Quantitative Methods for Business
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Course Introduction
Quantitative Methods for Business provides students with the analytical and statistical tools necessary to make informed business decisions. The course covers fundamental concepts such as data analysis, probability, descriptive and inferential statistics, linear programming, and decision-making models. Emphasis is placed on applying quantitative techniques to solve real-world business problems in areas like operations, finance, and marketing. Through case studies, practical exercises, and the use of software tools, students develop a strong foundation in quantitative reasoning, critical thinking, and decision support, preparing them to analyze and interpret business data effectively.
Recommended Textbook
Business Statistics Communicating with Numbers 3rd Edition by Sanjiv Jaggia
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Chapter 1: Statistics and Data
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Sample Questions
Q1) What are the primary reasons that sampling is necessary?
Answer: Gathering population data can sometimes be impossible, very time-consuming, or very expensive.
Q2) We would like to determine whether there is a difference between the height of a college team of basketball players at the Ohio State University and the height of the overall student body. Identify the two populations in this study.
Answer: Varsity basketball players at OSU, all students at OSU
Q3) We would like to determine the average height of a college team of basketball players at Ohio State University. Is it necessary to take a sample of basketball players? Explain.
Answer: No, it is a small population and it is very easy to get the heights of the entire basketball team.
Q4) All mathematical operations can be performed on ratio-scaled data.
A)True
B)False
Answer: True
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Chapter 2: Tabular and Graphical Methods
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Sample Questions
Q1) Frequency distributions may be used to describe which of the following types of data?
A) Nominal and ordinal data only
B) Nominal and interval data only
C) Nominal, ordinal, and interval data only
D) Nominal, ordinal, interval, and ratio data
Answer: D
Q2) For qualitative data, a frequency distribution groups data into ________ and records the number of ________.
Answer: categories; observations
Q3) The relative frequency of a category is calculated by dividing the category's frequency by the total number of observations.
A)True
B)False
Answer: True
Q4) Scatterplot is a graphical tool that is focused on describing one variable.
A)True
B)False
Answer: False
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Chapter 3: Numerical Descriptive Measures
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Sample Questions
Q1) In its standard form, Chebyshev's theorem provides a lower bound on ________.
A) the number of observations lying within a certain interval
B) the number of observations lying outside a certain interval
C) the proportion (or percentage) of observations lying within a certain interval
D) the proportion (or percentage) of observations lying outside a certain interval
Answer: C
Q2) Which of the following statements about the mean absolute deviation (MAD) is the most accurate?
A) It is the square root of the standard deviation.
B) It can be a positive number or a negative number.
C) It is measured in the same units as the original data.
D) It is the arithmetic mean of the squared deviations from the mean.
Answer: C
Q3) The mean absolute deviation (MAD) is a less effective measure of variation when compared with the average deviation from the mean.
A)True
B)False
Answer: False
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Chapter 4: Introduction to Probability
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Sample Questions
Q1) A company is bidding on two projects, A and B. The probability that the company wins project A is 0.40 and the probability that the company wins project B is 0.25. Winning project A and winning project B are independent events. What is the probability that the company wins project A or project B?
A) 0.55
B) 0.65
C) 0.30
D) 0.25
Q2) The probability of a union of events can be greater than 1.
A)True
B)False
Q3) How many ways can a committee of four students be selected from a 15-member club?
A) 15!/44!
B) 15!/(11! × 4!)
C) 15 × 14 × 13
D) 15!/(11! × 4!) and 15 × 14 × 13
Q4) Subjective probability is assigned to an event by drawing on logical analysis.
A)True
B)False
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Chapter 5: Discrete Probability Distributions
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Sample Questions
Q1) For a particular clothing store, a marketing firm finds that 16% of $10-off coupons delivered by mail are redeemed. Suppose six customers are randomly selected and are mailed $10-off coupons. What is the expected number of coupons that will be redeemed?
A) 0.81
B) 0.96
C) 3.42
D) 5.04
Q2) What are the two key properties of a discrete probability distribution?
A) 0 P(X = x) 1 and P(X = x<sub>i</sub> ) = 0
B) 0 P(X = x) 1 and P(X = x<sub>i</sub> ) = 1
C) -1 P(X = x) 1 and P(X = x<sub>i</sub> ) = 1
D) -1 P(X = x) 1 and P(X = x<sub>i</sub> ) = 0
Q3) Thirty percent of the CFA candidates have a degree in economics. A random sample of three CFA candidates is selected. What is the probability that none of them has a degree in economics?
