Operations Management Statistics
Study Guide Questions
Course Introduction
Operations Management Statistics focuses on the application of statistical methods and analytical tools to optimize decision-making within operations management. The course covers topics such as data collection and analysis, probability distributions, hypothesis testing, process control, forecasting, and quality improvement. Students will learn how to use statistical software to model real-world operational problems, interpret results, and make data-driven recommendations that enhance efficiency and productivity in manufacturing and service organizations. The course emphasizes practical skills and critical thinking to address challenges in inventory management, resource allocation, and process optimization.
Recommended Textbook
Business Statistics Communicating with Numbers 3rd Edition by Sanjiv Jaggia
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Page 2
Chapter 1: Statistics and Data
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Sample Questions
Q1) The data represents the stock price for Google at the end of the past four quarters. Which of the following types of data best describe these values?
A) Cross-sectional
B) Nominal
C) Time series
D) Ordinal
Answer: C
Q2) The branch of statistical studies called inferential statistics refers to drawing conclusions about sample data by analyzing the corresponding population.
A)True
B)False
Answer: False
Q3) Which of the following characteristics does the interval scale not have?
A) Values can be categorized.
B) Values can be ranked.
C) There is a true zero point.
D) The differences between values are valid.
Answer: C
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Chapter 2: Tabular and Graphical Methods
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Sample Questions
Q1) A bar chart depicts the frequency or relative frequency of each category of qualitative data as a bar rising vertically from the horizontal axis. It is also acceptable for the bar to extend horizontally from the vertical axis.
A)True
B)False
Answer: True
Q2) What may be revealed from a scatterplot?
A) No relationship between two variables
B) A linear relationship between two variables
C) A curvilinear relationship between two variables
D) All of the above
Answer: D
Q3) When constructing a frequency distribution for quantitative data classes are mutually ________ and ________.
Answer: exclusive; exhaustive
Q4) A stem-and-leaf diagram most resembles a(n) ________.
Answer: histogram
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Chapter 3: Numerical Descriptive Measures
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Sample Questions
Q1) The coefficient of variation is a unit-free measure of dispersion.
A)True
B)False
Answer: True
Q2) Suppose the wait to pass through immigration at JFK Airport in New York is thought to be bell-shaped and symmetrical with a mean of 22 minutes. It is known that 68% of travelers will spend between 16 and 28 minutes waiting to pass through immigration. The standard deviation for the wait time through immigration is ________.
A) 6 minutes
B) 8 minutes
C) 9 minutes
D) 10 minutes
Answer: A
Q3) In quality control settings, businesses prefer a larger standard deviation, which is an indication of more consistency in the process.
A)True
B)False
Answer: False
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5
Chapter 4: Introduction to Probability
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Sample Questions
Q1) Alison has all her money invested in two mutual funds, A and B. She knows that there is a 40% chance that fund A will rise in price, and a 60% chance that fund B will rise in price given that fund A rises in price. What is the probability that both fund A and fund B will rise in price?
A) 0.24
B) 0.40
C) 0.76
D) 1.00
Q2) For two independent events A and B, the probability of their intersection is zero. A)True
B)False
Q3) The intersection of events A and B, denoted by A B, ________.
A) contains outcomes that are either in A or B
B) contains outcomes that are both in A and B
C) does not contain outcomes that are either in A or B
D) does not contain outcomes that are both in A and B
Q4) A(n) ________ ________ of an experiment records all possible outcomes of the experiment.
Q5) Probabilities can be expressed as fractions, percentages, and ________.
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Chapter 5: Discrete Probability Distributions
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Sample Questions
Q1) An Excel's function ________ is used for calculating Poisson probabilities.
Q2) What is a characteristic of the mass function of a discrete random variable X?
A) The sum of probabilities P(X = x) over all possible values x is 1.
B) For every possible value x, the probability P(X = x) is between 0 and 1.
C) Describes all possible values x with the associated probabilities P(X = x).
D) All of the above.
Q3) An urn contains 12 balls, five of which are red. The selection of a red ball is desired and is therefore considered to be a success. If a person draws three balls from the urn, what is the probability of two successes?
A) 0.1591
B) 0.3182
C) 0.6810
D) 0.8409
Q4) You have inherited a lottery ticket may be a $10,000 winner. You have a 0.25 chance of winning the $10,000 and a 0.75 chance of winning $0. You have an opportunity to sell the lottery ticket for $2,500. What is your expected return and what should you do if are risk averse?
