Business Statistics
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Course Introduction
Business Statistics provides students with the foundational tools and techniques necessary for analyzing and interpreting data within a business context. The course covers descriptive statistics, probability distributions, sampling methods, hypothesis testing, regression analysis, and the use of statistical software. Emphasis is placed on applying quantitative reasoning to real-world business problems, aiding effective decision making, and communicating analytical findings clearly to stakeholders. Students will gain practical experience in collecting, organizing, and analyzing data, enabling them to make informed, data-driven decisions in various business environments.
Recommended Textbook
Business Analytics Data Analysis and Decision Making 5th Edition by S. Christian Albright
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Page 2
Chapter 1: Introduction to Data Analysis and Decision Making
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Sample Questions
Q1) Which of the following is an Excel add-in for simulation?
A) PrecisionTree
B) TopRank
C) Solver
D) @Risk
E) StatTools
Answer: D
Q2) The decision-making concepts covered in Data Analysis & Decision Making book include which of the following?
A) Optimization techniques
B) Decision analysis with uncertainty
C) Structured sensitivity analysis
D) All of these options
Answer: D
Q3) Graphical models can be very helpful for simple problems.For complex problems,however,graphical models usually fail to show the important elements of a problem and how they are related.
A)True
B)False
Answer: False
Page 3
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Chapter
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Sample Questions
Q1) The count of categories is the only meaningful way to summarize categorical data.
A)True
B)False
Answer: True
Q2) A population includes all elements or objects of interest in a study,whereas a sample is a subset of the population used to gain insights into the characteristics of the population.
A)True
B)False
Answer: True
Q3) Expressed in percentiles,the interquartile range is the difference between the
A) 10<sup>th</sup> and 60<sup>th</sup> percentiles
B) 15<sup>th</sup> and 65<sup>th</sup> percentiles
C) 20<sup>th</sup> and 70<sup>th</sup> percentiles
D) 25<sup>th</sup> and 75<sup>th</sup> percentiles
E) 35<sup>th</sup> and 85<sup>th</sup> percentiles
Answer: D
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4
Chapter 3: Finding Relationships Among Variables
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Sample Questions
Q1) Statisticians often refer to the pivot tables that display counts as contingency tables or crosstabs.
A)True
B)False
Answer: True
Q2) The cutoff for defining a large correlation is
A)True
B)False
Answer: False
Q3) We are usually on the lookout for large correlations near
A) +1
B) -1
C) Either of these options
D) Neither of these options
Answer: C
Q4) Relationships between two variables are less evident when counts are expressed as percentages of row totals or column totals.
A)True
B)False
Answer: False
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Chapter 4: Probability and Probability Distributions
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Sample Questions
Q1) Suppose A and B are two events where P(A)= 0.5,P(B)= 0.4,and P(A and B)= 0.2,then P(B/A)= 0.5.
A)True
B)False
Q2) Probabilities that can be estimated from long-run relative frequencies of events are
A) objective probabilities
B) subjective probabilities
C) complementary probabilities
D) joint probabilities
Q3) Given that events A and B are independent and that P(A)= 0.8 and P(B/A)= 0.4,then P(A and B)= 0.32.
A)True
B)False
Q4) The time students spend in a computer lab during one day is an example of a continuous random variable.
A)True
B)False
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Chapter 5: Normal, Binomial, Poisson, and Exponential
Distributions
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Sample Questions
Q1) The binomial distribution deals with consecutive trials,each of which has two possible outcomes.
A)True
B)False
Q2) We assume that the outcomes of successive trials in a binomial experiment are: A) probabilistically independent B) probabilistically dependent C) identical from trial to trial D) random number between 0 and 1
Q3) If the mean of an exponential distribution is 2,then the value of the parameter \(\lambda\) Is
A) 4
B) 2
C) 1
D) 0.5
Q4) The total area under the normal distribution curve is equal to one.
A)True
B)False
7
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Chapter 6: Decision Making Under Uncertainty
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Sample Questions
Q1) In a single-stage decision tree problem,all ___________ are made first and then all ___________ is (are)resolved.
A) decisions;uncertainty
B) calculations;probabilities
C) EMV calculations;posterior probabilities
D) likelihoods;posterior probabilities
E) prior probabilities;joint probabilities
Q2) When you use the expected monetary value (EMV)criterion,you are not using all of the information that is shown in the risk profiles of alternatives,since you are only comparing the means.
A)True
B)False
Q3) A risk profile lists all possible monetary values and their corresponding probabilities. A)True
B)False
Q4) In making decisions,we choose the decision with the largest expected monetary value.
A)True
B)False
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Chapter 7: Sampling and Sampling Distributions
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Sample Questions
Q1) In stratified sampling with proportional sample sizes,the proportion of each stratum selected differs from stratum to stratum.
A)True
B)False
Q2) A sample chosen in such a way that every possible subset of same size has an equal chance of being selected is called a(n)
A) interval estimation
B) point estimation
C) simple random sample.
