Operations Research
Practice Exam
Course Introduction
Operations Research is an interdisciplinary field that utilizes mathematical modeling, statistical analysis, and optimization techniques to aid in decision-making and problem-solving within complex organizations. The course covers fundamental concepts such as linear programming, network flows, queuing theory, inventory models, simulation, and project management. By applying these analytical methods, students learn to formulate and solve real-world problems in areas such as logistics, manufacturing, transportation, and service systems, ultimately enhancing efficiency and effectiveness in operational processes.
Recommended Textbook
Statistics for Management and Economics 11th Edition by Gerald Keller
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Page 2
Chapter 1: What Is Statistics
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Q1) What name do we give to a descriptive measure of a population?
Answer: A parameter.
Q2) A resort employs 3,500 managers and staff.To ascertain their employees' opinions of a proposed health insurance plan,350 employees are surveyed at random.The proportion of the 350 employees who favor the health insurance plan represents a parameter in this scenario.
A)True
B)False
Answer: False
Q3) A descriptive measure that is computed from a sample is called a statistic.
A)True
B)False
Answer: True
Q4) In a sample of 350 students selected from a large college of business,25% are found to be marketing majors.The 25% is a statistic.
A)True
B)False
Answer: True
Q5) What name do we give to a descriptive measure of a sample?
Answer: A statistic.
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Chapter 2: Graphical Descriptive Techniques 1
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Q1) A pie chart is used to represent ____________________ data.
Answer: nominal categorical qualitative
Q2) We can summarize nominal data in a table that presents the categories and their counts.This table is called a(n)____________________ distribution.
Answer: frequency
Q3) Which situation identifies when to use pie charts and/or bar charts?
A)You want to describe a single set of data.
B)Your data is nominal.
C)You want to show the number or the percentage of individuals in each category.
D)All of these choices are true.
Answer: D
Q4) The Chief of Police conducted a survey of the officers on his squad.An officer's shooting score at target practice is an example of a(n)____________________ variable.
Answer: interval quantitative numerical
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Chapter 3: Graphical Descriptive Techniques 2
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Q1) Which of the following is the method statisticians use to draw the best fitting straight line through the data on a scatter diagram?
A)The fit best method.
B)The least squares method.
C)The point-intercept method.
D)None of these choices.
Answer: B
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) A(n)____________________ is a graphical display consisting of a set of points,each point representing one variable measured along the horizontal axis,and another variable measured along the vertical axis.
Answer: scatter diagram
Q4) A graph of the frequency distribution for interval data is called a(n)____________________.
Answer: histogram
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Chapter 4: Numerical Descriptive Techniques
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Q1) There are three measures of central location; the mean,the ____________________,and the ____________________.
Q2) If the observations are in the millions,a standard deviation of 10 would be considered small.If the observations are all less than 50,a standard deviation of 10 would be considered large.
A)True
B)False
Q3) Generally speaking,if two variables are unrelated (as one increases,the other shows no pattern),the covariance will be:
A)a large positive number.
B)a large negative number.
C)a positive or negative number close to zero.
D)None of these choices.
Q4) {Ages of Retirees Narrative} Describe the shape of the distribution of ages by comparing the quartiles.
Q5) The ____________________ measures the spread between the middle 50% of the observations.
Q6) {Ages of Retirees Narrative} Calculate the third quartile of the ages of the uninsured retirees.
Page 6
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Chapter 5: Data Collection and Sampling
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Q1) A simple random sample is chosen in such a fashion that every possible subset of the same size has an equal chance of being selected.
A)True
B)False
Q2) The Chairman of a College of Business with five departments wants to estimate the average number of student-hours lost per month due to illness of their professors.Describe a sampling plan that will help the Dean compare the average student-loss hours for the five departments.
Q3) Excluding some members of the target population results in ____________________ bias.
Q4) List one advantage and one disadvantage of a personal interview as a method of data collection.
