Quantitative Methods for Business Review Questions
Course Introduction
Quantitative Methods for Business introduces students to the essential mathematical and statistical techniques used in business decision-making. The course covers topics such as data analysis, probability, sampling, hypothesis testing, regression analysis, linear programming, and forecasting. Through real-world business applications, students learn how to interpret quantitative data and apply various models to solve problems and make informed decisions. Emphasis is placed on developing analytical skills, using quantitative tools, and utilizing software for data analysis to enhance managerial effectiveness in a dynamic business environment.
Recommended Textbook
Introduction to Business Statistics 7th Edition by Ronald M. Weiers
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Page 2
Chapter 1: A Preview of Business Statistics
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Sample Questions
Q1) Six classmates told you their scores on the last statistics exam.Based on this information,you conclude that the average exam score for the entire class was 82.This is an example of descriptive statistics.
A)True
B)False
Answer: False
Q2) qualitative variable
A)a characteristic of the population
B)indicates that a person or object belongs in a category
C)the entire set of people or objects of interest
D)the arithmetic average of the data
E)a measurement scale with an absolute zero
F)a measured characteristic of a sample
G)helps us determine how much of something is possessed
H)a subset of people or objects that exist within the entire set
Answer: B
Q3) What was the primary use of statistics in ancient times?
Answer: In ancient times,statistics was mainly employed for counting people or possessions to facilitate taxation.
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Page 3
Chapter 2: Visual Description of Data
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Sample Questions
Q1) Define and give a real or hypothetical example of cross-tabulation.
Answer: In cross-tabulation,we express a count of how many people or items are in combinations of categories.Example: we may express a count of how many students in a class are males majoring in accounting and how many are females majoring in finance.
Q2) The following stem-and-leaf output has been generated by Minitab. Stem-and-leaf of C2 \(\quad \mathrm { N } = 10\)
Leaf Unit \(= 0.10\)
\(\begin{array} { l c } 2 & - 153 \\ 4 & - 097 \\ ( 2 ) & - 065 \\ 4 & 03 \\ 3 & 06 \\ 2 & 13 \\ 1 & 18 \end{array}\) Which of the following statements are correct?
A) This data set has a mean that is negative.
B) This data set has a median less than -0.5
C) There is no modal class
D) This data set has six negative values
E) All of these are correct
Answer: E
Q3) ____________________ is also known as marginal or one-way tabulation.
Answer: Simple tabulation
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Page 4
Chapter 3: Statistical Description of Data
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Sample Questions
Q1) A sample of 13 monthly sales figures (in thousands of dollars)are: 10,6,5,10,9,7,10,9,6,8,9,6,and 6.
Calculate the sample standard deviation.
Answer: 1.83
Q2) The numerical value of the coefficient of determination r <sup>2</sup>
A) is the proportion of the variation in the dependent variable y that is explained by the best-fit linear equation.
B) is the proportion of the variation in the independent variable x that is explained by the best-fit linear equation.
C) indicates the direction of the relationship between the dependent variable y and the independent variable x.
D) Both A and B are correct.
E) A,B,and C are all correct.
Answer: A
Q3) Calculate the average number of calls per day.
Answer: 4.6 calls per day
Q4) Calculate the interquartile range.
Answer: 936.75
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Page 5
Chapter 4: Data Collection and Sampling Methods
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Sample Questions
Q1) In practice,most studies involve relatively large populations for which taking a sample can provide satisfactory results much more quickly and at considerably lower cost than a census.
A)True
B)False
Q2) Which of the following is not an example of primary data?
A) Data published by the United States Bureau of Census.
B) Data published by Statistics Canada.
C) Data published by the New York Stock Exchange.
D) Financial data tapes that contain data compiled from the New York Stock Exchange.
Q3) One weakness of a systematic sample is that:
A) it is difficult to separate the population into strata.
B) geographic areas may not be known.
C) taking the sample requires judgment on the part of the researcher.
D) the data may exhibit a pattern of periodicity.
E) the observations are chosen because they are not typical of the population.
Q4) A(n)____________________ questionnaire leaves respondents free to formulate their own answers and expand on the subject of the questionnaire.
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Page 6
Chapter 5: Probability: Review of Basic Concepts
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Sample Questions
Q1) For a randomly selected consumer,find the following probability: P(A or D).
Q2) The union of events describes two or more events occurring at the same time.
A)True
B)False
Q3) What is the probability that a randomly selected respondent was a Republican and undecided about the proposed law?
Q4) ____________________ probabilities find their greatest application in games of chance,but they are not so useful when the underlying processes are not well known.
Q5) Sometimes it is useful to revise a probability on the basis of additional information that we didn't have before.
A)True
B)False
Q6) If the event of interest is A,then:
A) the probability that A will not occur is [1 - P(A)].