D) statistic
Q3) The probability of being chosen in a simple random sample of size n from a population of size N is:
A) 1/N
B) N - 1/n
C) N/n
D) n/N
Q4) Ideally,we prefer estimates that have large standard errors.
A)True
B)False
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Chapter 8: Confidence Interval Estimation
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Sample Questions
Q1) When samples of size n are drawn from a population,then the sampling distribution of the sample mean \(x\) is approximately normal,provided that n is reasonably large. A)True
B)False
Q2) The mean of the sampling distribution of the sample proportion \(\hat { p }\) ,when the sample size n = 100 and the population proportion p = 0.15,is 15.0.
A)True
B)False
Q3) The lower limit of the 95% confidence interval for the population proportion p,given that n = 300;and \(\hat { p }\) = 0.10 is 0.1339.
A)True B)False
Q4) If the standard error of the sampling distribution of the sample proportion \(\hat { pp }\) is 0.0324 for samples of size 200,then the population proportion must be 0.30.
A)True
B)False
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Chapter 9: Hypothesis Testing
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Sample Questions
Q1) The test statistic employed to test \(H _ { 0 } : \sigma _ { 1 } ^ { 2 } / \sigma _ { 2 } ^ { 2 } = 1 \text { is } F = s _ { 1 } ^ { 2 } / s _ { 2 } ^ { 2 }\) ,which is F distributed with \(n _ { 1 } - 1 \text { and } n _ { 2 } - 1\) degrees of freedom.
A)True B)False
Q2) A null hypothesis can only be rejected at the 5% significance level if and only if: A) a 95% confidence interval includes the hypothesized value of the parameter B) a 95% confidence interval does not include the hypothesized value of the parameter C) the null hypothesis is biased D) the null hypotheses includes sampling error
Q3) The power of a test is the probability of rejecting the null hypothesis when the alternative hypothesis is true.
A)True B)False
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11
Chapter 10: Regression Analysis: Estimating Relationships
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Sample Questions
Q1) The covariance is not used as much as the correlation because A) is not always a valid predictor of linear relationships B) it is difficult to calculate C) it is difficult to interpret D) all of these options
Q2) A correlation value of zero indicates.
A) a strong linear relationship
B) a weak linear relationship
C) no linear relationship
D) a perfect linear relationship
Q3) The regression line \[\hat { Y }\] = 3 + 2X has been fitted to the data points (4,14), (2,7),and (1,4).The sum of the residuals squared will be 8.0.
A)True
B)False
Q4) The multiple R for a regression is the correlation between the observed Y values and the fitted Y values.
A)True
B)False
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Chapter 11: Regression Analysis: Statistical Inference
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Sample Questions
Q1) Which of the following is not one of the guidelines for including/excluding variables in a regression equation?
A) Look at t-value and associated p-value
B) Check whether t-value is less than or greater than 1.0
C) Variables are logically related to one another
D) Use economic or physical theory to make decision
E) All of these options are guidelines
Q2) The term autocorrelation refers to:
A) analyzed data refers to itself
B) sample is related too closely to the population
C) data are in a loop (values repeat themselves)
D) time series variables are usually related to their own past values
Q3) The objective typically used in the tree types of equation-building procedures are to:
A) find the equation with a small s<sub>e</sub>
B) find the equation with a large R<sup>2</sup>
C) find the equation with a small s<sub>e</sub> and a large R<sup>2</sup>
D) find the equation with the largest F-statistic
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Chapter 12: Time Series Analysis and Forecasting
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Sample Questions
Q1) In a regression model with seasonal dummy variables,the coefficients on the dummy variables represent the additive factor relative to the reference quarter value,not the multiplicative factor.
A)True
B)False
Q2) A meandering pattern is an example of a random time series.
A)True
B)False
Q3) Examples of non-random patterns that may be evident on a time series graph include:
A) trends
B) increasing variance over time
C) a meandering pattern
D) too many zigzags
E) all of these options
Q4) If the span of a moving average is large - say,12 months - then few observations go into each average,and extreme values have relatively large effect on the forecasts.
A)True
B)False
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Chapter 13: Introduction to Optimization Modeling
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Sample Questions
Q1) There are two primary ways to formulate a linear programming problem,the traditional algebraic way and in spreadsheets.
A)True
B)False
Q2) Proportionality,additivity,and divisibility are three important properties that LP models possess,which distinguish them from general mathematical programming models:.
A)True
B)False
Q3) It is often useful to perform sensitivity analysis to see how,or if,the optimal solution to a linear programming problem changes as we change one or more model inputs.
A)True
B)False
Q4) Suppose the allowable increase and decrease for shadow price for a constraint are $25 (increase)and $10 (decrease).If the right hand side of that constraint were to increase by $10 the optimal value of the objective function would change.
A)True
B)False
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Chapter 14: Optimization Models
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Sample Questions
Q1) In a transportation problem,if it costs $4 per item to ship up to 200 items between cities,and $2 per item for each additional item,the proportionality assumption of LP is satisfied.
A)True
B)False
Q2) Logistics problems are problems of finding the least expensive way to transport products from their origin to their destination.