Q5) Selection bias is a systematic tendency to favor including individuals with particular characteristics,while excluding individuals with other characteristics. A)True
B)False
Q6) {Soft Drink Narrative} Is this study observational or experimental? Explain.
Q7) Briefly describe three types of nonsampling errors.
Page 7
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Chapter 6: Probability
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Q1) {Cysts Narrative} In the absence of any test,what is the probability that the cyst is benign?
Q2) Posterior probability of an event is the revised probability of the event after new information is available.
A)True
B)False
Q3) The ____________________ rule is used to calculate the joint probability of two events.
Q4) {Certification Test Narrative} If the selected candidate passed the test,what is the probability that the candidate took the test at location B?
Q5) {Mutual Fund Price Narrative} Which approach was used to produce this figure?
Q6) {Certification Test Narrative} What is the probability that the selected candidate passed the test?
Q7) {Hobby Shop Sales Narrative} What approach would you use in determining the probabilities for next week's sales? Assign probabilities to the outcomes.
Q8) {Drunk Drivers Narrative} Given alcohol was involved,what proportion of accidents involved a single vehicle?
Page 8
Q9) {Marital Status Narrative} Develop the joint probability table.
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Chapter 7: Random Variables and Discrete Probability
Distributions
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Q1) {Shopping Outlet Narrative} Find the variance and standard deviation of the number of stores entered.
Q2) {Montana Highways Narrative} Find the expected number of vehicles that are traveling on Montana highways and exceeding the speed limit.
Q3) {Katie's Portfolio Narrative} Compute the expected value of the portfolio composed of 30% stock 1 and 70% stock 2.
Q4) The variance of the sum always equals the sum of the variances.
A)True
B)False
Q5) A function or rule that assigns a numerical value to each outcome of an experiment is called:
A)a sample space.
B)a probability distribution.
C)a random variable.
D)None of these choices.
Q6) {Montana Highways Narrative} Find P(4 < X < 9).
Q7) A probability distribution for a single random variable is referred to as a(n)____________________ distribution.
Q8) {Number of Horses Narrative} Find the variance and standard deviation of X. Page 9
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Chapter 8: Continuous Probability Distributions
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Q1) {IT Graduates Salary Narrative} What is the probability of a new graduate getting a starting salary in excess of $55,000?
Q2) {Phone Orders Narrative} What is the probability that a randomly selected caller is placed on hold for fewer than 6 minutes?
Q3) If the random variable X is exponentially distributed with parameter = 1.5,then the probability P(2 X 4),up to 4 decimal places,is
A)0.6667
B)0.0473
C)0.5000
D)0.2500
Q4) {Waiting Time Narrative} What is the probability density function for this uniform distribution?
Q5) The sum of all values of f(x)over the range of [a,b] must equal one.
A)True B)False
Q6) {Phone Orders Narrative} What proportion of callers are put on hold longer than 3 minutes?
Q7) P(1 < Z < 2)= P(Z < 2) ____________________.
Page 11
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Chapter 9: Sampling Distributions
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Q1) As a general rule in computing the standard error of the sample mean,the finite population correction factor is used only if the:
A)sample size is smaller than 5% of the population size.
B)sample size is greater than 5% of the sample size.
C)sample size is more than half of the population size.
D)None of these choices.
Q2) {Temporary Worker Productivity Narrative} What is the probability that in any single day worker 1 will outproduce worker 2?
Q3) Given that X is a binomial random variable with very large n,the binomial probability P(X 5)is approximated by the area under a normal curve to the right of
A)4.5
B)5.5
C)4
D)6
Q4) In general,the binomial probability P(X x)is approximated by the area under the normal curve to the left of x + .5.
A)True
B)False
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Chapter 10: Introduction to Estimation
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Q1) An unbiased estimator is said to be consistent if the difference between the estimator and the parameter grows larger as the sample size grows larger.
