
B)four-period moving averages
C)mean absolute deviation
D)smoothing constant
Q2) Smoothing time series data by the moving average method or exponential smoothing method is an attempt to remove the effect of the:
A)trend component
B)cyclical component
C)seasonal component
D)random variation component
Q3) We compute the five-period moving averages for all time periods except the first two and last two time periods.
A)True
B)False
Q4) MAD stands for ____________________ absolute deviation.
Q5) It must be understood that the ____________________ of a forecast decreases rapidly for predictions more than one time period into the future.
Q6) {Microprocessors Narrative} Plot the percentage of trend.
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Chapter 21: Statistical Process Control
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Q1) ____________________ variation is caused by specific events or factors that are frequently temporary.
Q2) {30 Samples Production Narrative} Calculate the mean and standard deviation of each sample.
Q3) Discuss what we mean by assignable variation in a process and give an example.
Q4) The letter p in p chart stands for ____________________.
Q5) When no point lies outside the control limits of a chart,we conclude that variation in the process is:
A)caused by chance and there is not enough evidence to infer that the process is out of control.
B)caused by chance and there is enough evidence to infer that the process is out of control.
C)caused by assignable causes and there is enough evidence to infer that the process is under control.
D)caused by assignable causes and there is not enough evidence to infer that the process is out of control.
Q6) Describe what a Type I error is,and what its impact is,in terms of a production process.
Q7) {30 Samples Production Narrative} Construct an S chart.
Page 24
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Chapter 22: Decision Analysis
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Q1) {Demolition Company Narrative} Determine the EMV decision.
Q2) Worker safety laws would be considered a state of nature for a business firm.
A)True
B)False
Q3) {Maintenance Company Narrative} Use the prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome I<sub>2</sub>.
Q4) {Gross Profits Narrative} If the probability of s<sub>1</sub> is 0.5,then the expected opportunity loss (EOL)for a<sub>3</sub> is ____________________.
Q5) An opportunity loss is the difference between what the decision maker's profit for an act (alternative)is and what the profit could have been had the best decision been made.
A)True
B)False
Q6) {Lingerie Store Narrative} Calculate the expected value of perfect information.
Q7) {Video Business Narrative} Convert the payoff table to an opportunity loss table.
Q8) {Maintenance Company Narrative} What is the expected payoff with perfect information?
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Chapter 23: Conclusion
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Q1) Describe a plan for estimating the average GPA at your university by using inferential statistics.Include which statistical technique you plan to use to draw your conclusions.
Q2) There are three types of data: ____________________; ____________________; and ____________________.
Q3) Which of the following data collection methods is more likely to lead to a definitive conclusion?
A)Data collected through observation.
B)Data collected through an experiment.
C)Data collected through the use of volunteers.
D)Data collected through a survey.
Q4) The sampling distributions that are used for interval data are the Student-t and the:
A)Chi-squared distribution.
B)Binomial distribution.
C)Discrete distribution.
D)F-distribution.
Q5) To ensure the validity of a statistical technique,we must first check the required
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