Quantitative Methods for Business Final Exam
Course Introduction
Quantitative Methods for Business introduces students to the fundamental mathematical, statistical, and analytical techniques essential for informed business decision-making. The course covers topics such as data collection and analysis, probability theory, hypothesis testing, linear programming, regression analysis, and forecasting. Emphasizing practical application, students learn to use quantitative models and software tools to analyze real-world business problems, evaluate alternatives, and support strategic planning in areas such as operations, finance, marketing, and management. By mastering these quantitative methods, students gain valuable skills to interpret data effectively and make evidence-based decisions in dynamic business environments.
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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Q1) Ratio variables have the following unique characteristic:
A)Meaningful order
B)An arbitrarily defined zero value
C)Categorical in nature
D)Predictable with 100% accuracy
E)Equal distance between points
Answer: E
Q2) __________ is a necessary component of a runs plot.
A)Observation over time
B)A qualitative variable
C)Random sampling of the data
D)Voluntary response data
E)A Likert scale survey
Answer: A
Q3) A _____ is a subset of the units in a population.
Answer: sample
Q4) In a voluntary response sample,what types of opinions are usually expressed?
Answer: Strong/negative.
Q5) Any characteristic of a population unit is called a _____.
Answer: variable
3
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Chapter 2: Descriptive Statistics
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Q1) If specifications for a process are (1.6,1.8),and a 99.73 percent tolerance interval is (1.62,1.83),is the process capable?
Answer: No
Q2) If there are 7 classes in a frequency distribution,then the fourth class will always contain the median.
A)True
B)False
Answer: False
Q3) What is the 10<sup>th</sup> percentile?
A)65.5
B)67.3
C)66.75
D)73.85
E)77.0
Answer: A
Q4) A Pareto chart is a type of histogram.
A)True
B)False Answer: False
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Chapter 3: Probability
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Q1) Probabilities must be assigned to experimental outcomes so that the probability assigned to each experimental outcome must be between the values ____ and ____ inclusive.
Answer: 0,1
Q2) Suppose that you draw one card from a standard deck of 52 cards.If the card you draw is a red card,what is the probability it is also a face card?
Answer: 3/13 \[P ( \text { Face } \mid \operatorname { Re } d ) = \frac { P ( \operatorname { Re } d \cap F a c e ) } { P ( \operatorname { Re } d ) } = \frac { 6 / 52 } { 26 / 52 } = \frac { 3 } { 13 }\]
Q3) When the probability of one event is not influenced by whether or not another event occurs,the events are said to be _____.
Answer: Independent
Q4) What is the probability that an undergraduate is in a Greek organization given that the undergraduate is a female?
Answer: .127
P(G|F)= .07/.55 = .127
Q5) The _____ is the set of all of the distinct possible outcomes of an experiment. Answer: Sample Space
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Chapter 4: Discrete Random Variables
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Q1) Determine the probability of 6 patients arriving in a five-hour period.
A)019
B)136
C)233
D)369
E)401
Q2) Determine the probability of at least 4 but no more than 8 patients arriving in a three-hour period.
A)281
B)708
C)898
D)617
E)463
Q3) Would you accept or reject the claim? Explain.
Q4) If 3 calculators are selected at random,what is the probability that exactly one of the calculators will be defective?
Q5) If x is a Poisson random variable with a mean of 10,what is the probability that x is equal to 8?
Q6) Find the standard deviation of X.
Q7) At least 3 of the individuals have type A blood
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Chapter 5: Continuous Random Variables
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Q1) In a statistical study,the random variable X = 1,if the house is colonial,and X = 0 if the house is not colonial,then it is appropriate to model this variable with a continuous probability distribution.
A)True
B)False
Q2) Let X be a binomial random variable with n = 150 and p = 0.3.Approximate P(X \(\geq\)
50))
A)0.7881
B)0.9909
C)0.2119
D)0.0091
E)0.5644
Q3) For the 10% who spend the most The average time a subscriber spends reading the local newspaper is 49 minutes. Assume the standard deviation is 16 minutes and that the times are normally distributed.me reading the paper,how much time do they spend?
Q4) All continuous random variables are normally distributed.
A)True
B)False
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Chapter 6: Sampling Distributions
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Q1) The _______________________ of the sample mean \(\bar { x }\) is the probability distribution of the population of all possible sample means that could be obtained from all possible samples of the same size.
Q2) What is the probability that less than 64 patients will not be satisfied with the after-surgery care?
