Statistical Methods for Managers
Exam Answer Key
Course Introduction
Statistical Methods for Managers provides an essential foundation in statistical concepts and techniques relevant to business decision-making. The course covers descriptive statistics, probability distributions, sampling methods, hypothesis testing, regression analysis, and analysis of variance, all within the context of managerial applications. Emphasis is placed on interpreting data, drawing actionable conclusions, and using statistical software to support evidence-based management. Real-world business cases and datasets are utilized to help students develop the quantitative analysis skills needed to solve problems and make informed decisions in a managerial setting.
Recommended Textbook
Business Statistics For Contemporary Decision Making 9th Edition by Ken Black
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Chapter 1: Introduction to Statistics
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Sample Questions
Q1) Which of the following measurement processes is least likely to yield usable data?
A) Counting the number of shoppers entering the department store between 12 pm and 2 pm.
B) Studying cell phone bills and recording the number of text messages sent per month.
C) Performing a consumer survey of preferences in fast food chains
D) Asking students to list three things that are important to them.
E) Calculating the percent of college students who work at least 20 hours while attending school.
Answer: D
Q2) A descriptive measure of the population is called a parameter.
A)True
B)False
Answer: True
Q3) The complete collection of all entities under study is called the sample.
A)True
B)False
Answer: False
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Chapter 2: Charts and Graphs
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Sample Questions
Q1) In a frequency distribution,the first class interval begins at 18.The midpoint of the first class interval is 19.5,and the last class interval ends at 51.How many class intervals are there?
A) 11
B) 17
C) 22
D) 33
E) 34
Answer: A
Q2) A person has decided to construct a frequency distribution for a set of data containing 60 numbers. The lowest number is 23 and the highest number is 68. If 7 classes are used,the class width should be approximately _______.
A) 5
B) 7
C) 9
D) 11
E) 12
Answer: B
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Page 4
Chapter 3: Descriptive Statistics
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Sample Questions
Q1) A sample was taken of the salaries of four employees from a large company.The following are their salaries (in thousands of dollars)for this year: 33,36,41,and 47.The variance of their salaries is approximately
A) 28.19
B) 75.59
C) 37.58
D) 6.13
E) 5.31
Answer: C
Q2) According to Chebyshev's Theorem how many values in a data set will be within 3 standard deviations of the mean?
A) At least 75%
B) At least 68%
C) At least 95%
D) At least 89%
E) At least 99%
Answer: D
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Chapter 4: Probability
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Sample Questions
Q1) Let F be the event that a student is enrolled in a finance course,and let S be the event that a student is enrolled in a statistics course. It is known that 40% of all students are enrolled in a finance course and 35% of all students are enrolled in statistics. Included in these numbers are 15% who are enrolled in both statistics and finance. A student is randomly selected,and it is found that the student is enrolled in finance. What is the probability that this student is also enrolled in statistics?
A) 0.15
B) 0.75
C) 0.375
D) 0.50
E) 0.80
Q2) Inferring the value of a population parameter from the statistic on a random sample drawn from the population is an inferential process under uncertainty. A)True B)False
Q3) The list of all elementary events for an experiment is called the sample space. A)True B)False
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Chapter 5: Discrete Distributions
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Sample Questions
Q1) Suppose that during a given week,20 new customers have signed up for a specialized service your company provides.Eight of these new customers are automotive companies,and the remaining twelve are financial services firms.If a random sample of 5 of these new customers will be selected for a study of customer satisfaction in one month,what is the probability that 2 of the selected customers are financial services firms?
A) 0.232
B) 0.234
C) 0.236
D) 0.238
E) 0.240
Q2) Ten policyholders file claims with CareFree Insurance. Three of these claims are fraudulent. Claims manager Earl Evans randomly selects three of the ten claims for thorough investigation. If x represents the number of fraudulent claims in Earl's sample,P(x=0)is _______________.
A) 0.0083
B) 0.3430
C) 0.0000
D) 0.2917
E) 0.8917
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Page 7
Chapter 6: Continuous Distributions
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Sample Questions
Q1) Assuming an equal chance of a new baby being a boy or a girl (that is,p= 0.5),we would like to find the probability of 40 or more of the next 100 births at a local hospital will be boys.Using the normal approximation for binomial with a correction for continuity,we should use the z-score _______
A) 0.4
B) -2.1
C) 0.6
D) 2
E) -1.7
Q2) For an exponential distribution,the mean and the median are equal.
A)True
B)False
Q3) Let z be a normal random variable with mean 0 and standard deviation 1.What is P(z > -1.1)?