A)True
B)False
Q2) It is desired to estimate the average total compensation of CEOs in the publishing industry.Data were randomly collected from 18 CEOs and 95% confidence interval was calculated to be ($2,190,000,$4,720,000).Based on the interval above,do you believe the actual average total compensation of CEOs in the publishing industry could be $3,000,000?
A)Yes,and I am sure of that.
B)Yes,and I am 95% confident of that.
C)No,and I am sure of that.
D)No,and I am 95% confident of that.
Q3) The sample ____________________ is an unbiased estimator for the population mean.
Q4) The sampling error for a confidence interval is also defined as the ____________________ of ____________________.
Q5) An unbiased estimator is ____________________ if its variance gets smaller as n gets larger.
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Chapter 11: Introduction to Hypothesis Testing
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Q1) Suppose that 9 observations are drawn from a normal population whose standard deviation is 2.The observations are: 15,9,13,11,8,12,11,7,and 10.At 95% confidence,you want to determine whether the mean of the population from which this sample was taken is significantly different from 10.
a.State the null and alternative hypotheses.
b.Compute the value of the test statistic.
c.Compute the p-value.
d.Interpret the results.
Q2) {Production Filling Narrative} Using a standardized test statistic,test the hypothesis at the 5% level of significance if the sample mean filling weight is 48.6 ounces.
Q3) {Watching the News Narrative} Determine the p-value.
Q4) {LSAT Scores Narrative} Use the p-value to test the hypotheses.
Q5) You cannot commit a(n)____________________ error when the null hypothesis is true.
Q6) The hypothesis testing procedure begins with the assumption that the null hypothesis is ____________________.
A)True
B)False
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Chapter 12: Inference About a Population
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Q1) {Tractor Dealership Narrative} Estimate with 95% confidence the total amount of monetary error for the month of July.
Q2) {Physicians Narrative} Construct a 99% confidence interval estimate of the population proportion of physicians who make at least $400,000 a year,and explain how to use it to test the hypotheses.
Q3) In order to determine the p-value associated with hypothesis testing about the population mean ,it is necessary to know the value of the test statistic.
A)True
B)False
Q4) The degrees of freedom for the test statistic for when is unknown is:
A)1
B)n
C)n 1
D)None of these choices.
Q5) The 95% confidence interval would indicate that,for this shipment,the proportion of defective fuses is between 0 and 0.28.
A)True
B)False
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Chapter 13: Inference About Comparing Two Populations
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Q1) In testing the difference between the means of two normally distributed populations,the number of degrees of freedom associated with the unequal-variances t-test statistic usually results in a non-integer number.It is recommended that you: A)round to the nearest integer.
B)change the sample sizes until the number of degrees of freedom becomes an integer. C)assume that the population variances are equal,and then use df = n<sub>1</sub> + n<sub>2</sub> 2.
D)None of these choices.
Q2) The expected value of the difference between two sample proportions is the difference between their corresponding population proportions. A)True B)False
Q3) The pooled variance estimator is the ____________________ average of the two sample variances.
Q4) The test statistic for testing for the equality of two population variances has an F-distribution with ____________________ and ____________________ degrees of freedom.
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16
Chapter 14: Analysis of Variance
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Sample Questions
Q1) Tukey's multiple comparison method is more powerful than Fisher's LSD Method at finding differences in pairwise population means.
A)True
B)False
Q2) Which of the following statements about multiple comparison methods is false?
A)They are to be use once the F-test in ANOVA has been rejected.
B)They are used to determine which particular population means differ.
C)There are many different multiple comparison methods but all yield the same conclusions.
D)All of these choices are true.
Q3) Which of the following components in an ANOVA table is not additive?
A)Sum of squares
B)Degrees of freedom
C)Mean squares
D)All of these choices are additive.
Q4) The equation: SS(Total)= SS(A)+ SS(B)+ SS(AB)+ SSE applies to which ANOVA model?
A)One-way ANOVA with 2 treatments.