A)0.4772
B)0.0228
C)0.9772
D)0.9544
E)0.0197
Q3) Find P ( \(\bar { x }\) < 48).
Q4) What is the probability the mean length of the bolt is at most 3.1 cm?
A)0.8413
B)1
C)0.7157
D)0.2843
E)0.1587
Q5) What is the probability of finding an average less than 3.85 grams of this ingredient from randomly inspected 64L of regular unleaded gasoline?
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Chapter 7: Confidence Intervals
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Q1) Calculate the test statistic and test the claim at
Q2) You suspect that women tend to be more in favour of this tax than men.If you wish to conduct a hypothesis test,what is the value of appropriate test statistic?
A)0.45
B)2.31
C)1.34
D)1.84
E)5.13
Q3) The level of significance indicates the probability of rejecting a false null hypothesis. A)True B)False
Q4) A Cohen's d value of 0.1 means that the effect is ___________.
Q5) The rejection of a true null hypothesis is called a ______________ error.
Q6) What is the p-value for this test?
Q7) Everything else being constant,increasing the sample size decreases the probability of committing a Type II error.
A)True
B)False
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Chapter 8: Hypothesis Testing
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Q1) In general,the shape of the F distribution is skewed _________.
Q2) The appropriate test statistic to test the hypotheses is _____.
A)1.00
B)-1.00
C)2.80
D)1.41
E)-1.41
Q3) What is the p-value for this test?
Q4) What is the critical value for this test at alpha = .05?
Q5) In comparing the difference between two independent population means,by using two small independent samples,the sampling distributions of the population means must be at least approximately _____________.
Q6) How would you define the rejection region for this test at ? = .05?
A)t < -2.821
B)t < -1.761
C)t > 2.492 and t < -2.492
D)t > 2.306 and t < -2.306
E)t > 3.787
Q7) Test the claim at \(a\) = .01
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Chapter 9: Statistical Inferences Based on Two Samples
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Q1) 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.
Q2) An auditor was hired to verify the accuracy of a company's new billing system.Thirty-five (35)invoices produced since the system was installed were sampled.The average error on the invoices was $1.00.Historically,the population standard deviation is around $124.00.A 97% confidence interval for the mean error per invoice would be _____.
A)[-268.08,270.08]
B)[-6.69,8.69]
C)[-44.48,46.48]
D)[-38.40,40.40]
E)[-9.17,11.66]
Q3) What sample size is needed to obtain a 95 percent confidence interval for the proportion of fat in meat that is within 2 percent of the true value?
Q4) Interpret the 95% confidence interval for the difference in mean price.
Q5) What is the estimated standard deviation of the sample proportion?
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Chapter 10: Experimental Design and Analysis of Variance
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Q1) Compute an individual 95% confidence interval for the first group mean.
Q2) What is the degrees of freedom for error?
Q3) In a two-factor factorial experiment,the interaction effect between two factors can only be measured if there are multiple observations in each cell (combination of levels of two factors).
A)True
B)False
Q4) In performing an ANOVA for a randomized block design,the between-groups sum of squares equals:
A)SST - SSE - SS(int)
B)SST - SSBL - SSE
C)SST - SS(int)- SSBL
D)SST - SSBL
E)SST - SSE
Q5) Complete the analysis of variance table and test to determine whether the means for factor B differ at a = .10.Interpret the results.
Q6) What is the total sum of squares?
Q7) Determine the degrees of freedom for groups (treatments).
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Q8) In an experiment,the response variable is also known as the _______ variable.
Chapter 11: Correlation Coefficient and Simple Linear
Regression Analysis
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Q1) The simple linear regression model assumes there is a _____ relationship between the dependent variable and the independent variable.
Q2) In simple linear regression,the __________ assumption requires that all variation around the regression line should be equal at all possible values (levels)of the independent variable.
Q3) Provide an interpretation of the y-intercept estimate.
Q4) One of the metal sheets used in the experiment was heated for 4 minutes had an observed strength of 6 g per square cm.Calculate the value of the residual for this observation.
Q5) The coefficient of determination is the proportion of total variation explained by the regression line.
A)True
B)False
Q6) Calculate the coefficient of determination.
Q7) Using the sums of the squares given above,determine the 90% confidence interval for the mean value of monthly tire sales when the advertising expenditure is $5000.
Page 13
Q8) Determine the normal score for the third residual in the ordered array.
