Business Decision Making
Exam Answer Key
Course Introduction
Business Decision Making explores the strategic and analytical processes involved in making effective managerial decisions in organizations. This course introduces students to various decision-making models, tools, and techniques used to analyze business challenges, assess risks, and evaluate potential solutions. Emphasizing both quantitative and qualitative approaches, the curriculum covers topics such as data-driven analysis, scenario planning, critical thinking, ethical considerations, and group decision dynamics. Through case studies and practical exercises, students will develop the skills to formulate, implement, and communicate impactful decisions in diverse business contexts.
Recommended Textbook
Business Statistics in Practice 3rd Canadian Edition by Bruce L. Bowerman
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Page 2
Chapter 1: An Introduction to Business Statistics
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Sample Questions
Q1) A _________ variable records into which of several categories a population unit falls.
Answer: qualitative
Q2) Jersey numbers of soccer players are an example of a(n)___________ variable.
A)nominative
B)ordinal
C)interval
D)ratio
E)random
Answer: A
Q3) The two levels of measurement for qualitative variables are
A)ordinal and ratio.
B)interval and ordinal.
C)nominative and ordinal.
D)interval and ratio.
E)nominative and interval.
Answer: C
Q4) A _____ is a subset of the units in a population. Answer: sample
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Chapter 2: Descriptive Statistics
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Sample Questions
Q1) What is the range?
A)22.72
B)12.00
C)4.77
D)516.20
E)144.00
Answer: B
Q2) What is the 10<sup>th</sup> percentile?
A)$1,304.50
B)$2,617
C)$3,415.75
D)$3,587
E)$4,212
Answer: A
Q3) If a frequency histogram were to be created using these data,how many classes would you create?
Answer: 6
Q4) If the median of a data set is 760 and the upper quartile is 950,and the lower quartile is 650,what is the interquartile range?
Answer: 300 Interquartile range = 950 - 650 = 300
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Chapter 3: Probability
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Sample Questions
Q1) A machine is made up of 3 components: an upper part,a mid part,and a lower part.The machine is then assembled.3 percent of the upper parts are defective;2 percent of the mid parts are defective;5 percent of the lower parts are defective.Assuming that the parts function independently of each other,what is the probability that a machine is non-defective?
Answer: .90307
(.97)(.98)(.95)= .90307
Q2) If two events are independent,we can _____ their probabilities to determine the intersection probability.
A)divide
B)add
C)multiply
D)subtract
Answer: C
Q3) Events that have no sample space outcomes in common,and,therefore cannot occur simultaneously are referred to as independent events.
A)True
B)False
Answer: False
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Page 5
Chapter 4: Discrete Random Variables
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Sample Questions
Q1) One fair die is thrown.What is the expected value of the number of dots on the top face of the die?
Q2) A multiple-choice test has 30 questions and each one has five possible answers,of which one is correct.If all answers were guesses,find the probability of getting exactly four correct answers.
A)0604
B)1325
C)2000
D)2552
E)8000
Q3) When using hypergeometric distribution,it is assumed that the trials are __________ and the probability of success ________ from trial to trial.
A)independent,does not change
B)dependent,does not change
C)independent,changes
D)dependent,changes
Q4) Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store.Determine the expected number of customer arrivals for a five-minute period
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Chapter 5: Continuous Random Variables
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Sample Questions
Q1) What percentage of students scored between 65 and 89?
Q2) The area under the curve of a valid continuous probability distribution must equal _____.
Q3) If the random variable X has a mean of \(\mu\) And a standard deviation \(\sigma\) ,then \(( X - \mu ) / \sigma\)
Has a mean of ____ and standard deviation of _____.
A) \(\mu\) and \(\sigma\)
B) \(\bar { X }\) and s
C)1 and 0
D)0 and 1
E)Cannot be determined without more information.
Q4) The _____________ distribution would most likely be used to describe the distribution of time between arrivals of customers at the grocery store.
A)normal
B)exponential
C)Poisson
D)binomial
E)uniform
Q5) What is the probability of finding a person who scores less than 10?