Q5) A risk-averse consumer demands a(n) ________ expected gain as compensation for taking risk.
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Chapter 6: Continuous Probability Distributions
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Sample Questions
Q1) Find the variance of the lognormal variable if the mean and variance of the underlying normal variable are 2 and 1, respectively.
A) 0
B) 12.18
C) 15.97
D) 255.02
Q2) Cumulative distribution functions can only be used to compute probabilities for continuous random variables.
A)True
B)False
Q3) Suppose Jennifer is waiting for a taxicab. A taxicab's arrival time is equally likely at any constant time range in the next 12 minutes.
A) Compute the expected arrival time.
B) What is the probability that a taxi arrives in three minutes or less?
Q4) A normal random variable X has a mean of 17 and a variance of 5.
A) Find the value x for which P(X x) = 0.0020.
B) Find the value of x for which P(X > x) = 0.0122.
Q5) The z table provides ________ probabilities for positive and negative values of z.
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Page 8
Chapter 7: Sampling and Sampling Distributions
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Sample Questions
Q1) Selection bias occurs when ________.
A) the population has been divided into strata
B) portions of the population are excluded from the consideration for the sample
C) cluster sampling is used instead of stratified random sampling
D) those responding to a survey or poll differ systematically from the nonrespondents
Q2) Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis. Due to a decade-long rivalry between the Patriots and the city's own team, the Colts, most Indianapolis residents were rooting heartily for the Giants. Suppose that 90% of Indianapolis residents wanted the Giants to beat the Patriots. What is the probability that from a sample of 200 Indianapolis residents, fewer than 170 were rooting for the Giants in Super Bowl XLVI?
A) 0.0092
B) 0.0212
C) 0.4954
D) 0.9908
Q3) Stratified random sampling is preferred when the objective is to ________.
Q4) The ________ variation in the production process is caused by specific events or factors that can usually be identified and eliminated.
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Page 9
Chapter 8: Interval Estimation
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Sample Questions
Q1) A confidence interval is generally associated with a(n) ________.
Q2) Suppose taxi fare from Logan Airport to downtown Boston is known to be normally distributed with a standard deviation of $2.50. The last seven times John has taken a taxi from Logan to downtown Boston, the fares have been $22.10, $23.25, $21.35, $24.50, $21.90, $20.75, and $22.65. What is a 95% confidence interval for the population mean taxi fare?
A) [$17.46, $27.26]
B) [$20.46, $24.16]
C) [$20.80, $23.91]
D) [$21.66, $23.06]
Q3) In an examination of holiday spending (known to be normally distributed) of a sample of 16 holiday shoppers at a local mall, an average of $54 was spent per hour of shopping. Based on the current sample, the standard deviation is equal to $21. Find a 90% confidence interval for the population mean level of spending per hour.
A) [$44.83, $63.17]
B) [$44.79, $63.20]
C) [$45.36, $62.63]
D) [$46.96, $61.04]
Q4) The parameter p represents the ________ of successes in the population.
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10
Chapter 9: Hypothesis Testing
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Sample Questions
Q1) A Type II error occurs when we ________.
A) reject the null hypothesis when it is actually true
B) reject the null hypothesis when it is actually false
C) do not reject the null hypothesis when it is actually true
D) do not reject the null hypothesis when it is actually false
Q2) The Department of Education would like to test the hypothesis that the average debt load of graduating students with a bachelor's degree is equal to $17,000. A random sample of 34 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $4,200. The is set to 0.05. The p-value for this hypothesis test would be ________.
A) 0.1310
B) 0.0957
C) 0.0475
D) 0.0219
Q3) For a given sample size, any attempt to reduce the likelihood of making one type of error (Type I or Type II) will increase the likelihood of the other error.
A)True
B)False
Q4) The hypothesis statement H: < 60 is an example of a(an) ________ hypothesis.
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Chapter 10: Statistical Inference Concerning Two Populations
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Sample Questions
Q1) When constructing a confidence interval for the mean difference <sub>D</sub>, we follow the same general format of point estimate ± ________.
Q2) For a hypothesis test about the difference of two proportions, the standard error can be improved on when the hypothesized difference does not equal zero.
A)True
B)False
Q3) A recent Health of Boston report suggests that 14% of female residents suffer from asthma as opposed to 6% of males. Suppose 250 females and 200 males responded to the study. Which of the following is the correct value of the test statistics?