A) 0.36432
B) 0.8643
C) 0.1357
D) -0.1357
E) -0.8643
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Chapter 7: Sampling and Sampling Distributions
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Sample Questions
Q1) If the population is normally distributed,the sample means of size n=5 are normally distributed.
A)True
B)False
Q2) Albert Abbasi,VP of Operations at Ingleside International Bank,is evaluating the service level provided to walk-in customers. Accordingly,he plans a sample of waiting times for walk-in customers. If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes,the probability that Albert's sample of 64 will have a mean less than 15 minutes is ________.
A) 0.5000
B) 0.0228
C) 0.9072
D) 0.9544
E) 1.0000
Q3) With cluster sampling,there is homogeneity within a subgroup or stratum.
A)True
B)False
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Chapter 8: Statistical Inference: Estimation for Single Populations
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Sample Questions
Q1) The z value associated with a two-sided 99% confidence interval is _______.
A) 1.28
B) 1.645
C) 1.96
D) 2.575
E) 2.33
Q2) Brian Vanecek,VP of Operations at Portland Trust Bank,is evaluating the service level provided to walk-in customers. Accordingly,his staff recorded the waiting times for 64 randomly selected walk-in customers and determined that their mean waiting time was 15 minutes. Assume that the population standard deviation is 4 minutes. The 90% confidence interval for the population mean of waiting times is ________.
A) 14.27 to 15.73
B) 14.18 to 15.82
C) 9.88 to 20.12
D) 13.86 to 16.14
E) 18.12 to 19.87
Q3) A t-distribution is similar to a normal distribution,but with flatter tails.
A)True
B)False
Page 10
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Chapter 9: Statistical Inference: Hypothesis Testing for
Single Populations
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Sample Questions
Q1) The value of committing a Type II error is defined by the researcher prior to the study. A)True
B)False
Q2) Discrete Components,Inc.manufactures a line of electrical resistors. Presently,the carbon composition line is producing 100 ohm resistors. The population variance of these resistors "must not exceed 4" to conform to industry standards. Periodically,the quality control inspectors check for conformity by randomly select 10 resistors from the line,and calculating the sample variance. The last sample had a variance of 4.36. Assume that the population is normally distributed. Using \(\alpha\) = 0.05,the critical value of chi-square is _________________.
A) 18.31
B) 16.92
C) 3.94
D) 3.33
E) 19.82
Q3) The probability of committing a Type I error is called the power of the test.
A)True
B)False
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Chapter 10: Statistical Inferences About Two Populations
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Sample Questions
Q1) A researcher wishes to determine the difference in two population means. To do this,she randomly samples 9 items from each population and computes a 90% confidence interval.The sample from the first population produces a mean of 780 with a standard deviation of 240.The sample from the second population produces a mean of 890 with a standard deviation of 280.Assume that the values are normally distributed in each population and that the population variances are approximately equal.The critical t value used from the table for this is _______.
A) 1.860
B) 1.734
C) 1.746
D) 1.337
E) 2.342
Q2) If the sample sizes are small,but the populations are normally distributed and the population variances are known,the z-statistic can be used as the basis for statistical inferences about the difference in two population means using two independent random samples.
A)True
B)False
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Chapter 11: A Nalysis of Variance and Design of Experiments
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Sample Questions
Q1) In an experimental design,treatment variables are response variables.
A)True
B)False
Q2) BigShots,Inc.is a specialty e-tailer that operates 87 catalog Web sites on the Internet. Kevin Conn,Sales Director,feels that the style (color scheme,graphics,fonts,etc.)of a Web site may affect its sales. He chooses three levels of design style (neon,old world and sophisticated)and randomly assigns six catalog Web sites to each design style.In Kevin's experiment "style" is _______.
A) the dependent variable
B) a treatment variable
C) a concomitant variable
D) a blocking variable
E) a response variable
Q3) In experimental design,a characteristic of the subjects that was present prior to the experiment and is not the result of the experimenter's manipulations or control is called a classification variable.
A)True
B)False
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Chapter 12: Simple Regression Analysis and Correlation
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Sample Questions
Q1) Which of the following assertions is true about the regression line?
A) The regression line is also called the least cubes line and is found minimizing the sum of the cubes of the residuals.
B) It is found minimizing the sum of the residuals squared, but-even though it would be unnecessarily complicated-it could also be found minimizing the sum of the residuals cubed.
C) Depending on the data, some regression lines could have only positive residuals.
D) Depending on the data, some regression lines could have all residuals equal to zero.
E) Depending on the data, some regression lines could have only negative residuals.
Q2) The standard error of the estimate,denoted s<sub>e</sub>,is the square root of the sum of the squares of the vertical distances between the actual Y values and the predicted values of Y.