7
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Chapter 6: Sampling Distributions
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Sample Questions
Q1) The _____ says that if the sample size is sufficiently large,then the sample means are approximately normally distributed even if the sampled population is not normal.
Q2) A golf tournament organizer is attempting to determine whether hole (pin)placement has a significant impact on the average number of strokes for the 13<sup>th</sup>hole on a given golf course.Historically,the pin has been placed in the front right corner of the green,and the historical mean number of strokes for the hole has been 4.25,with a standard deviation of 1.6 strokes.On a particular day during the most recent golf tournament,the organizer placed the hole (pin)in the back left corner of the green.64 golfers played the hole with the new placement on that day.Determine the probability of the sample average number of strokes exceeding 4.75.
Q3) Suppose you take a random sample of size n = 100 from a population with \(\mu\) = 400.If P( \(\bar { x }\) < 380)= 0.0668,find \(\sigma\) .
Q4) Find P( \(\hat { p }\) < .18).
Q5) As the sample size ___________,the variability of the sampling distribution of the sample proportion increases.
Q6) The _________ theorem allows us to approximate the sampling distribution of a sample mean with a normal probability distribution whenever the sample size is sufficiently large.
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Chapter 7: Confidence Intervals
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Sample Questions
Q1) A new company is in the process of evaluating its customer service.The company offers two types of sales: 1.Internet sales;2.Store sales.The marketing research manager believes that the Internet sales are more than 10% higher than store sales.The null hypothesis would be:
A)P<sub>internet</sub> - P<sub>store</sub> > .10
B)P<sub>internet</sub> - P<sub>store</sub> < .10
C)P<sub>internet</sub> - P<sub>store</sub> .10
D)P<sub>internet</sub> - P<sub>store</sub> .10
E)P<sub>internet</sub> - P<sub>store</sub> = .10
Q2) Is the proportion of customers who prefer chicken higher at the West Coast? Test at
Q3) When carrying out a test of H<sub>0</sub>: p = .4 versus H<sub>a</sub>: p < .4 and z is the calculated test statistic,we reject H<sub>0</sub> at level of significance \(\alpha\)When:
A)z < - \(z _ { \alpha / 2 }\)
B)z < - \(z _ { \alpha }\)
C)z > \(z _ { \alpha }\)
D)p-value > \(\alpha\)
E)p-value > 2 \(\alpha\)
Q4) What is the decision at \(\alpha\) = 0.10?
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Chapter 8: Hypothesis Testing
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Sample Questions
Q1) The appropriate hypotheses to test that the process is performing satisfactorily is
A)H <sub>0</sub>: µ ? 0.250 H<sub>a</sub> :µ < 0.250
B)H <sub>0</sub> :µ = 0.250 H<sub>a</sub> :µ ? 0.250
C)H <sub>0</sub> :µ ? 0.250 H<sub>a</sub> :µ > 0.250
D)H <sub>0</sub>: µ ? 0.250 H<sub>a</sub> :µ = 0.250
E)H <sub>0</sub> :µ ? 0.2525 H<sub>a</sub> :µ > 0.2525
Q2) How much evidence do we have that the system differs from 15.5?
A)No evidence
B)Some evidence
C)Strong evidence
D)Very strong evidence
E)Extremely strong evidence
Q3) The null and alternative hypotheses to test the claim that the entertainment expenses per month are less than the estimate is _____.
A)H<sub>0</sub>: ? = 123 vs.H<sub>a</sub>: ? ? 123
B)H<sub>0</sub>: ? ? 123 vs.H<sub>a</sub>: ? < 123
C)H<sub>0</sub>: ? ? 113.03 vs.H<sub>a</sub>: ? < 113.03
D)H<sub>0</sub>: ? ? 123 vs.H<sub>a</sub>: ? = 123
E)H<sub>0</sub>: ? ? 123 vs.H<sub>a</sub>: ? > 123
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Chapter 9: Statistical Inferences Based on Two Samples
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Sample Questions
Q1) A statistical quality control process for cereal production measures the weight of a cereal box.The population standard deviation is known to be .05 grams.In order to achieve a 97% confidence with a margin of error of .02g,how large a sample should be used?