A) 1.76
B) 2.76
C) 2.76
D) 1.76
Q4) Two random samples are considered independent if the observations in the first sample are related to the observations in the second sample.
A)True
B)False
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Chapter 11: Statistical Inference Concerning Variance
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Sample Questions
Q1) How does the width of the interval respond to the changes in the confidence level?
A) The width of the interval decreases with an increase in the confidence level.
B) The width of the interval increases with an increase in the confidence level.
C) The width of the interval is halved with the increase in the confidence level.
D) The width of the interval is doubled with the decrease in the confidence level.
Q2) Consider the following hypotheses: H<sub>0</sub>: <sup>2</sup> = 169, H<sub>A</sub>: <sup>2</sup> 169
A sample variance of 98 is obtained from a random sample of 10 observations drawn from a normally distributed population. At 1% significance level, conduct a test for the population variance using the critical value approach.
Q3) The skewness of the chi-square distribution depends on the degrees of freedom.
A)True
B)False
Q4) Statistical inference for <sup>2</sup> is based on the F distribution.
A)True
B)False
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Chapter 12: Chi-Square Tests
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Sample Questions
Q1) The chi-square test statistic measures the difference between the observed frequencies and the expected frequencies assuming the null hypothesis is true.
A)True B)False
Q2) For the Jarque-Bera test for normality, the test statistic is assumed to have a chi-square distribution with two degrees of freedom.
A)True B)False
Q3) For a multinomial experiment with k categories, the goodness-of-fit test statistic is assumed to follow a chi-square distribution with k degrees of freedom.
A)True
B)False
Q4) When applying the goodness-of-fit test for normality, the data are divided into k non-overlapping intervals.
A)True B)False
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Chapter 13: Analysis of Variance
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Sample Questions
Q1) In a two-way ANOVA test, how many null hypotheses are tested?
A) 1
B) 1 or 2
C) 2 or 3
D) More than 3
Q2) For a two-way ANOVA with no interaction, which of the following is the correct formula for the error sum of squares SSE?
A) SSE = SST - (SSA + SSB + SSAB)
B) SSE = SST - (SSA - SSB)
C) SSE = SST + SSA + SSB
D) SSE = SST - (SSA + SSB)
Q3) If the interaction between two factors is not significant, the next tests to be done are
A) none, the analysis is complete
B) none, gather more data
C) tests about the population means of factor A or factor B using two-way ANOVA without interaction
D) Tukey's confidence intervals
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Chapter 14: Regression Analysis
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Sample Questions
Q1) The coefficient of determination R<sup>2</sup> is ________.
A) sometimes negative
B) always lower than adjusted R<sup>2</sup> <sup>
C) </sup>usually higher than adjusted R<sup>2</sup> <sup>
D) </sup>always equal to adjusted R<sup>2</sup>
Q2) Simple linear regression includes more than one explanatory variable.
A)True
B)False
Q3) The covariance and correlation coefficient are measures that quantify the non-linear relationship between two variables.
A)True
B)False
Q4) Simple linear regression analysis differs from multiple regression analysis in that ________.
A) simple linear regression uses only one explanatory variable
B) the coefficient of correlation is meaningless in simple linear regression
C) goodness-of-fit measures cannot be calculated with simple linear regression
D) the coefficient of determination is always higher in simple linear regression
Q5) The correlation coefficient captures only a ________ relationship.
Page 16
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Chapter 15: Inference With Regression Models
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Sample Questions
Q1) Serial correlation occurs when the error term is ________.
A) dispersed evenly
B) randomly distributed
C) correlated across observations
D) uncorrelated across observations
Q2) Consider the following simple linear regression model: y = <sub>0</sub> + <sub>1</sub>x + . When determining whether x significantly influences y, the null hypothesis takes the form ________.
A) H<sub>0</sub>: <sub>1</sub> = 0
B) H<sub>0</sub>: <sub>1</sub> = 1
C) H<sub>0</sub>: b<sub>1</sub> = 0
D) H<sub>0</sub>: b<sub>1</sub> = 1
Q3) If the variance of the error term is not the same for all observations, we ________.
A) get estimators that are biased
B) can perform tests of significance
C) cannot conduct tests of significance
D) Both get estimators that are biased and cannot conduct tests of significance are correct.
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Chapter 16: Regression Models for Nonlinear Relationships
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Sample Questions
Q1) Which of the following is a quadratic regression equation?