A) 0.027
B) 0.300
C) 0.343
D) 0.900
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Chapter 6: Continuous Probability Distributions
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Sample Questions
Q1) An analyst is forecasting net income for Excellence Corporation for the next fiscal year. Her low-end estimate of net income is $250,000, and her high-end estimate is $350,000. Prior research allows her to assume that net income follows a continuous uniform distribution. The probability that net income will be greater than or equal to $337,500 is ________.
A) 12.5%
B) 29.6%
C) 87.5%
D) 96.4%
Q2) You are considering the risk-return profile of two mutual funds for investment. The relatively risky fund promises an expected return of 9%, with a standard deviation of 12%. The relatively less risky fund promises an expected return and standard deviation of 5% and 8%, respectively.
A) Which mutual fund will you pick if your objective is to minimize the probability of earning a negative return?
B) Which mutual fund will you pick if your objective is to maximize the probability of earning a return of between 8% and 12%?
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Chapter 7: Sampling and Sampling Distributions
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Sample Questions
Q1) Suppose residents in a well-to-do neighborhood pay an average overall tax rate of 25% with a standard deviation of 8%. Assume tax rates are normally distributed. What is the probability that the mean tax rate of 16 randomly selected residents is between 20% and 30%.
Q2) According to the recent report, scientists in New England say they have identified a set of genetic variants that predicts extreme longevity with 77% accuracy. Assume 150 patients decide to get their genome sequenced. If the claim by scientists is accurate, what is the probability that fewer than 70% of the patients will get a correct diagnosis for extreme longevity?
A) 0.1422
B) 0.0722
C) 0.2214
D) 0.0208
Q3) The central limit theorem approximation improves as the sample size decreases.
A)True
B)False
Q4) Cluster sampling is preferred when the objective is to increase precision.
A)True
B)False
Q5) Cluster sampling is preferred when the objective is to ________.
Page 9
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Chapter 8: Interval Estimation
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Sample Questions
Q1) A confidence interval is generally associated with a(n) ________.
Q2) The required sample size for the interval estimation of the population mean can be computed if we specify the population standard deviation , the value of z<sub> </sub><sub>/2</sub> based on the confidence level 100(1 )% and the desired margin of error D.
A)True
B)False
Q3) The snowfall (in inches) during the month of January in a particular geographic region is normally distributed with a standard deviation of 16.75. In the last 12 years, the sample average of snowfall is computed as 122.50.
A) Construct a 90% confidence interval of the average snowfall in this region.
B) Construct a 95% confidence interval of the average snowfall in this region.
C) Comment on the width of the preceding confidence intervals.
Q4) A company manager thinks he is overpaying for fertilizer at $174 per ton. To find out, he collects fertilizer prices per ton from five distributors. Construct a 90% confidence interval from his results: 128, 140, 170, 166, and 156.
Q5) It is important to know that ________ is increased when we estimate the population standard deviation with the sample standard deviation.
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Chapter 9: Hypothesis Testing
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Sample Questions
Q1) The national average for an eighth-grade reading comprehension test is 73. A school district claims that its eighth-graders outperform the national average. In testing the school district's claim, how does one define the population parameter of interest?
A) The mean score on the eighth-grade reading comprehension test
B) The number of eighth graders who took the reading comprehension test
C) The standard deviation of the score on the eighth-grade reading comprehension test
D) The proportion of eighth graders who scored above 73 on the reading comprehension test
Q2) Expedia would like to test if the average round-trip airfare between Philadelphia and Dublin is less than $1,200. Which of the following hypothesis tests should be performed?
A) Left-tailed
B) Right-tailed
C) Two-tailed
D) There is not enough information to answer.
Q3) The hypothesis statement H: < 60 is an example of a(an) ________ hypothesis.
Q4) We define the allowed probability of making a Type I error as , and we refer to 100 % as the ________.
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Chapter 10: Statistical Inference Concerning Two Populations
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Sample Questions
Q1) A tutor promises to improve GMAT scores of students by more than 50 points after three lessons. To see if this is true, the tutor takes a sample of 49 students' test scores after and before they received tutoring. The mean difference was 53 points better after tutoring, with a standard deviation of the difference equal to 12 points. Let µ<sub>D</sub> denote the mean of the difference: score after tutoring minus score before tutoring. Which of the following hypotheses will determine if the students improved their test scores by more than 50 points after being tutored?
A) H<sub>0</sub>: µ<sub>D</sub> 0, H<sub>A</sub>: µ<sub>D </sub>> 0
B) H<sub>0</sub>: µ<sub>D</sub> 0, H<sub>A</sub>: µ<sub>D </sub><<sub> </sub>0
C) H<sub>0</sub>: µ<sub>D</sub> 50, H<sub>A</sub>: µ<sub>D </sub>><sub> </sub>50
D) H<sub>0</sub>: µ<sub>D</sub> 50, H<sub>A</sub>: µ<sub>D </sub><<sub> </sub>50
Q2) The hypothesis test H<sub>0</sub>: p<sub>1</sub> - p<sub>2</sub> d<sub>0</sub>; H<sub>A</sub>: p<sub>1</sub> - p<sub>2</sub> > d<sub>0</sub> is a left-tailed test.
