Quantitative Methods for Business Exam
Answer Key
Course Introduction
Quantitative Methods for Business introduces students to the application of mathematical, statistical, and analytical techniques to solve business problems and support decision-making processes. The course covers foundational topics such as data collection, probability, descriptive and inferential statistics, linear programming, forecasting, and decision analysis, with a focus on real-world business scenarios. Students learn how to use quantitative models and tools to analyze data, assess risk, optimize resources, and interpret results to make informed managerial decisions. Through practical exercises and case studies, students develop critical thinking and problem-solving skills essential for various functional areas in business, including finance, operations, and marketing.
Recommended Textbook
Statistics for Business and Economics 11th Edition by David R. Anderson
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Page 2
Chapter 1: Data and Statistics
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Q1) Data
A)are always be numeric
B)are always nonnumeric
C)are the raw material of statistics
D)None of these alternatives is correct.
Answer: C
Q2) The scale of measurement that has an inherent zero value defined is the A)ratio scale
B)nominal scale
C)ordinal scale
D)interval scale
Answer: A
Q3) Statistical inference
A)refers to the process of drawing inferences about the sample based on the characteristics of the population
B)is the same as descriptive statistics
C)is the process of drawing inferences about the population based on the information taken from the sample
D)is the same as a census
Answer: C
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Chapter 2: Descriptive Statistics: Tabular and Graphical Presentations
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Q1) A histogram is
A)a graphical presentation of a frequency or relative frequency distribution
B)a graphical method of presenting a cumulative frequency or a cumulative relative frequency distribution
C)the history of data elements
D)the same as a pie chart
Answer: A
Q2) In a cumulative percent frequency distribution,the last class will have a cumulative percent frequency equal to A)one
B)100
C)the total number of elements in the data set
D)None of these alternatives is correct.
Answer: B
Q3) Refer to Exhibit 2-3.The lower limit of the first class is A)5
B)80
C)0
D)20
Answer: C
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Chapter 3: Descriptive Statistics: Numerical Measures
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Q1) Which of the following symbols represents the size of the sample A)\(\sigma\)<sup>2</sup> B)\(\sigma\)
C)N
D)n
Answer: D
Q2) Given the following information: Standard deviation = 8
Coefficient of variation = 64%
The mean would then be
A)12.5
B)8
C)0.64
D)1.25
Answer: A
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Chapter 4: Introduction to Probability
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Sample Questions
Q1) Two events,A and B,are mutually exclusive and each have a nonzero probability.If event A is known to occur,the probability of the occurrence of event B is
A)one
B)any positive value
C)zero
D)any value between 0 to 1
Q2) Any process that generates well-defined outcomes is A)an event
B)an experiment
C)a sample point
D)a sample space
Q3) If X and Y are mutually exclusive events with P(X)= 0.295,P(Y)= 0.32,then P(X | Y)=
A)0.0944
B)0.6150
C)1.0000
D)0.0000
Q4) A committee of 4 is to be selected from a group of 12 people.How many possible committees can be selected?
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Chapter 5: Discrete Probability Distributions
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Q1) A measure of the average value of a random variable is called a(n)
A)variance
B)standard deviation
C)expected value
D)coefficient of variation
Q2) Refer to Exhibit 5-7.The probability that Pete will catch fish on exactly one day is
A).008
B).096
C).104
D).8
Q3) An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment.The random variable in this experiment is a
A)discrete random variable
B)continuous random variable
C)complex random variable
D)simplex random variable
Q4) Determine the probability of being dealt 4 kings in a 5-card poker hand.
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Chapter 6: Continuous Probability Distributions
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Q1) Refer to Exhibit 6-2.The probability of a player weighing more than 241.25 pounds is
A)0.4505
B)0.0495
C)0.9505
D)0.9010
Q2) A uniform probability distribution is a continuous probability distribution where the probability that the random variable assumes a value in any interval of equal length is A)different for each interval
B)the same for each interval
C)at least one
D)None of these alternatives is correct.
Q3) X is a normally distributed random variable with a mean of 8 and a standard deviation of 4.The probability that X is between 1.48 and 15.56 is
A)0.0222
B)0.4190
C)0.5222
D)0.9190
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Chapter 7: Sampling and Sampling Distributions
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Sample Questions
Q1) An automotive repair shop has determined that the average service time on an automobile is 130 minutes with a standard deviation of 26 minutes.A random sample of 40 automotive services is selected.
a.Compute the standard error of the mean.
b.What is the probability that the sample of 40 automotive services will have a mean service time greater than 136 minutes?
c.Assume the population consists of 400 automotive services.Determine the standard error of the mean.
