Managerial Statistics Review
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Course Introduction
Managerial Statistics introduces students to the application of statistical tools and methodologies in managerial decision-making environments. The course covers fundamental concepts such as probability, statistical inference, hypothesis testing, regression analysis, and data interpretation, with an emphasis on solving real business problems. Students learn to collect, analyze, and interpret data relevant to operations, marketing, finance, and human resources, enabling evidence-based decision making. By leveraging statistical software and case studies, the course aims to build analytical skills essential for effective management in a data-driven business world.
Recommended Textbook Business Statistics Communicating with Numbers 3rd Edition by Sanjiv Jaggia
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Page 2
Chapter 1: Statistics and Data
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Sample Questions
Q1) A qualitative variable assumes meaningful numerical values.
A)True
B)False
Answer: False
Q2) For which of the following population parameters is sampling not necessary?
A) The average height of NBA players
B) The average life of light bulbs produced by a manufacturer
C) The average content of cereal boxes produced by a manufacturer
D) The percentage of the U.S. public school teachers who support Democrats
Answer: A
Q3) Which of the following are examples of cross-sectional data?
A) The test scores of students in a class
B) The current average prices of regular gasoline in different states
C) The sales prices of single-family homes sold last month in California
D) All of these choices are correct.
Answer: D
Q4) Data and data interpretation do not show up in every facet of life.
A)True
B)False
Answer: False
Page 3
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Chapter 2: Tabular and Graphical Methods
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Sample Questions
Q1) For qualitative data, a frequency distribution groups data into ________ and records the number of ________.
Answer: categories; observations
Q2) A ________ ________ is a table that shows the number of data observations that fall into specific interval.
Answer: frequency distribution
Q3) When constructing a frequency distribution for quantitative data, it is important to remember that ________.
A) classes are mutually exclusive
B) classes are collectively exhaustive
C) the total number of classes usually ranges from 5 to 20
D) All of the above
Answer: D
Q4) A stem-and-leaf diagram most resembles a(n) ________.
Answer: histogram
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Page 4
Chapter 3: Numerical Descriptive Measures
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Sample Questions
Q1) What is(are) characteristic(s) of the geometric mean?
A) It is always greater than the arithmetic mean.
B) It is the mathematical equivalent to the median.
C) It is always less than or equal to the arithmetic mean.
D) Both it is the mathematical equivalent to the median and it is always less than or equal to the arithmetic mean.
Answer: C
Q2) In a data set, an outlier is a large or small value regarded as an extreme value in the data set.
A)True
B)False
Answer: True
Q3) For k > 1, Chebyshev's theorem is useful in estimating the proportion of observations that fall within ________.
A) k standard deviations from the mean
B) k<sup>2</sup> standard deviations from the mean
C) (1 - 1/k) standard deviations from the mean
D) (1 - 1/k<sup>2</sup>) standard deviations from the mean
Answer: A
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Page 5
Chapter 4: Introduction to Probability
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Sample Questions
Q1) Mutually exclusive events ________.
A) contain all possible outcomes
B) may share common outcomes
C) do not share common outcomes
D) do not contain all possible outcomes
Q2) Let P(A) = 0.6, P(B) = 0.3, and P(A B<sup>C</sup>) = 0.1. Calculate P(A B).
A) 0
B) 0.3
C) 0.9
D) Not enough information to calculate.
Q3) A recent survey shows that the probability of a college student drinking alcohol is 0.6. Further, given that the student is over 21 years old, the probability of drinking alcohol is 0.8. It is also known that 30% of the college students are over 21 years old. The probability of drinking or being over 21 years old is ________.
A) 0.24.
B) 0.42.
C) 0.66.
D) 0.90.
Q4) Probabilities can be expressed as fractions, percentages, and ________.
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Chapter 5: Discrete Probability Distributions
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Sample Questions
Q1) It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that at least one in a random sample of four calculators is defective?
A) 0.0010
B) 0.2916
C) 0.3439
D) 0.6561
Q2) Assume that the mean success rate of a Poisson process is six successes per hour.
A) Find the expected number of successes in a 40-minute period.
B) Find the expected number of successes in a three-hour period.
C) Find the probability of at least two successes in a 30-minute period.
Q3) It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that none in a random sample of four calculators is defective?
A) 0.0010
B) 0.2916
C) 0.3439
D) 0.6561
Q4) An Excel's function ________ is used for calculating Poisson probabilities.
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Chapter 6: Continuous Probability Distributions
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Sample Questions
Q1) If an exponential distribution has the rate parameter = 5, what is its variance?