Q9) What is the explained variation?
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Chapter 12: Multiple Regression and Model Building
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Q1) As we increase the number of independent variables in a multiple regression model,the F statistic in the analysis of variance table for the multiple regression model will ________ increase.
A)always
B)sometimes
C)never
Q2) What is the mean square error?
Q3) What is the explained variation?
Q4) When the F test is used to test the overall significance of a multiple regression model,if the null hypothesis is rejected,it can be concluded that all of the independent variables x<sub>1</sub>,x<sub>2</sub>, x<sub>k</sub> are significantly related to the dependent variable y.
A)True
B)False
Q5) Using the results above,what is the total sum of squares?
A)1053.09
B)1790.00
C)1858.50
D)3630.90
E)2911.59
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Chapter 13: Nonparametric Methods
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Q1) The ______________ test is a nonparametric method that requires data consisting of matched pairs.
Q2) In a Wilcoxon Rank Sum Test,when two or more observations are equal,we assign to each tied observation a rank equal to the ______ of the consecutive ranks.
Q3) Which one of the following nonparametric methods can be considered as an extension of the Wilcoxon rank sum test to three or more populations?
A)Wilcoxon signed rank test
B)Sign test
C)Kruskall-Wallis test
D)Spearman's test
E)Adcock Addition test
Q4) The sign test is a nonparametric test for a population mean that is valid for any sample size and population shape.
A)True
B)False
Q5) The Wilcoxon rank sum test is used to compares the locations of two _____________ populations.
Q6) State the null and alternative hypotheses.
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Chapter 14: Chi-Square Tests
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Q1) Determine the expected frequencies for the chi-square test of independence.
Q2) A special version of the chi-square goodness of fit test that involves testing the null hypothesis that all of the multinomial probabilities are equal is called the test for
Q3) When we carry out a goodness of fit chi-square test,the expected frequencies are based on the alternative hypothesis.
A)True
B)False
Q4) At\(\alpha\) = .05,determine the tabular value of the chi-square statistic used to test for the independence of Factors A and B?
Q5) Use a significance level of 0.05 and determine if the use of a cell phone and having an auto accident are independent.
Q6) Calculate the value of the chi-square statistic.
Q7) At a significance level of .05,test H<sub>0</sub>: the set of 50 measurements came from a normal population.
Q8) At a significance level of .01,determine the appropriate degrees of freedom and the rejection point condition for this test.
Q9) Compute the expected frequencies in row 1.
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Chapter 15: Decision Theory
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Q1) Find the expected monetary value for each of the alternatives and determine the best alternative (course of action)for the EKA manufacturing company using the expected monetary value criterion.
A)EMV<sub>1</sub> = $98,000,EMV<sub>2</sub> = $95,000,choose strategy 1
B)EMV<sub>1</sub> = $58,000,EMV<sub>2</sub> = $95,000,choose strategy 2
C)EMV<sub>1</sub> = $58,000,EMV<sub>2</sub> = $85,000,choose strategy 1
D)EMV<sub>1</sub> = $66,667,EMV<sub>2</sub> = $76,667 choose strategy 2
E)EMV<sub>1</sub> = $120,000,EMV<sub>2</sub> = $110,000,choose strategy 1
Q2) An accident has just been reported.What is the probability that the insured driver is under the age of 25?
Q3) Which investment would the investor select if the maximax criterion is used?
Q4) Construct the revised probability table for poor weather conditions and find the probability of high demand given that the weather conditions are poor.
Q5) The expected value criterion is used for decision-making under
Q6) Find the expected monetary value for each of the alternatives and determine the best alternative (course of action)for the EKA manufacturing company using the expected monetary value criterion.
Q7) The __________________ criterion is preferred by optimistic decision-makers.
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Chapter 16: Time Series Forecasting
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Q1) The _______________ index is most useful if the base quantities provide a reasonable representation of consumption patterns in succeeding time periods.
Q2) If a time series has constant seasonal variation,then the forecaster should use the multiplicative decomposition method to forecast future values of the time series.
A)True
B)False
Q3) Calculate the mean square deviation (MSD).
A)2.8
E)2.4
Q4) Calculate the ratio of actual production to the centered moving average values (snt* irt)for the entire time series.
Q5) Which model is the most accurate? Why?
Q6) Consider the following data and calculate S<sub>1</sub> using simple exponential smoothing and = 0.3.
Q7) Calculate the aggregate price index.
19
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