B) the probability that A will not occur is the complement of A.
C) the probability is zero if event A is impossible.
D) the probability is one if event A is certain.
E) All of these are true.
Q7) Determine the probability of event B.
Page 7
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Chapter 6: Discrete Probability Distributions
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Sample Questions
Q1) The ____________________ for a discrete random variable lists all possible values the variable can assume,along with their respective probabilities of occurrence.
Q2) The binomial distribution is best used to describe the number of customers arriving at a service point during a given period of time.
A)True
B)False
Q3) Which of the following statements are true?
A) For the Poisson distribution = 3.2,the mean and standard deviation are both equal to 3.2.
B) For the Poisson distribution = 3.2,the mean and variance are both equal to 3.2.
C) For the Poisson distribution = 3.2,the mean is 3.2 and the standard deviation is 1.79.
D) Both B and C are correct.
E) All of these are correct.
Q4) Use the Poisson distribution to compute the binomial probability that one or more checks are returned.
Q5) What is the probability that less than two of the five canoes will capsize?
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8
Chapter 7: Continuous Probability Distributions
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Sample Questions
Q1) A very large logging operation has serious problems keeping their skidders operating properly.The equipment fails at the rate of 3 breakdowns every 48 hours.Assume that x is time between breakdowns and is exponentially distributed.The probability of two or less breakdowns in the next 48-hour period is:
A) 0.9672.
B) 0.0307.
C) 0.2231.
D) 0.7769.
Q2) For a normal curve,if the mean is 20 minutes and the standard deviation is 5 minutes,find the area to the left of 10 minutes.
Q3) A continuous random variable x is normally distributed with a mean of $250 and a standard deviation of $50.Find the z-score for x = 175.
Q4) In any normal distribution,the mean,median,mode,and standard deviation are all at the same position on the horizontal axis.
A)True
B)False
Q5) What are continuous probability distributions?
Q6) Assuming a standard normal distribution,determine P(z -0.75).
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Chapter 8: Sampling Distributions
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Sample Questions
Q1) The sampling distribution of the mean will have the same standard deviation as the original population from which the samples were drawn.
A)True
B)False
Q2) The concept that allows us to draw conclusions about the population based strictly on sample data without having any knowledge about the distribution of the underlying population is
A) the central limit theorem.
B) the standard error of the mean.
C) the normal distribution.
D) the standard deviation.
E) the variance.
Q3) In order to estimate the mean salary for a population of 500 employees,the president of a certain company selected at random a sample of 40 employees.What is the probability that the sample mean salary of the employees will be within \(\pm\) $200 of the population mean salary?
Q4) Briefly,what is the difference between a standard deviation and a standard error?
Q5) Why is the central limit theorem basic to the concept of statistical inference?
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Chapter 9: Estimation From Sample Data
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Sample Questions
Q1) Under what conditions is it appropriate to use the normal approximation to the binomial distribution in constructing the confidence interval for the population proportion \(\pi\) ?
Q2) If the population mean \(\mu\) is unknown,one can use sample data as the basis from which to make probability statements about the true (but unknown)value of \(\mu\) .
A)True
B)False
Q3) Texas passed a law requiring drivers and passengers in the front seat to wear seat belts.In order to estimate the compliance with the law an unmarked car will operate in a selected county and the officer will observe whether or not seat belts are in use.The proportion complying, \(\pi\) ,in the county is to be estimated by randomly selecting the cars to examine.A confidence coefficient of 0.98 is desired with the estimate,p,to be within 0.05 of the true proportion.How many cars are needed in this sample?
Q4) If a sample has 16 observations and a 95% confidence estimate for \(\mu\) is needed,the appropriate t-score is 1.746.
A)True
B)False
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Page 11
Chapter 10: Hypothesis Tests Involving a Sample Mean or Proportion
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Sample Questions
Q1) Use the given information to calculate the p-value and interpret the result:
H<sub>0</sub>: \(\mu\) = 20,H<sub>1</sub>: \(\mu\) < 20 \(\text { }\) = 8.1 ,n = 100, \(\bar { x }\) = 18.1, \(\alpha\) = 0.025
p-value = ____________________
Interpretation: ____________________
Q2) What is an operating characteristic curve and how is it related to the power curve for a test?
Q3) State the null and alternative hypothesis.
Q4) The Admissions officer for the graduate programs at Michigan State University (MSU)believes that the average score on the GRE exam at his university is significantly higher than the national average of 1300.Assume that the population standard deviation is 125 and a random sample of 25 scores had an average of 1375.
A)State the appropriate null and alternative hypotheses.
H<sub>0</sub>: ____________________
H<sub>1</sub>: ____________________
B)Calculate the value of the test statistic.
C)What is your conclusion?
Q5) What is the conclusion?