Q2) A population has a mean of 84 and a standard deviation of 12.A sample of 36 observations will be taken.The probability that the sample mean will be between 80.54 and 88.9 is
A)0.0347
B)0.7200
C)0.9511
D)8.3600
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Chapter 8: Interval Estimation
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Sample Questions
Q1) Refer to Exhibit 8-6.The value of the margin of error at 95% confidence is
A)80.83
B)7
C)0.8083
D)1.611
Q2) A sample of 60 students from a large university is taken.The average age in the sample was 22 years with a standard deviation of 6 years.Construct a 95% confidence interval for the average age of the population.
Q3) In a sample of 200 individuals,120 indicated they are Democrats.Develop a 95% confidence interval for the proportion of people in the population who are Democrats.
Q4) A sample of 144 cans of coffee showed an average weight of 16 ounces.The standard deviation of the population is known to be 1.4 ounces.
a.Construct a 68.26% confidence interval for the mean of the population.
b.Construct a 97% confidence interval for the mean of the population.
c.Discuss why the answers in Parts a and b are different.
Q5) A simple random sample of 144 items resulted in a sample mean of 1257.85 and a standard deviation of 480.Develop a 95% confidence interval for the population mean.
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Chapter 9: Hypothesis Tests
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Sample Questions
Q1) For a lower tail test,the p-value is the probability of obtaining a value for the test statistic
A)at least as small as that provided by the sample
B)at least as large as that provided by the sample
C)at least as small as that provided by the population
D)at least as large as that provided by the population.
Q2) In the last presidential election,a national survey company claimed that no more than 50% (i.e. ,< 50%)of all registered voters voted for the Republican candidate.In a random sample of 400 registered voters,208 voted for the Republican candidate.
a.State the null and the alternative hypotheses.
b.Compute the test statistic.
c.At 95% confidence,compute the p-value and test the hypotheses.
Q3) A machine is designed to fill toothpaste tubes with 5.8 ounces of toothpaste.The manufacturer does not want any underfilling or overfilling.The correct hypotheses to be tested are
A)H<sub>0</sub>: \(\mu\)\(\neq\) 5.8 H<sub>a</sub>: \(\mu\) = 5.8
B)H<sub>0</sub>: \(\mu\) = 5.8 H<sub>a</sub>: \(\mu\)\(\neq\)5.8
C)H<sub>0</sub>: \(\mu\) > 5.8 H<sub>a</sub>: \(\mu\) \(\le\) 5.8
D)H<sub>0</sub>: \(\mu\) \(\ge\) 5.8 H<sub>a</sub>: \(\mu\) < 5.8
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Page 11
Chapter 10: Statistical Inference About Means and
Proportions With Two Populations
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Q1) To compute an interval estimate for the difference between the means of two populations,the t distribution
A)is restricted to small sample situations
B)is not restricted to small sample situations
C)can be applied when the populations have equal means
D)None of these alternatives is correct.
Q2) Refer to Exhibit 10-9.The test statistic is
A)1.645
B)1.96
C)2.096
D)2.256
Q3) Refer to Exhibit 10-2.Based on the results of question 18,the
A)null hypothesis should be rejected
B)null hypothesis should not be rejected
C)alternative hypothesis should be accepted
D)None of these alternatives is correct.
Q4) In a sample of 40 Democrats,6 opposed the President's foreign policy,while of 50 Republicans,8 were opposed to his policy.Determine a 90% confidence interval estimate for the difference between the proportions of the opinions of the individuals in the two parties.
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Chapter 11: Inferences About Population Variances
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Q1) A company claims that the standard deviation in their delivery time is less than 5 days.A sample of 27 past customers is taken.The average delivery time in the sample was 14 days with a standard deviation of 4.5 days.At 95% confidence,test the company's claim.Use the critical value approach.
