Quantitative Methods for Business Practice Exam
Course Introduction
Quantitative Methods for Business introduces students to the mathematical and statistical tools widely used in business decision-making. The course covers key topics such as data analysis, probability, statistical inference, regression models, forecasting techniques, and optimization methods. Emphasizing real-world applications, it enables students to interpret quantitative data, solve business problems, and make informed decisions under uncertainty. Through a combination of lectures, case studies, and hands-on exercises, students learn to utilize quantitative methods to enhance productivity, efficiency, and strategic planning within organizations.
Recommended Textbook
Business Statistics in Practice 3rd Canadian Edition by Bruce L. Bowerman
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Chapter 1: An Introduction to Business Statistics
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Sample Questions
Q1) A set of units we wish to study is called a _____. Answer: population
Q2) A population is a set of units (usually people,objects,or events).
A)True
B)False
Answer: True
Q3) A _____ is a subset of the units in a population.
Answer: sample
Q4) Describe one weakness and one advantage to mailed surveys.
Answer: Advantages:inexpensive,unobtrusive.Disadvantages:low response rate,uncertain person meant to complete survey was actually the one who completed it,uncertain person fully understood questions.
Q5) When a population unit selected as part of the sample cannot be contacted or refuses to participate,then we say that _________ has occurred. Answer: nonresponse
Q6) The change in daily price of a stock is what type of variable?
Answer: quantitative
Q7) A ____ is a graph of individual process measurements versus time. Answer: runs plot
Page 3
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Chapter 2: Descriptive Statistics
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Sample Questions
Q1) What is the mode?
A)375
B)368
C)389.9
D)200
E)346.6
Answer: A
Q2) Determine the median of the data 2,4,6,8,10,12,14.
Answer: 8
Q3) What is the standard deviation?
A)1359
B)4993
C)1846575
D)3587
E)1976454
Answer: A
Q4) A measurement located between the inner and outer fences of a box-and-whisker display is a(n)_____.
Answer: mild outlier
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Chapter 3: Probability
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Sample Questions
Q1) If you roll a fair die,what is the probability that at least 5 dots appear?
Answer: 1/3 \[\frac { 2 } { 6 }\]
Q2) An advertising campaign is being developed to promote a new bookstore opening in the newest mall development.To develop an appropriate mailing list,it has been decided to purchase lists of credit card holders from MasterCard and Visa.Combining the lists,they find the following: 40% of the people on the list have only a MasterCard and 10% have only a Visa card.Another 20% hold both MasterCard and Visa.Finally,30% of those on the list have neither card.Suppose a person on the list is known to have a MasterCard.What is the probability that person also has a Visa Card?
Answer: .33
P(AE|MC)= .20/.60 = .33 \[\begin{array} { | l | l | l | l | }
\hline & \text { MasterCard } & \text { No MasterCard } & \\
\hline \text { Visa } & .20 & .10 & .30 \\
\hline \text { No Visa } & .40 & .30 & .70 \\
\hline & .60 & .40 & 1.00 \\
\hline
\end{array}\]
Q3) What is the probability that the citizen is male and has a favorable opinion
Answer: .40
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Chapter 4: Discrete Random Variables
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Sample Questions
Q1) Find the probability that none of the students voted.
A)0.0000
B)0.0014
C)0.0148
D)0.2500
E)0.4997
Q2) A fair die is rolled 10 times.What is the average number of even number (2,4,or 6)outcomes?
A)3
B)4
C)5
D)6
E)7
Q3) Find the premium that the insurance company should charge if it wants its expected net profit to be $2000?
Q4) If 100 calculators are selected at random,what is the standard deviation of the number of defectives?
Q5) The distribution whose mean is equal to its variance is the _________ distribution.
Q6) Find the probability of more than 7 customers arriving within a minute.
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Chapter 5: Continuous Random Variables
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Sample Questions
Q1) Complete the following statement: Only 12.5% of their retired employees will receive payment beyond age ______.
Q2) The mean and median are the same for a normal distribution.
A)True
B)False
Q3) What is the probability that a randomly selected depth is within 1 standard deviation of the mean?
Q4) Find the probability that a household spent more than $10.00
Q5) The mean and median are the same for an exponential distribution.
A)True
B)False
Q6) A movie theatre manager knows that the number of patrons per movie is normally distributed with a mean of 200 and a standard deviation of 20.What is the number of patrons,x,where 50% are less than x?
A)532
B)597
C)413
D)200
E)332
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Chapter 6: Sampling Distributions
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Sample Questions
Q1) Find P ( \(\bar { x }\) > 49).
Q2) What is the probability the mean length of the bolt is at least 3.16 cm?