Q6) What are the appropriate hypotheses?
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Chapter 11: Hypothesis Tests Involving Two Sample Means
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Sample Questions
Q1) Use Minitab or Excel to conduct a two-sample t-test to test the hypotheses:
H<sub>0</sub>: \(\mu _ { 1 } = \mu _ { 2 }\) H<sub>1</sub>: \(\mu _ { 1 } \neq \mu _ { 2 }\) at the 5% significance level.
Q2) Can they infer at the 5% significance level that sales increase during the campaign?
H<sub>0</sub>: ____________________
H<sub>1</sub>: ____________________
Test statistic = ____________________
Conclusion: ________________________________________
Q3) A test for the equality of average number of tickets per driver for the two groups is desired.Use \(\alpha\) = 0.01.What is the value of the test statistic?
Appropriate test: ____________________
Test statistic = ____________________
Q4) The test question is: At the 0.05 level of significance,is the gluing of seams better than sewing? What are the null and alternative hypotheses?
H<sub>0</sub>: ____________________
H<sub>1</sub>: ____________________
Q5) Explain what the interval estimate tells you.
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Page 13
Chapter 12: Analysis of Variance Tests
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Sample Questions
Q1) In using the ANOVA models,the assumptions made about the data are:
A) the samples are independent.
B) the population variances are equal.
C) the population distributions are normal.
D) A,B,and C are all assumptions made about the data.
E) the samples are dependent.
Q2) In the randomized block design,what benefit is gained from blocking?
Q3) State the null and alternative hypotheses to test for a difference in average number of customers per day for each store.
Q4) The F-statistic in a one-way ANOVA represents the:
A) variation between the treatments plus the variation within the treatments.
B) variation within the treatments minus the variation between the treatments.
C) variation between the treatments divided by the variation within the treatments.
D) variation within the treatments divided by the variation between the treatments.
Q5) A(n)____________________ variable is the variable for which a value is measured or observed.
Q6) Calculate the total sum of squares (SST).
Q7) Calculate the treatment sum of squares (SSTR).
Page 14
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Chapter 13: Chi-Square Applications
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Sample Questions
Q1) In carrying out a chi-square goodness-of-fit test,what are the "k" and "m" terms in the "df = k - 1 - m" expression and why is each term present?
Q2) The goodness-of-fit test requires that the sample data be arranged into categories that are both mutually exclusive and exhaustive.
A)True
B)False
Q3) Should the assumption of a binomial distribution with a probability of purchase \(\pi\)
equal to 0.50 be rejected at the 5% significance level? Hypotheses: ____________________
Test statistic = ____________________
Critical Value = ____________________ Conclusion: ____________________________
Q4) In a goodness-of-fit chi-square test,a large amount of discrepancy between the frequencies that are observed and those that are expected tend to cause us to fail to reject the null hypothesis.
A)True
B)False
Q5) What is the value of the test statistic?
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Chapter 14: Nonparametric Methods
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Sample Questions
Q1) State the null and alternative hypotheses.
H<sub>0</sub>: _____________________________
H<sub>1</sub>: _____________________________
Q2) What is the rank assigned to the three observations of value 1.8?
Q3) For one sample,the Wilcoxon signed rank method tests whether the sample could have been drawn from a population having a hypothesized value as its
Q4) The Wilcoxon signed rank test assumes sample data to be
A) continuous with either nominal or ordinal measurement scale.
B) continuous with either interval or ratio measurement scale.
C) discrete with either nominal or ordinal measurement scale.
D) discrete with either interval or ratio measurement scale.
E) continuous with any measurement scale.
Q5) A Nonparametric test is one that assumes that the population from which a sample is drawn is normally distributed or approximately so.
A)True
B)False
Q6) The test question is: Do the three airlines have the same median number of complaints? State the appropriate conclusion employing a 0.025 significance level.
Page 16
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Chapter 15: Simple Linear Regression and Correlation
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Sample Questions
Q1) Construct a 95% confidence interval for the slope of the population regression line.
Q2) In publishing the results of some research work,the following values of the coefficient of determination were listed.Which one would appear to be incorrect?
A) 0.91
B) 0.06
C) 0.47
D) -0.64
E) 0.00
Q3) The values of y and x are inversely related,and 84.64% of the variation in y is explained by the regression equation.What is the coefficient of correlation?
Q4) Construct a 95% confidence interval for the mean GPA when GMAT = 6.5.
Q5) A simple linear regression problem produced the following sum of squares: \(\sum \left( y _ { i } - \bar { y } \right) ^ { 2 }\) = 240, \(\sum \left( y _ { i } - \hat { y } _ { i } \right) ^ { 2 }\) = 60, \(\sum \left( \hat { y } _ { i } - \bar { y } \right) ^ { 2 }\) = 180 What percentage of the variation in y is not explained by the regression line?