A) y = <sub>0</sub> +
B) y = <sub>0</sub> + <sub>1</sub>x +
C) y = <sub>0</sub> + <sub>1</sub>x + <sub>2</sub>x<sup>2</sup>+
D) y = <sub>0</sub> + <sub>1</sub>x + <sub>2</sub>x<sup>2</sup> + <sub>3</sub>x<sup>3</sup> +
Q2) The quadratic regression model allows for one change in ________.
Q3) How many coefficients need to be estimated in the quadratic regression model?
A) 4
B) 3
C) 2
D) 1
Q4) Although allowing for nonlinear trends, polynomials are still linear in the ________. A) response
B) explanatory variables
C) coefficients
D) none of these options
Q5) When not all variables are transformed with logarithms, the models are called ________ models.
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Chapter 17: Regression Models With Dummy Variables
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Sample Questions
Q1) Which of the following predictions can be described by a binary choice model?
A) Predict the day's temperature in degrees Fahrenheit.
B) Predict whether a student will pass or fail a test.
C) Predict today's price of gasoline per gallon in dollars.
D) Predict the rainfall in millimeters today.
Q2) In a model y = <sub>0</sub> + <sub>1</sub>x + <sub>2</sub>d + <sub>3</sub>xd + , the ________ F test for the joint significance of d and xd can be performed.
Q3) For the model y = <sub>0 </sub>+ <sub>1</sub>x + <sub>2</sub>d + , which test is used for testing the significance of a dummy variable d?
A) F test
B) chi-square test
C) z test
D) t test
Q4) Including as many dummy variables as there are categories is referred to as the dummy variable ________.
Q5) Variables employed in a regression model can be quantitative or qualitative.
A)True
B)False
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Chapter 18: Time Series and Forecasting
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Sample Questions
Q1) Smoothing techniques are suitable for use when forecasts need to be updated frequently due to new observations that become available.
A)True
B)False
Q2) Which of the following is a centered moving average?
A) The average of all moving averages in a series.
B) The average of all observations of a series.
C) The average of alternative moving averages in a series.
D) The average of two consecutive moving averages in a series.
Q3) In the time series decomposition method, to obtain the ________, we divide the original observations by their corresponding adjusted seasonal indices.
A) seasonal dummy variables
B) seasonally adjusted series
C) unadjusted seasonal indices
D) adjusted seasonal indices
Q4) A linear trend can be estimated using ________ technique.
Q5) To extract the trend from a time series, we first eliminate seasonal ________ by dividing the original series y, by its corresponding adjusted seasonal index.
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Chapter 19: Returns, Index Numbers, and Inflation
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Sample Questions
Q1) A ________ series is obtained by adjusting the given time series for changes in prices, or inflation.
Q2) Amy Peterson's annual salary when she started working in 2006 was $35,000. In 2011, her annual salary had increased to $44,000. Using 2006 as the base year, the consumer price index for 2011 was computed to be 112. Use this information to determine if Amy was better off in 2006 or in 2011.
Q3) Katie Jones started her career with an annual salary of $30,000 in 2006. Five years later, in 2011, her salary had increased to $55,000 a year. If the values of the CPI (with a base of 1982 1984) for 2006 and 2011 are 201.6 and 224.9, respectively, compute the increase in Katie's real income.
A) 64.34%
B) 83.33%
C) 105.31%
D) 164.34%
Q4) The aggregate price index is used to represent relative price movements for a group of items.
A)True
B)False
Q5) The Paasche index uses the ________ period quantities in deriving the weights.
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Chapter 20: Nonparametric Tests
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Sample Questions
Q1) The Kruskal-Wallis test is the nonparametric alternative to one-way ANOVA.
A)True
B)False
Q2) An airline claims that the median price of a round-trip ticket is less than $503. For a random sample of 400 tickets, the value of the Wilcoxon sign-ranks test is T = T<sup>+</sup> = 37,230.
A) Specify the competing hypothesis to determine whether the median ticket price is less than $503.
B) Assume the normal approximation for the distribution of T, and calculate the value of the corresponding test statistic.
C) At the 10% significance level, what is the decision and conclusion?
Q3) A magician has a coin that may or may not be fair. The results of 30 flips of the coin are H H T H T H
T. For the Wald-Wolfowitz runs test, the value of the total number of runs R is ________.
A) 8
B) 11
C) 16
D) 19
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