A)0.9772
B)0.0548
C)0.9452
D)0.4452
E)0.0228
Q3) Suppose you take a random sample from a normally distributed population with mean \(\mu\) = 16 and compute the sample mean \(\bar { x }\) .If \(\sigma _ { \bar { x } } ^ { 2 }\) = 4,find P( \(\bar { x }\) < 25).
A)0300
B)1.000
C)1732
D)0577
E)8413
Q4) As the sample size ___________,the variability of the sampling distribution of the sample proportion increases.
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Chapter 7: Confidence Intervals
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Sample Questions
Q1) How much evidence do we have to reject the null hypothesis in favour of the alternative hypothesis that more than 20 percent of undergraduate students stay in residence for their four years as students?
A)No evidence
B)Some evidence
C)Strong evidence
D)Very strong evidence
E)Extremely strong evidence
Q2) The appropriate test statistic to test the hypotheses is _____.
A)56.09
B)3.74
C)22.34
D)-3.74
E)-22.34
Q3) The test statistic is _____.
A)-2.83
B)-1.41
C)-2.00
D)2.83
E)1.41
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Chapter 8: Hypothesis Testing
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Sample Questions
Q1) Calculate the pooled variance where sample 1 has data: 16,14,19,18,19,20,15,18,17,18,and sample 2 has data: 13,19,14,17,21,14,15,10,13,15.
Q2) The appropriate test statistic to test the hypotheses is _____.
A)6.20
B)1.72
C)0.477
D)-6.20
E)-1.72
Q3) Suppose we are testing a null hypothesis about the population mean of a normally distributed population.If the population standard deviation is unknown and n = 14,the appropriate test statistic is based on the ___________ distribution.
A)t
B)z
C)F
D)chi-square
E)exponential
Q4) In general,the shape of the F distribution is skewed _________.
Q5) What is the critical value for this test at alpha = .01?
Q6) Two parameters of the F distribution are:
Page 10
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Chapter 9: Statistical Inferences Based on Two Samples
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Sample Questions
Q1) An experiment was conducted to determine the effectiveness of a method designed to remove oil wastes found in soil.Three contaminated soil samples were treated.After 95 days,the percentage of contamination removed from each soil sample was measured with a mean of 49.3% and a standard deviation of 1.5%.If the percentage of contamination is normally distributed,the mean percentage of contamination removed at a 98% confidence level would be _____.
A)[48.36,50.24]
B)[43.27,55.33]
C)[47.29,51.31]
D)[47.88,50.72]
E)[46.47,52.13]
Q2) A test of spelling ability is given to a random sample of 10 students before and after they completed a spelling course.The mean score before the course was 119.60 and after the course the mean score was 130.80.The standard deviation of the difference was 16.061.Assume that the difference in scores is normally distributed.Calculate a 99% confidence interval for the mean change in score.
Q3) What is the estimated standard deviation of the sample proportion?
Q4) As the sample size n increases,the width of the confidence interval for a population mean or proportion _______________.
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Chapter 10: Experimental Design and Analysis of Variance
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Sample Questions
Q1) Determine the degrees of freedom for groups (treatments).
Q2) A _____ design,is an experimental design that compares p groups by using b blocks,where each block is used exactly once to measure the effect of each treatment.
Q3) Find Tukey's simultaneous 95 percent confidence interval for the difference between the means of block 2 and block 4.
Q4) What is the error sum of squares?
Q5) In a one-way analysis of variance for a completely randomized design with three treatments groups,each with five measurements,what are the degrees of freedom associated with the error sum of squares?
A)6
B)8
C)2
D)12
E)15
Q6) In one-way ANOVA for a completely randomized design,the total sum of squares is equal to _______________________.
Q7) Compute a 95% confidence interval for the fourth group (diet)mean.
Q8) Test H<sub>0</sub>: There is no difference between blocks at a=.05.
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Chapter 11: Correlation Coefficient and Simple Linear
Regression Analysis
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Sample Questions
Q1) A simple linear regression on a data set of 12 ordered pairs (x,y)gave the following results: \[\hat { y } = 54.23 + 1.45 x\]
MSE = 1.1816
SS<sub>xx</sub> = 0.9814 \[\bar { x } = 10.8\]
Compute a 95% confidence interval for the mean value of y when x = 8?
Q2) What is the explained variation?
Q3) The coefficient of determination measures the proportion of observed variation in the _______ explained by the simple linear regression model.
Q4) You wish to perform a simple linear regression analysis using x as the independent variable and y as the dependent variable.What is the standard error? A)212
B)189
C)106
D)460 E)590
Q5) Determine the normal score for the second largest residual (ninth residual in the ordered array).
Q6) What is the estimated slope?