Q6) Determine the standard error of estimate.
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Chapter 16: Multiple Regression and Correlation
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Sample Questions
Q1) What is the coefficient of determination? What does this statistic tell you?
Q2) For each y term in the multiple regression equation,the corresponding \(\beta\) is referred to as the partial regression coefficient.
A)True
B)False
Q3) The adjusted multiple coefficient of determination is adjusted for the:
A) number of regression parameters including the y-intercept.
B) number of dependent variables and the sample size.
C) number of independent variables and the sample size.
D) coefficient of correlation and the significance level.
Q4) Explain each of the terms in the multiple regression model: \[y _ { i } = \beta _ { 0 } + \beta _ { 1 } x _ { 1 i } + \beta _ { 2 } x _ { 2 i } + \ldots \ldots + \beta _ { \mathrm { ki } } x _ { \mathrm { ki } } + \epsilon _ { 1 }\] .
Q5) Compute the multiple standard error of estimate (s<sub>e</sub>)from the regression results.
Q6) Discuss residual analysis in terms of the assumptions required for using the multiple regression model.
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Chapter 17: Model Building
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Sample Questions
Q1) The second-order polynomial model \(E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }\) allows the plotted line to reverse the direction in which it is curving.
A)True B)False
Q2) If two or more independent variables are highly correlated with each other,multicollinearity is present,and the partial regression coefficients will be unreliable.
A)True B)False
Q3) The regression model \(\hat{ Y }\) = 180 + 6x<sub>1</sub> - 2x<sub>2</sub> has been fitted to a set of data.If x<sub>2</sub> = 20,what will be the effect on \(\hat{ Y }\) if x<sub>1</sub> increases by 1 unit? \(\hat{ Y }\) will ____________________ by
Q4) What is the general idea of stepwise regression?
Q5) Discuss some of the signals for the presence of multicollinearity.
Q6) A practical way to identify multicollinearity is to generate a standard deviation matrix.
A)True B)False
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Chapter 18: Models for Time Series and Forecasting
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Sample Questions
Q1) The occupancy rate for motel and hotel rooms in a small city in Michigan from 1993 to 2002 follow:
\(\begin{array}{llcc}
65.7&67.3&61.8&60.9&77.7&82.5&72.4&85.5&59.5 \\
\end{array}\) Compute a five-year moving average of the occupancy rate.
Q2) The time series component that reflects a wavelike pattern describing a long-term trend that is generally apparent over a number of years is called:
A) trend.
B) cyclical.
C) seasonal.
D) random variation.
Q3) According to the chapter,regression models based on time series data are especially susceptible to autocorrelation.Why?
Q4) When values in a time series are highly correlated with each other,____________________ forecasting models can be useful.
Q5) What can you conclude from your time-series smoothing?
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Chapter 19: Decision Theory
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Sample Questions
Q1) A new car salesman is being paid a straight salary,but has the choice to (a)continue with straight salary,(b)change to straight commission,or (c)change to a combination that includes a lower base salary and a commission on each sale of a new car.What states of nature might be useful in constructing a payoff table for this situation?
Q2) A silk screen T-shirt Company buys T-shirts and places designs on them.The cost of the T-shirt is $2.00.Placing the designs on shirts costs $3.00.The shirts sell for $12.Unsold shirts are donated to charity.The monthly demand for T-shirts with designs runs at a mean of 400 and a standard deviation of 50 T-shirts and is approximately normally distributed.What is the profit maximizing number of T-shirts to purchase each month?
Q3) If the probability of the competitor setting their price High,Medium,and Low is 40%,25%,and 35% respectively,what is the expected value of perfect information?
Q4) Why should we bother determining the expected value of perfect information when such information is practically never available?
Q5) Which decision has the minimum expected opportunity loss?
Q6) How many canoes should be leased using the maximin criterion?
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21
Chapter 20: Total Quality Management
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Sample Questions
Q1) What is competitive benchmarking,and how can it be used?
Q2) Costs of preventing poor quality are also known as ____________________.
Q3) ____________________ involves inspection of a sample of products after an entire production run or shipment lot has been produced.
Q4) What is the Deming PDCA cycle and how is it applicable to total quality management?
Q5) What is the "80/20" rule,and how does it apply to total quality management?
Q6) Forty samples of size 1,000 were drawn from a manufacturing process and the number of defectives in each sample was counted.The mean sample proportion was 0.05.The centerline for the p chart is:
A) 0.05.
B) 50.0.
C) 2.00. D) 25.0.
Q7) Calculate the centerline and control limits for the p-chart.
Centerline = ____________________
Lower value = ____________________
Upper value = ____________________
Q8) What is process capability,and how can its presence be ascertained?
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