Q2) The sampling distribution of the ratio of independent sample variances extracted from two normal populations with equal variances is the
A)chi-square distribution
B)normal distribution
C)Z distribution
D)t distribution
Q3) Refer to Exhibit 11-1.The test statistic is
A)44.08
B)79.08
C)81.67
D)3.24
Q4) A random sample of 25 employees of a local utility firm showed that their monthly incomes had a sample standard deviation of $112.Provide a 90% confidence interval estimate for the standard deviation of the incomes for all the firm's employees.
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Chapter 12: Tests of Goodness of Fit and Independence
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Sample Questions
Q1) Refer to Exhibit 12-1.The p-value is
A)larger than 0.1
B)less than 0.1
C)less than 0.05
D)larger than 0.9
Q2) The degrees of freedom for a contingency table with 6 rows and 3 columns is
A)18
B)15
C)6
D)10
Q3) Refer to Exhibit 12-5.With a .05 level of significance,the critical value for the test is
A)1.645
B)7.815
C)14.067
D)15.507
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Chapter 13: Analysis of Variance and Experimental Design
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Sample Questions
Q1) An ANOVA procedure is applied to data obtained from 6 samples where each sample contains 20 observations.The degrees of freedom for the critical value of F are
A)6 numerator and 20 denominator degrees of freedom,
B)5 numerator and 20 denominator degrees of freedom
C)5 numerator and 114 denominator degrees of freedom
D)6 numerator and 20 denominator degrees of freedom
Q2) Refer to Exhibit 13-3.The null hypothesis for this ANOVA problem is
A)\(\mu\)<sub>1</sub>=\(\mu\)<sub>2</sub>
B)\(\mu\)<sub>1</sub>=\(\mu\)<sub>2</sub>=\(\mu\)<sub>3</sub>
C)\(\mu\)<sub>1</sub>=\(\mu\)<sub>2</sub>=\(\mu\)<sub>3</sub>=\(\mu\)<su b>4</sub>
D)\(\mu\)<sub>1</sub>=\(\mu\)<sub>2</sub>= ...=\(\mu\)<sub>12</sub>
Q3) Refer to Exhibit 13-1.The mean square between treatments (MSTR)equals
A)400
B)500
C)1,687.5
D)2,250
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Chapter 14: Simple Linear Regression
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Sample Questions
Q1) In regression analysis,the unbiased estimate of the variance is
A)coefficient of correlation
B)coefficient of determination
C)mean square error
D)slope of the regression equation
Q2) Refer to Exhibit 14-5.The coefficient of correlation is
A)0
B)-1
C)0.5
D)1
Q3) Refer to Exhibit 14-1.The coefficient of determination is
A)0.7096
B)- 0.7906
C)0.625
D)0.375
Q4) Refer to Exhibit 14-9.The least squares estimate of b<sub>1</sub> equals A)0.923
B)1.991
C)-1.991
D)-0.923
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Chapter 15: Multiple Regression
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Q1) Refer to Exhibit 15-6.The interpretation of the coefficient of X<sub>1</sub> is that
A)a one unit change in X<sub>1</sub> will lead to a 3.682 unit decrease in Y
B)a one unit increase in X<sub>1</sub> will lead to a 3.682 unit decrease in Y when all other variables are held constant
C)a one unit increase in X<sub>1</sub> will lead to a 3.682 unit decrease in X<sub>2</sub> when all other variables are held constant
D)It is impossible to interpret the coefficient.
Q2) In order to test for the significance of a regression model involving 14 independent variables and 255 observations,the numerator and denominator degrees of freedom (respectively)for the critical value of F are
A)14 and 255
B)255 and 14
C)13 and 240
D)14 and 240
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Chapter 16: Regression Analysis: Model Building
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Q1) Refer to Exhibit 16-4.The p-value for testing the significance of the regression model is
A)less than 0.01
B)between 0.01 and 0.025
C)between 0.025 and 0.05
D)between 0.05 and 0.10
Q2) Refer to Exhibit 16-2.The value of MSR is
A)10.40
B)348
C)10.83
D)52
Q3) Refer to Exhibit 16-2.The coefficient of determination for this model is
A)0.6923
B)0.1494
C)0.1300
D)0.8700
Q4) Thirty-four observations of a dependent variable (Y)and two independent variables resulted in an SSE of 300.When a third independent variable was added to the model,the SSE was reduced to 250.At 95% confidence,determine whether or not the third independent variable contributes significantly to the model.