B)Two-factor ANOVA with interaction.
C)Two-factor ANOVA with no interaction.
D)None of these choices.
Page 17
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Chapter 15: Chi-Squared Tests
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Q1) If you want to compare two populations that each have more than two categories,you can use a chi-squared test of a(n)____________________.
Q2) If two events A and B are independent,the P(A and B)= P(A)+ P(B).
A)True
B)False
Q3) There are two critical factors in identifying the technique used when the data are nominal.The first is the problem objective.The second is the number of ____________________ that nominal variable can assume.
Q4) The chi-squared distribution is used in:
A)a goodness-of-fit test.
B)a test of a contingency table.
C)describing a population having more than two categories.
D)All of these choices are true.
Q5) The expected values of a contingency table are calculated based on the assumption that H<sub>0</sub> is ____________________.
Q6) The rule of ____________________ states that in order to conduct the chi-squared goodness-of-fit test,the expected value for each cell must be ____________________ or more.
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Chapter 16: Simple Linear Regression and Correlation
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Q1) Data that exhibit an autocorrelation effect violate the regression assumption of independence.
A)True
B)False
Q2) There is ____________________ error in estimating a mean than in predicting an individual value.
Q3) In simple linear regression,the coefficient of correlation r and the least squares estimate b<sub>1</sub> of the population slope <sub>1</sub>:
A)must be equal.
B)must have the same sign.
C)are not related.
D)None of these choices.
Q4) {Income and Education Narrative} Determine the least squares regression line.
Q5) {UV's and Skin Cancer Narrative} Calculate the Pearson coefficient.What sign does it have? Why?
Q6) For a regression analysis to be valid,the value of the error variable associated with any particular value of y is ____________________ of the value of the error variable associated with any other value of y.
Q7) {Cost of Textbooks Narrative} Determine the least squares regression line.
Page 19
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Chapter 17: Multiple Regression
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Q1) The parameter estimates are biased when multicollinearity is present in a multiple regression equation.
A)True
B)False
Q2) {Student's Final Grade Narrative} Interpret the coefficient b<sub>1</sub>.
Q3) An adverse effect of multicollinearity is that the estimated regression coefficients of the independent variables that are correlated tend to have large sampling
Q4) A multiple regression model involves 40 observations and 4 independent variables produces a total variation in y of 100,000 and SSR = 80,400.Then,the value of MSE is 560.
A)True
B)False
Q5) {Real Estate Builder Narrative} What percentage of the variability in house size is explained by this model?
Q6) To use the Durbin-Watson test to test for positive first-order autocorrelation,the null hypothesis will be H<sub>0</sub>: ____________________ (there is/there is no)first-order autocorrelation.
Q7) {Real Estate Builder Narrative} Interpret the value of the Adjusted R-Square.
Page 20
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Chapter 18: Model Building
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Q1) {Hockey Teams Narrative} Predict the winning percentage for a hockey team with an average of 6 years of professional experience.
Q2) The model y = <sub>0</sub> + <sub>1</sub>x<sub>1</sub> + <sub>2</sub>x<sub>2</sub> + <sub>3</sub>x<sub>1</sub>x<sub>2</sub> + is referred to as a:
A)first-order model with two predictor variables with no interaction.
B)first-order model with two predictor variables with interaction.
C)second-order model with three predictor variables with no interaction.
D)second-order model with three predictor variables with interaction.
Q3) The model y = <sub>0</sub> + <sub>1</sub>x + <sub>2</sub>x<sup>2</sup> + is referred to as a:
A)simple linear regression model.
B)first-order model with one predictor variable.
C)second-order model with one predictor variable.
D)third order model with two predictor variables.
Q4) The model y = <sub>0</sub> + <sub>1</sub>x<sub>1</sub> + <sub>2</sub>x<sub>2</sub> + <sub>3</sub>x<sub>1</sub>x<sub>2</sub> + is a(n)____________________-order polynomial model with ____________________ predictor variables and ____________________.