Page 13
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Chapter 12: Multiple Regression and Model Building
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Sample Questions
Q1) What is the total sum of squares,explained variation,and mean square error?
Q2) What is the mean square error?
Q3) R<sup>2</sup>is defined as the proportion of the observed variation in the dependent variable that is explained by the fitted regression model.
A)True
B)False
Q4) What is the value of F?
A)40.686
B)31.308
C)17.81
D)9.324
E)5.861
Q5) Completely randomized analysis of variance models (one-way ANOVA)can always be converted to a multiple regression models with dummy independent variables. A)True
B)False
Q6) Test the overall usefulness of the model at alpha =.05.Calculate the F statistic and make your decision.
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Chapter 13: Nonparametric Methods
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Sample Questions
Q1) On the average,can it be concluded that the machines distribute the same amount? Test at \(\alpha\) = .05
Cannot reject the null hypothesis that the distributions of amounts are equal. T = 117
Q2) An e-business/e-commerce information technology consulting company wants to compare the effectiveness of three programming languages that its programmers use.Currently each programming language is used by approximately 1/3 of the programmers employed by the company.The director of the programming division randomly selected 5 programmers from the users of each of the three programming languages and assigned the same simple programming task to each programmer.It is known that all three populations have highly skewed distributions with extreme outliers.Which one of the following nonparametric tests is appropriate for this problem?
A)Wilcoxon signed rank test
B)Wilcoxon rank sum test
C)Sign test
D)Kruskall-Wallis test
E)Spearman's rank correlation test
Q3) Calculate the value of T<sub>I</sub> and T<sub>E</sub>.
Q4) What is the rejection point T<sub>0</sub> for \(\alpha\) = .05?
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Chapter 14: Chi-Square Tests
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Sample Questions
Q1) Compute the expected frequencies in row 3.
Q2) Calculate the expected enrolment (frequency)for all 7 regions (hint: p<sub>1</sub> = p<sub>2</sub> = p<sub>3</sub> = p<sub>4</sub> = p<sub>5</sub> = p<sub>6</sub> = p<sub>7</sub>).
Q3) What is the rejection point condition?
A)Reject H<sub>0</sub> if ?<sup>2</sup> > .10257
B)Reject H<sub>0</sub> if ?<sup>2</sup> > 9.3484
C)Reject H<sub>0</sub> if ?<sup>2</sup> > 5.99147
D)Reject H<sub>0</sub> if ?<sup>2</sup> > 7.37776
E)Reject H<sub>0</sub> if ?<sup>2</sup> > 7.81473
Q4) Calculate the expected absences for all 5 days.
Q5) Assume that H<sub>0</sub>: p<sub>1</sub> = p<sub>2</sub> = p<sub>3</sub> = p<sub>4</sub> = p<sub>5</sub> = p<sub>6</sub> = p<sub>7</sub> is rejected.State a one sentence managerial conclusion.
Q6) In performing a chi-square goodness of fit test for a normal distribution,if there are 7 intervals,then the degrees of freedom for the chi-square statistic is ______________.
Q7) A chi-square test of independence is performed and the null hypothesis is rejected.Provide a one-sentence interpretation of the outcome of the test.
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Chapter 15: Decision Theory
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Sample Questions
Q1) The expected monetary value criterion is used for decision-making under
A)certainty
B)uncertainty
C)risk
D)alternatives
E)states of nature
Q2) The expected value criterion is used for decision-making under
Q3) When making a decision in an environment of ________________,the decision maker knows which of the states of nature will actually occur.
Q4) What alternative action should be selected according to expected monetary value criterion?
Q5) In a decision tree,the branches emanating from a circular node represent the possible ___________________.
Q6) In utility analysis,a utility curve that shows a rapid increase in utility for initial amounts of money followed by a gradual leveling off for larger amounts of money is appropriate for a risk seeking decision maker.
A)True
B)False
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Chapter 16: Time Series Forecasting
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Sample Questions
Q1) What is the predicted value of y when t = 20?
Q2) The forecaster who uses MSD (mean squared deviations)to measure the effectiveness of forecasting methods would prefer method 1 that results in several smaller forecast errors to method 2 that results in one large forecast error equal to the sum of the absolute values of several small forecast errors given by method 1.
A)True
B)False
Q3) Calculate the mean absolute deviation (MAD)for Model 2.
Q4) The upward or downward movement that characterizes a time series over a period of time is referred to as _____.
Q5) Calculate the mean absolute deviation (MAPE).
A)2.8
B)13.4
C)7.5
D)1.6
E)2.4
Q6) Compute the mean absolute deviation (MAD).
Q7) Compute the forecast errors for period 7 and period 8.
Q8) The _____ test is a test for first-order positive autocorrelation.
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