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Chapter 17: Index Numbers
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Q1) The Laspeyres index is a weighted aggregate price index where the weight for each item is its
A)current-period quantity
B)base-period price
C)current-period price
D)base-period quantity
Q2) Refer to Exhibit 17-1.The price relative for item A in 2010 (use 2005 as the base year)is
A)1.082
B)7
C)92.391
D)108.235
Q3) A monthly price index that uses the price changes in consumer goods and services for measuring the changes in consumer prices over time is known as the A)Paasche Index
B)Consumer Price Index
C)Producer Price Index
D)Laspeyres Index
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Chapter 18: Forecasting
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Sample Questions
Q1) The model that assumes that the actual time series value is the product of its components is the
A)forecast time series model
B)multiplicative time series model
C)additive time series model
D)None of these alternatives is correct.
Q2) A method of smoothing a time series that can be used to identify the combined trend/cyclical component is
A)the moving average
B)the percent of trend
C)exponential smoothing
D)the trend/cyclical index
Q3) One measure of the accuracy of a forecasting model is
A)the smoothing constant
B)a deseasonalized time series
C)the mean square error
D)None of these alternatives is correct.
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Chapter 19: Nonparametric Methods
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Q1) Refer to Exhibit 19-6.The conclusion is that there
A)is no significant difference between the proportions B)is a significant difference between the proportions C)could be a difference in proportions,depending on the sample size D)None of these alternatives is correct.
Q2) In a sample of 200 racquetball players,120 indicated they prefer Penn racquetballs,75 favored Ektelon,and 5 were indifferent.We want to use the sign test to determine if there is evidence of a significant difference in the preferences for the two types of racquetballs.
a.Provide the hypotheses to be tested.
b.Compute the mean.
c.Compute the standard deviation.
d..At 95% confidence,test to determine if there is evidence of a significant difference in the preferences for the two types of racquetballs.
Q3) Refer to Exhibit 19-1.The null hypothesis that is being tested is
A)H<sub>0</sub>: \(\mu\)= 5
B)H<sub>0</sub>: \(\mu\) = 0.5
C)H<sub>0</sub>: P = 5
D)H<sub>0</sub>: P = 0.5
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Chapter 20: Statistical Methods for Quality Control
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Sample Questions
Q1) The quality control department of a company has decided to select a sample of 20 items from each shipment of goods it receives and inspect them for defects.It has been decided that if the sample contains no defective parts,the entire lot will be accepted.
a.What is the probability of accepting a lot that contains 10% defective items?
b.What is the probability of accepting a lot that contains 5% defective items?
c.What is the probability of rejecting a lot that contains 15% defective items?
Q2) The upper and lower control limits of the proportions of defectives of a process are 0.33 and 0.27.
a.What has been the proportion of defectives in this process?
b.What has been the sample size?
Q3) A production process is set up to fill containers with 16 ounces of liquid.The standard deviation \(\sigma\) is known to be 0.5 ounces.The quality control department periodically selects samples of 25 containers and measures the contents.(Assume the distribution of filling volumes is normal. )
a.
a.Determine the upper and lower control limits.
b.Explain the meaning of the values you found in part
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Chapter 21: Decision Analysis
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Q1) Nodes indicating points where a decision is made are known as
A)decision nodes
B)chance nodes
C)marginal nodes
D)conditional nodes
Q2) Information about a state of nature is known as
A)natural information
B)states information
C)a sampling method
D)an indicator
Q3) For a decision alternative,the weighted average of the payoffs is known as
A)the expected value of perfect information
B)the expected value
C)the expected probability
D)perfect information
Q4) Refer to Exhibit 21-3.The expected value of perfect information equals
A)13,000
B)14,000
C)15,000
D)16,000
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Chapter 22: Sample Survey
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Q1) The error that occurs because a sample,and not the entire population,is used to estimate a population parameter is a
A)nonsampling error
B)sampling error
C)judgment error
D)standard error
Q2) A version of cluster sampling in which the elements are formed into clusters on the basis of their geographic proximity is
A)stratified simple random sampling
B)random sampling
C)judgment sampling
D)area sampling
Q3) Simple random sampling has been used to obtain a sample of 81 elements from a population of size 500.The sample mean is 120,and the sample standard deviation is determined to be 36.
a.Estimate the standard error of the mean.
b.Develop an approximate 95% confidence interval for the population mean.
c.Estimate the population total.
d.Develop an approximate 95% confidence interval for the population total.
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