A) 5
B) 1/5
C) 1/25
D) 5/2
Q2) The annual return of a well-known mutual fund has historically had a mean of about 10% and a standard deviation of 21%. Suppose the return for the following year follows a normal distribution, with the historical mean and standard deviation. What is the probability that you will lose money in the next year by investing in this fund?
Q3) The time for a professor to grade a student's homework in statistics is normally distributed with a mean of 12.6 minutes and a standard deviation of 2.5 minutes. What is the probability that randomly selected homework will require less than 16 minutes to grade?
A) 0.1401
B) 0.5910
C) 0.7734
D) 0.9131
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8
Chapter 7: Sampling and Sampling Distributions
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Sample Questions
Q1) If the expected value of a sample mean equals the population mean, the sample mean is biased.
A)True
B)False
Q2) Selection bias occurs when the sample is mistakenly divided into strata, and random samples are drawn from each stratum.
A)True
B)False
Q3) Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13. If during a typical month Susan bowls 64 games, what is the probability that her average score in this month is above 227?
A) 0.1092
B) 0.4404
C) 0.5596
D) 0.8907
Q4) A preferred approach to quality control is the ________ approach.
Q5) Stratified random sampling is preferred when the objective is to ________.
Q6) Cluster sampling is preferred when the objective is to ________.
Page 9
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Chapter 8: Interval Estimation
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Sample Questions
Q1) A budget airline wants to estimate what proportion of customers would pay $10 for in-flight wireless access. Given that the airline has no prior knowledge of the proportion, how many customers would it have to sample to ensure a margin of error of no more than 5% for a 95% confidence interval?
Q2) Pure-bred dogs competing in shows must often meet specific height criteria to be considered to be within the breed standard. A new breed of dog, the pug-cock-a-poo, has been approved by a kennel club. The variance of pug-cock-a-poo height is known to be 2.25 inches squared. You would like to estimate the mean height of all pug-cock-a-poo breeds of dogs.
A) Find the appropriate sample size to achieve a margin of error of 0.3 when maintaining a 90% level of confidence.
B) Find the appropriate sample size to achieve a margin of error of 0.3 when maintaining a 95% level of confidence.
Q3) The t<sub>df </sub>distribution consists of a family of distributions where the actual shape of each one depends on the degrees of freedom, df. For lower values of df, the t<sub>df</sub> distribution is similar to the z distribution.
A)True
B)False
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Chapter 9: Hypothesis Testing
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Sample Questions
Q1) The alternative hypothesis typically ________.
A) corresponds to the presumed default state of nature
B) contests the status quo, for which a corrective action may be required
C) states the probability of rejecting the null hypothesis when it is false
D) states the probability of rejecting the null hypothesis when it is true
Q2) A university wants to know if the average salary of its graduates has increased since 2015. The average salary of graduates prior to 2015 was $48,000. Since 2015, the university surveyed 256 graduates and found an average salary of $48,750. Assume that the standard deviation of all graduates' salaries is $7,000.
A) Specify the null and alternative hypotheses to determine whether the average salary of graduates has increased.
B) Calculate the value of the test statistic and the p-value at a 5% significance level.
C) At the 5% significance level, can you conclude that salaries have increased? Explain.
Q3) Construct the null and alternative hypotheses for the following claims.
A) "The school's mean GPA differs from 2.50 GPA."
B) "The school's mean GPA is less than 2.50 GPA."
Q4) The hypothesis statement H: µ = 25 is an example of a(an) ________ hypothesis.
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11
Chapter 10: Statistical Inference Concerning Two Populations
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Sample Questions
Q1) A restaurant chain has two locations in a medium-sized town and, believing that it has oversaturated the market for its food, is considering closing one of the restaurants. The manager of the restaurant with a downtown location claims that his restaurant generates more revenue than the sister restaurant by the freeway. The CEO of this company, wishing to test this claim, randomly selects 36 monthly revenue totals for each restaurant. The revenue data from the downtown restaurant have a mean of $360,000 and a standard deviation of $50,000, while the data from the restaurant by the freeway have a mean of $340,000 and a standard deviation of $40,000. Assume there is no reason to believe the population standard deviations are equal, and let <sub>1</sub> and <sub>2</sub> denote the mean monthly revenue of the downtown restaurant and the restaurant by the freeway, respectively. At the 5% significance level, does the evidence support the manager's claim?
A) No, because the test statistic value is less than the critical value.
B) Yes, because the test statistic value is less than the critical value.