A)True
B)False
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Chapter 13: Multiple Regression Analysis
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Sample Questions
Q1) The F value that is used to test for the overall significance of a multiple regression model is calculated by dividing the sum of mean squares regression (SS<sub>reg</sub>)by the sum of squares error (SS<sub>err</sub>).
A)True
B)False
Q2) In a multiple regression model,the proportion of the variation of the dependent variable,y,accounted for the independent variables in the regression model is given by the coefficient of multiple correlation.
A)True
B)False
Q3) A real estate appraiser is developing a regression model to predict the market value of single family residential houses as a function of heated area,number of bedrooms,number of bathrooms,age of the house,and central heating (yes,no).The response variable in this model is _______.
A) heated area
B) number of bedrooms
C) market value
D) central heating
E) residential houses
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Chapter 14: Building Multiple Regression Models
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Sample Questions
Q1) An "all possible regressions" search of a data set containing 7 independent variables will produce ______ regressions.
A) 13
B) 127
C) 48
D) 64
E) 97
Q2) If a data set contains k independent variables,the "all possible regression" search procedure will determine 2<sup>k</sup> - 1 different models.
A)True
B)False
Q3) An appropriate method to identify multicollinearity in a regression model is to ____.
A) examine a residual plot
B) examine the ANOVA table
C) examine a correlation matrix
D) examine the partial regression coefficients
E) examine the R<sup>2</sup> of the regression model
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Chapter 15: Time-Series Forecasting and Index Numbers
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Sample Questions
Q1) When the error terms of a regression forecasting model are correlated the problem of autocorrelation occurs.
A)True
B)False
Q2) Unweighted price indexes compare across the entire time period for which there is data.
A)True
B)False
Q3) Index numbers facilitate comparison of ____________.
A) means
B) data over time
C) variances
D) samples
E) deviations
Q4) When a trucking firm uses the number of shipments for January of the previous year as the forecast for January next year,it is using a naïve forecasting model.
A)True
B)False
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Chapter 16: Analysis of Categorical Data
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Sample Questions
Q1) A goodness of fit test is to be performed to see if consumers prefer any of three package designs (A,B,and C)more than the other two. A sample of 60 consumers is used. What is the expected frequency for category A?
A) 1/3
B) 20
C) 60
D) 10
E) 30
Q2) In a chi-square goodness-of-fit test,actual frequencies are also called calculated frequencies.
A)True
B)False
Q3) In a chi-square test of independence the contingency table has 4 rows and 3 columns.The number of degrees of freedom for this test is 6.
A)True
B)False
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Chapter 17: Nonparametric Statistics
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Sample Questions
Q1) The degree of association of two variables cannot be estimated when only ordinal-level data are available.
A)True
B)False
Q2) Which of the following tests should be used to compare the means of three populations if the sample data is ordinal?
A) one-way analysis of variance
B) Kruskal-Wallis test
C) Wilcoxon test
D) Mann-Whitney test
E) Friedman test
Q3) Statistical techniques based on fewer assumptions about the population and the parameters are called _______.
A) population statistics
B) parametric statistics
C) nonparametric statistics
D) chi-square statistics
E) correlation statistics
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Chapter 18: Statistical Quality Control
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Sample Questions
Q1) Which of the following quality control chart conditions is an indicator that the process is,potentially,out-of-control?
A) several consecutive data points between the UCL and the LCL
B) a data point above the LCL
C) a data point below the UCL
D) an upward trend of nine data points
E) a data point in the outer 1/3 region
Q2) Ophelia O'Brien,VP of Consumer Credit of American First Banks (AFB),is designing a p chart to monitor the default rate on personal loans at the AFB member banks. Her data includes the proportion in default for 30 samples of personal loans.Each sample contains 50 loans,and the average of the 30 proportions is 0.05.The centerline for Ophelia's p chart is _____________.
A) 30
B) 0.50
C) 50
D) 1.5
E) 0.05
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Chapter 19: Decision Analysis
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Sample Questions
Q1) In decision-making under risk,the expected monetary value without information is
A) the weighted average of the best payoff for each state of nature
B) the largest of the EMVs for the different decision alternatives
C) never smaller than the expected monetary payoff with perfect information
D) the average of the EMVs
E) half the expected monetary value with information
Q2) In a decision-making under risk scenario,the expected monetary value of a decision alternative is the weighted average (using the probability of each state of nature as the weight)of the payoffs to the decision alternative in each state of the nature.
A)True
B)False
Q3) In a decision analysis problem,variables (such as general macroeconomic conditions)which are not under the decision maker's control are called prior probabilities.
A)True
B)False
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