A)True B)False
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Chapter 11: Statistical Inference Concerning Variance
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Sample Questions
Q1) The F distribution depends on ________ degrees of freedom.
Q2) The Excel's function ________ returns the p-value for a right-tailed test for the ratio of two population variances.
Q3) Becky owns a diner and is concerned about sustaining the business. She wants to ascertain if the standard deviation of the profits for each week is greater than $250. The details of the profits for the week are (in dollars) 1,743 1,438 1,212 1,705 1,985 1,857 1,916
Assume that profits are normally distributed. Which of the following is the correct value of the test statistic?
A) 6.146
B) 8.604
C) 6.652
D) 7.375
Q4) The formula for the confidence interval of the population variance <sup>2</sup> is valid only when the random sample is drawn from a ________ distributed population.
Q5) The skewness of the chi-square distribution depends on the degrees of freedom.
A)True B)False
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Chapter 12: Chi-Square Tests
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Sample Questions
Q1) When applying the goodness-of-fit test for normality, the data are divided into k non-overlapping intervals.
A)True
B)False
Q2) The chi-square goodness-of-fit test is a right-tailed test.
A)True
B)False
Q3) Suppose you want to determine if the quarterly returns for mutual funds have a normal distribution using the skewness and kurtosis coefficients. The most appropriate test is the ________.
A) goodness-of-fit test for a multinomial experiment
B) chi-square test for independence
C) goodness-of-fit test for normality
D) Jarque-Bera test for normality
Q4) The chi-square test of a contingency table is a test of independence for ________.
A) a single qualitative variable
B) two qualitative variables
C) two quantitative variables
D) three or more quantitative variables
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Chapter 13: Analysis of Variance
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Sample Questions
Q1) The between-treatments variance is based on a weighted sum of squared differences between the ________.
A) population variances and the overall mean of the data set
B) sample means and the overall mean of the data set
C) sample variances and the overall mean of the data set
D) population means and the overall mean of the data set
Q2) The between-treatments variance is the estimate of <sup>2</sup> based on the variability due to chance.
A)True
B)False
Q3) One of the disadvantages of Fisher's LSD method is that the probability of committing at least one ________.
A) Type II error increases as the number of pairwise comparisons increases
B) Type I error increases as the number of pairwise comparisons decreases
C) Type II error increases as the number of pairwise comparisons decreases
D) Type I error increases as the number of pairwise comparisons increases
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Chapter 14: Regression Analysis
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Sample Questions
Q1) The following data for five years of the annual returns for two of Vanguard's mutual funds, the Vanguard Energy Fund (x) and the Vanguard Healthcare Fund (y), were given as s<sub>x </sub>= 35.77, s<sub>y </sub>= 13.34, s<sub>xy </sub>= 447.68. Which of the following is the value of the sample correlation coefficient?
A) 0.88
B) 0.94
C) 0.78
D) 0.78
Q2) Which of the following is not true of the standard error of the estimate?
A) It can take on negative values.
B) Theoretically, its value has no predefined upper limit.
C) It is a measure of the accuracy of the regression model.
D) It is based on the squared deviations between the actual and predicted values of the response variable.
Q3) A correlation coefficient r = 0.85 could indicate a ________.
A) very weak positive linear relationship
B) very strong negative linear relationship
C) very weak negative linear relationship
D) very strong positive linear relationship
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Chapter 15: Inference With Regression Models
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Sample Questions
Q1) ________ plots can be used to detect common violations, and they can be used to detect outliers.
Q2) When estimating y = <sub>0</sub> + <sub>1</sub>x<sub>1</sub> + <sub>2</sub>x<sub>2 </sub>+ <sub>3</sub>x<sub>3</sub> + , you wish to test H<sub>0</sub>: <sub>1 </sub>= <sub>2 </sub>versus H<sub>A</sub>: <sub>1 </sub> <sub>2</sub>. The value of the test statistic is F<sub>(1,30)</sub> = 7.75 and its associated p-value is 0.0092. At the 1% significance level, the conclusion is to ________.
A) reject the null hypothesis; we cannot conclude that the influence of x<sub>1</sub> on y is different from the influence of x<sub>2</sub> on y.
B) reject the null hypothesis; we can conclude that the influence of x<sub>1</sub> on y is different from the influence of x<sub>2</sub> on y.
C) not reject the null hypothesis; we can conclude that the influence of x<sub>1</sub> on y is different from the influence of x<sub>2</sub> on y.