Q2) Sandwiches sold at a local grocery store claim to have 6 grams of fat per sandwich.Ten sandwiches are brought with results of a mean of 5.93g of fat and a standard deviation of 0.13g.If fat content is normally distributed,the 99% confidence interval for the true fat content would be _____.
A)[5.888,5.972]
B)[5.814,6.046]
C)[5.716,6.144]
D)[5.824,6.036]
E)[5.796,6.064]
Q3) The customer service manager for the XYZ Fastener Manufacturing Company examined 60 vouchers and found nine vouchers containing errors.Find a 95 percent confidence interval for the proportion of vouchers with errors.
Q4) In general,replacing a z with a t when using a preliminary sample to obtain an estimate of the variance is a _____ decision.
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Chapter 10: Experimental Design and Analysis of Variance
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Sample Questions
Q1) In testing the significance of factor 1,the numerator and denominator degrees of freedom for the ANOVA F test are:
A)4,60
B)3,48
C)4,48
D)3,12
E)4,12
Q2) What is the degrees of freedom for the error?
A)20
B)4
C)3
D)19
E)16
Q3) In a one-way ANOVA for a completely randomized design,all other things being held constant,as the between-treatment variation decreases,the probability of rejecting the null hypothesis increases.
A)True
B)False
Q4) What is the factor I mean square?
Q5) Test H<sub>0</sub>: There is no difference between blocks at a=.05.
Page 12
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Chapter 11: Correlation Coefficient and Simple Linear
Regression Analysis
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Sample Questions
Q1) Determine the 95% prediction interval for the mean value of y when x = 35 Givens: x = 277 and x<sup>2</sup> = 8705
Q2) Test to determine if there is a significant correlation between x and y Use H<sub>0</sub>: ? = 0 versus H<sub>a</sub>: ? ? 0 by setting \(\alpha\) = .01
Reject the null hypothesis,there is a significant correlation between x and y
Q3) Use the least squares regression equation and estimate the monthly tire sales when advertising expenditures is $4000
Q4) Complete the following partial ANOVA table from a simple linear regression analysis with a sample size of 16 observations.Use the F test to test the significance of the \[\begin{array} { l c c c c }
\text { Source } & \text { SS } & \text { DF } & \text { MS } & \text { F } \\
\text { Regression } & & & 309.9 \\
\text { Error } & & & & \\
\text { Total } & 995.95 & & \end{array}\] F = 6.33,reject H<sub>0</sub><sub> </sub>
Q5) Calculate the SSE.
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Chapter 12: Multiple Regression and Model Building
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Sample Questions
Q1) The general form of the quadratic multiple regression models is:
A)y = \(\beta\) <sub> </sub> <sub>1</sub>X<sub>1</sub>+ \(\beta\) <sub> </sub> <sub>2</sub>X<sub>2</sub>+ \(\varepsilon\)
B)y = \(\beta\) <sub> </sub> <sub>0</sub>+ \(\beta\) <sub> </sub> <sub>1</sub>X<sub>1</sub>+ \(\beta\) <sub> </sub> <sub>2</sub>X<sub>2</sub>+ \(\varepsilon\)
C)y = \(\beta\) <sub> </sub> <sub>0</sub>+ \(\beta\) <sub> </sub> <sub>1</sub>X + \(\beta\) <sub> </sub> <sub>2</sub>X<sup>2</sup>+ \(\varepsilon\)
D)y = \(\beta\) <sub> </sub> <sub>0</sub>+ \(\beta\) <sub> </sub> <sub>1</sub>X<sup>2</sup>+ \(\varepsilon\)
E)y = \(\beta\) <sub> </sub> <sub>0</sub>+ \(\beta\) <sub> </sub> <sub>1</sub>X<sub>1</sub>+ \(\beta\) <sub> </sub> <sub>2</sub>X<sub>2</sub><sup>2</sup>+ \(\varepsilon\)
Q2) Interpret the estimated model coefficient b3.