A)True
B)False
Q3) The LP relaxation of an integer programming (IP)problem is the same model as the IP model except that some integer constraints are omitted.
A)True
B)False
Q4) A common characteristic of integer programming models is that they:
A) are easy to solve graphically
B) produce the same answer and standard linear programming models
C) often produce multiple optimal solutions
D) all of these options
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Chapter 15: Introduction to Simulation Modeling
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Sample Questions
Q1) When we maximize or minimize the value of a decision variable by running several simulations simultaneously,we have found an optimal solution to the problem and attitude toward risk becomes irrelevant.
A)True
B)False
Q2) Which of the following statements are false?
A) A probability distribution is discrete if it has a finite number of possible values.
B) A probability distribution is continuous if its possible values are essentially some continuum.
C) An example of a discrete probability distribution is the amount of rain that falls during the month of June in Michigan.
D) None of these options
Q3) The deterministic (non-simulation)approach,using best guesses for the uncertain inputs,is:
A) better to use in complicated real world applications.
B) a good estimate of what the answer will be using a simulation approach.
C) generally not the appropriate model.
D) the preferred approach when there is correlation between input variables.
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Chapter 16: Simulation Models
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Sample Questions
Q1) In marketing models of customer loyalty,we are typically interested in modeling the rate of customer retention,called churn.
A)True
B)False
Q2) In a bidding model,once we have the bidding strategy that maximizes the expected profit,we no longer should consider the bidders risk aversion.
A)True
B)False
Q3) The @RISK function RISKDUNIFORM in the form = RISKDUNIFORM ({List})generates a random member of a given list,so that each member of the list has the same chance of being chosen.
A)True
B)False
Q4) A common distribution for modeling product lifetimes is the binomial distribution
A)True
B)False
Q5) Develop an @Risk model to estimate the NPV given an assumed capacity.What are the variable inputs and outputs?
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Chapter 17: Data Mining
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Sample Questions
Q1) Clustering is considered a supervised data mining technique.
A)True
B)False
Q2) The testing set in data partitioning is:
A) The first subset of data,which usually contains 70% of the records
B) The second subset of data,which usually contains less than 70% of the records
C) The initial dataset from which subsets are created
D) The first subset of data,which usually contains 30% of the records
Q3) In a facts table,a supermarket database is likely to have which item listed in rows?
A) The number of units sold
B) Revenue generated from a particular unit
C) The department in which the unit was purchased
D) The individual items purchased
Q4) Suppose the odds of Team A winning are 5 to 1.Then,the odds ratio is:
A) 5/1
B) 1/5
C) 6/1
D) 1/6
Q5) What does the pivot table indicate about spending habits?
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Chapter 18: Importing Data Into Excel
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Sample Questions
Q1) Repetitive tasks are best handled by copying and pasting.
A)True
B)False
Q2) Text files are also known as:
A) Excel spreadsheets
B) Excel workbooks
C) ASCII files
D) Notepad files
Q3) Real-world datasets usually do not require any cleansing because they do not contain missing data or typographical errors.
A)True
B)False
Q4) Text file extensions end with:
A) *·.prn,*·txt *·xls
B) *·prn,*·txt *·csv
C) *·prn,*·txt *·doc
D) *·prn,*·txt *·jpg
Q5) If you had imported the data using 'fixed width,' how would the output have changed?
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Chapter 19: Analysis of Variance and Experimental Design
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Sample Questions
Q1) Which p-value from a two-way ANOVA table indicates an effect that is not statistically significant?
A) 0.000
B) 0.011
C) 0.047
D) 0.110
Q2) In a one-way ANOVA test,we conclude there are differences across population means if the:
A) between variation is small relative to the within variation
B) between variation and within variation are equal
C) between variation is large relative to the within variation
D) between variation equals zero
Q3) The null hypothesis that indicates there are no differences in population means across levels is \(H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } = \mu _ { J }\)
A)True
B)False
Q4) Suppose Mook Corp.was interested in running a two-way ANOVA.What other factors might you recommend they include in the test?
Q5) What does the ANOVA output in the accompanying figure indicate?
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Chapter 20: Statistical Process Control
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Sample Questions
Q1) Out-of control indicators may include a number of conditions.What is not one of these?
A) At least 8 upward (or downward)consecutive changes
B) At least 8 consecutive points above (or below)the centerline
C) At least 1 point beyond two standard deviations from the centerline
D) At least 4 of 5 consecutive points beyond one standard deviation from the centerline
Q2) Michael has incorporated a vigorous cross-training program within his department.This is an example of which of Deming's 14 points?
A) Improve Every Process.
B) Institute Training.
C) Drive Out Fear.
D) Encourage Education.
Q3) Morgan decided the out-of-control behavior she observed might be due to the fact that she was using an extremely small sample.Therefore,she quadruples her sample size,and the sample is now much larger than even her original sample.Unfortunately,she forgets to adjust the upper and lower limits again to reflect the much larger sample size.What is likely to occur as she manually plots observations on the chart?
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