D) not reject the null hypothesis; we cannot conclude that the influence of x<sub>1</sub> on y is different from the influence of x<sub>2</sub> on y.
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Chapter 16: Regression Models for Nonlinear Relationships
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Sample Questions
Q1) A quadratic regression model is a polynomial regression model of order 2.
A)True
B)False
Q2) Which of the following is a typical application for the cubic regression model?
A) Average cost against output
B) Company's total cost curve
C) Rate of growth
D) None of the choices are correct
Q3) Which of the following nonlinear regression models is the polynomial regression model of order three?
A) Cubic regression model
B) Linear regression model
C) Logarithmic regression model
D) Quadratic regression model
Q4) For the logarithmic model y = <sub>0</sub> + <sub>1</sub>ln(x) + , <sub>1</sub> × 100% is the approximate percentage change in E(y) when x increases by 1%.
A)True
B)False
Q5) The cubic regression model allows for ________ change(s) in slope.
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Chapter 17: Regression Models With Dummy Variables
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Sample Questions
Q1) A model y = <sub>0</sub> + <sub>1</sub>x + , in which y is a binary variable, is called a linear probability model.
A)True
B)False
Q2) For the model y = <sub>0</sub> + <sub>1</sub>x + <sub>2</sub>xd + , which of the following are the hypotheses for testing the individual significance of the interaction variable xd?
A) H<sub>0</sub>: xd = 0, H<sub>A</sub>: xd 0
B) H<sub>0</sub>: b<sub>2</sub> = 0, H<sub>A</sub>: b<sub>2</sub> 0
C) H<sub>0</sub>: <sub>2</sub> = 0, H<sub>A</sub>: <sub>2</sub> 0
D) H<sub>0</sub>: <sub>2</sub> 0, H<sub>A</sub>: <sub>2</sub> = 0
Q3) Including as many dummy variables as there are categories is referred to as the dummy variable ________.
Q4) The logit model can be estimated with standard ordinary least squares.
A)True B)False
Q5) The method of maximum likelihood estimation (MLE) is used to ________ the parameters of a logit model.
Q6) A dummy variable is also referred to as a(n) ________ variable.
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Chapter 18: Time Series and Forecasting
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Sample Questions
Q1) In which of the following situations is the use of qualitative forecasts most appropriate?
A) A marketing manager has to forecast monthly sales for the coming financial year based on the past monthly sales figures.
B) A TV network executive has to forecast viewership figures for a daily talk show based on historical data from the past on a similar show on a rival network.
C) An economist has to forecast credit flow resulting from a newly introduced stimulus package by the federal government.
D) A country's annual rate of growth for the upcoming year has to be estimated based on the annual GDP data from the last 20 years.
Q2) Which of the following is an example of a time series?
A) The number of daily visitors to the Niagara Falls during the month of April.
B) The recorded exam scores of students in a class.
C) The sales prices of single family homes sold last month in Florida.
D) The current average prices of regular gasoline in different states of the U.S.
Q3) The mean of the absolute residuals defines the ________.
Q4) The seasonal component typically represents repetitions over a ________ period.
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Chapter 19: Returns, Index Numbers, and Inflation
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Sample Questions
Q1) Joanna Robertson bought a share of XYZ Corp. at $200 last year. She was paid a dividend of $30 during the same year. However, the same share is trading at $280 this year. Calculate the investment percent yield if Joanna sells the share at $280.
A) 70%
B) 110%
C) 15%
D) 55%
Q2) Nicole Watson purchased a share of McAllister Inc., a year back when it was trading at $75. She also earned a dividend of $4 on this. The price of the same share has now increased to $87.
A) Compute the annual capital gain from this share.
B) Compute the annual income yield from this share.
Q3) When the expected inflation rate is relatively low, a reasonable ________ to the Fisher equation is r = R - i.
Q4) The only possible income from an investment is the direct cash payment from the underlying asset.
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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Q1) A trading magazine wants to determine the number of hours stockbrokers work each week. In particular, the trading magazine wants to determine if the median number of hours worked per week differs from 100 hours. The magazine samples 18 traders. For the Wilcoxon signed-rank test, the value of the test statistic is T = T<sup>+</sup> = 153. At the 1% significance level, the critical value is ________.
A) 1.645
B) 1.96
C) 2.33
D) 2.575
Q2) In the Wald-Wolfowitz test a ________ is an uninterrupted sequence of one letter, symbol, or attribute.
Q3) Parametric tests typically assume the underlying population to be normally distributed.
A)True B)False
Q4) The method of runs above and below the median is especially useful in detecting trends and cyclical patterns in ________ data.
Q5) The Kruskal-Wallis test is always a ________-tailed test.
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