Q3) In the quadratic regression model y = ?<sub>0</sub>+ ?<sub>1</sub>x + ?<sub>2</sub>x<sup>2</sup>+ ?,if the value of the term ?<sub>1</sub>increases,then the parabola shifts to the _________.
Q4) Test the overall usefulness of the model at ? = .01.Calculate F and make your decision.
Page 14
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Chapter 13: Nonparametric Methods
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Sample Questions
Q1) Calculate T<sub>A</sub>,T<sub>B</sub>,T<sub>C</sub>,T<sub>D</sub> for the Kruskal-Wallis test.
Q2) At \(\alpha\) = .05,can it be concluded that the oral exam scores are higher than the written exam scores?
Q3) Based on this result of the test,provide a one sentence conclusion.
Q4) Nonparametric tests can be more powerful than the corresponding t or F tests if the population distribution is highly skewed or not normal.
A)True
B)False
Q5) An international economist believes that there is a significant relationship between the amount of debt and the rate of unemployment.The economist randomly selected six countries to determine if there is a significant relationship between debt and unemployment rate.In the following table,debt figures for the 6 countries are given in billions of dollars and the corresponding unemployment rate is given in percentages.The economist also discovered that both the distribution of debt and the distribution of unemployment rate were highly skewed.Use Spearman's rank correlation and determine if there is a significant correlation between debt and unemployment rate.
Q6) 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) Calculate the expected frequency for the interval 0-39.99.
Q2) Calculate the expected absences for all 5 days.
Q3) At ? = .05,test to determine if the grade distribution for Dr.Johnson's class is different than the historical grade distribution.
Q4) Calculate the value of the chi-square test statistic?
Q5) Calculate the expected number of defective units produced by Process 1. A)29
B)21.053
C)218.947
D)6.042
E)10.786
Q6) At a significance level of .01,test H<sub>0</sub>: the probabilities are equal for all seven regions.
Q7) Calculate the expected frequency for the interval 60 - 79.99.
Q8) Use a significance level of 0.05 and determine if the use of a cell phone and having an auto accident are independent.
Q9) At a significance level of .05,determine the appropriate degrees of freedom and the rejection point condition for this test.
Page 16
Q10) Calculate the chi-square statistic for this test of independence.
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Chapter 15: Decision Theory
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Sample Questions
Q1) The alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt.The level of demand affects the success of both strategies.The states of nature (S<sub>i</sub>,i = 1,2,3)represent the levels of demand for the company products.S<sub>1</sub>,S<sub>2</sub> and S<sub>3</sub> characterize high,medium,and low demand respectively.The payoff values are in thousands of dollars. \[\begin{array} { l c c c }
& { \text { States of nature } } \\ & \mathrm { s } _ { 1 } & \mathrm {~s} _ { 2 } & \mathrm {~s} _ { 3 } \\
\text { Alternative (strategy) 1 } & 10 & 80 & 70 \\
\text { Alternative (strategy) 2 } & 60 & 120 & 50 \end{array}\]
The best alternative (course of action)for the EKA manufacturing company using the maximax criterion is alternative 1.
A)True
B)False
Q2) Expected value of _________ is defined as the expected payoff under certainty subtracted by the expected payoff under risk.
Q3) Which investment would the investor select if the maximax criterion is used?
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Chapter 16: Time Series Forecasting
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Sample Questions
Q1) Calculate the Laspeyres index.
Q2) The recurring up-and-down movement of a time series around trend levels that last more than one calendar year is called _____.
Q3) When using moving averages to estimate the seasonal factors,we need to compute the centered moving average if there are an odd number of seasons.
A)True
B)False
Q4) Calculate the average seasonal factor for each quarter
Q5) Compute the total forecast error (sum of the forecast errors)
Q6) In the Durbin-Watson test,if the calculated d-statistic is greater than the upper value of the d-statistic,then:
A)We do not reject H<sub>0</sub>which says the error terms are not autocorrelated.
B)We do reject H<sub>0</sub>which says the error terms are not autocorrelated.
C)The test is inconclusive.
D)We do reject H<sub>0</sub>,which says the error terms are positively or negatively autocorrelated.
Q7) Using the following,compute the MPE and the MAPE.
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