Q5) {Silver Prices Narrative} Interpret the coefficient b<sub>1</sub>.
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Chapter 19: Nonparametric Statistics
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Q1) The Friedman test applies to which situation?
A)When the problem objective is to compare two or more populations.
B)The data are either ordinal or interval but not nominal.
C)The data are generated from a randomized block experiment.
D)All of these choices are true.
Q2) Statistical methods that require few assumptions,if any,about the population distribution are known as parametric techniques.
A)True
B)False
Q3) {Song Ratings Narrative} What statement can be made about the p-value for this test?
Q4) The Wilcoxon rank sum test statistic T is approximately normally distributed whenever the sample sizes are larger than:
A)25
B)20
C)15
D)10
Q5) {Airlines Ranking Narrative} Can we conclude at the 5% significance level that there are differences in service quality among the four airlines?
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Chapter 20: Time-Series Analytics and Forecasting
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Q1) The mean absolute deviation averages the absolute differences between the actual values of the time series at time t and the forecast values at time:
A)t + 1
B)t
C)t 1
D)t 2
Q2) If we want to measure the seasonal variations on stock market performance by month,we would need:
A)50 indicator variables since the stock market has a 5-day work per week
B)12 indicator variables to represent the 12 months
C)11 indicator variables
D)52 indicator variables
Q3) If we want to measure the seasonal variations on stock market performance by quarter,we would need:
A)4 indicator variables
B)3 indicator variables
C)2 indicator variables
D)1 indicator variable
Q4) {Carpet Outlet Narrative} What do the daily indexes tell us?
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Chapter 21: Statistical Process Control
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Q1) If a machine part is slowly losing its ability to work,causing the standard deviation of the process to increase,this is an example of assignable variation called a trend.
A)True
B)False
Q2) A malfunction in the process goes unnoticed and later causes great expense in terms of operator and machine downtime.What type of error was caused here and how could it be decreased?
Q3) In statistical process control,a Type I error occurs if we conclude that the process is not in control when it actually is and requires that production is temporarily stopped.
A)True
B)False
Q4) The p chart is an example of control charts for attributes. A)True B)False
Q5) If a control chart finds the standard deviation in the means is increasing,this could be an indicator of assignable variation called ____________________.
Q6) Discuss what we mean by assignable variation in a process and give an example.
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Chapter 22: Decision Analysis
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Q1) {Container Company Narrative} Which decision has the minimum expected opportunity loss?
Q2) {Gross Profits Narrative} If the probability of s<sub>1</sub> is 0.4,then the probability of s<sub>2</sub> is______________.
Q3) The objective of a preposterior analysis is to determine whether the value of the prediction is greater or less than the cost of the information.
A)True
B)False
Q4) {Hobby Shop Narrative} Determine the EOL decision.
Q5) {Car Audio Store Narrative} What is the expected value of perfect information?
Q6) In making decisions,we choose the decision with the largest expected monetary value,or the smallest expected opportunity loss.
A)True
B)False
Q7) {Car Audio Store Narrative} What is the expected payoff with perfect information?
Q8) {Video Business Narrative} Convert the payoff table to an opportunity loss table.
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Chapter 23: Conclusion
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Q1) The width of a confidence interval ____________________ when more data is collected.
Q2) Which of the following is an example of interval data?
A)The weight of a newborn baby.
B)The gender of a baby.
C)Whether or not a baby weighs more than 10 pounds.
D)Your order of preference of three baby names.
Q3) The standard normal distribution and the Chi-squared distribution are related to each other.
A)True
B)False
Q4) In any hypothesis test there are two possible errors,called ____________________ and ____________________.
Q5) Formulas for confidence intervals and test statistics all come from ____________________ distributions.
Q6) If the difference between our test statistic and the null hypothesis is large,we reject the ____________________ hypothesis.
Q7) We can improve the exactitude of a confidence interval estimator by increasing the
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