C) No, because the test statistic value is greater than the critical value.
D) Yes, because the test statistic value is greater than the critical value.
Q2) A left-tailed test determines whether <sub>1</sub> is ________ then <sub>2</sub>.
Q3) A common case of dependent sampling is usually referred to as ________ sampling.
Page 12
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Chapter 11: Statistical Inference Concerning Variance
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Sample Questions
Q1) Becky owns a diner and is concerned about sustaining the business. She wants to ascertain if the standard deviation of the profits for each week is greater than $250. The details of the profits for the week are (in dollars) 1,743 1,438 1,212 1,705 1,985 1,857 1,916
Assume that profits are normally distributed. Which of the following is the correct value of the test statistic?
A) 6.146
B) 8.604
C) 6.652
D) 7.375
Q2) Statistical inference about <sup>2</sup> is based on which of the following distributions?
A) The F distribution
B) The student's t distribution
C) The chi-square distribution
D) The normal distribution
Q3) The F distribution depends on ________ degrees of freedom.
Q4) Statistical inference for <sup>2</sup> is based on the F distribution.
A)True
B)False
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Chapter 12: Chi-Square Tests
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Sample Questions
Q1) If a test statistic has a value of X and is assumed to be <sup>2</sup> distributed with df degrees of freedom, then the p-value for a right-tailed test found by using Excel's command ________.
A) '=CHISQ.DIST.RT(X, Deg_freedom)'
B) '=CHISQ.DIST.RT(Deg_freedom, X)'
C) '=1-CHISQ.DIST.RT(X, Deg_freedom)'
D) '=1-CHISQ.DIST.RT(Deg_freedom, X)'
Q2) The chi-square test of a contingency table is a test of independence for ________.
A) a single qualitative variable
B) two qualitative variables
C) two quantitative variables
D) three or more quantitative variables
Q3) If the null hypothesis is rejected by the goodness-of-fit test, the alternative hypothesis specifies which of the population proportions differ from their hypothesized values.
A)True
B)False
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Chapter 13: Analysis of Variance
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Sample Questions
Q1) Tukey's Honestly Significant Differences (HSD) method ensures that the probability of at least one Type I error remains fixed irrespective of the number of ________.
A) pairwise comparisons
B) treatments
C) replications within each treatment
D) replications for each combination of factor A and factor B
Q2) One of the disadvantages of Fisher's LSD method is that the probability of committing at least one ________.
A) Type II error increases as the number of pairwise comparisons increases
B) Type I error increases as the number of pairwise comparisons decreases
C) Type II error increases as the number of pairwise comparisons decreases
D) Type I error increases as the number of pairwise comparisons increases
Q3) Which of these null hypotheses is applicable for a two-way ANOVA test with interaction?
A) There is interaction between factors A and B.
B) Factor A and factor B means differ.
C) There is no interaction between factors A and B.
D) Factor A and factor B means do not differ.
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Chapter 14: Regression Analysis
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Sample Questions
Q1) Which of the following R functions creates a linear model object?
A) cor.test
B) lm
C) summary
D) none of these options
Q2) The value 0.75 of a sample correlation coefficient indicates a stronger linear relationship than that of 0.60.
A)True
B)False
Q3) Which of the following Excel functions returns the sample correlation coefficient?
A) CORRELATION
B) CORREL
C) CORREL.S
D) COVARIANCE.S
Q4) The correlation coefficient captures only a ________ relationship.
Q5) Covariance can be used to determine if there is a linear relationship between two variables is positive or negative.
A)True
B)False
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Chapter 15: Inference With Regression Models
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Sample Questions
Q1) Consider the following simple linear regression model: y = <sub>0</sub> + <sub>1</sub>x + . When determining whether there is a negative linear relationship between x and y, the alternative hypothesis takes the form ________.
A) H<sub>A</sub>: <sub>1</sub> = 0
B) H<sub>A</sub>: <sub>1</sub> > 0
C) H<sub>A</sub>: <sub>1</sub> < 0
D) H<sub>A</sub>: b<sub>1</sub> > 0
Q2) Which of the following violates the assumptions of regression analysis?
A) The error term is normally distributed.
B) The error term has a zero mean.
C) The error term is correlated with an explanatory variable.
D) The error term has a constant variance.
Q3) Serial correlation occurs when the error term is ________.
A) dispersed evenly
B) randomly distributed
C) correlated across observations
D) uncorrelated across observations
Q4) ________ plots can be used to detect common violations, and they can be used to detect outliers.
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Chapter 16: Regression Models for Nonlinear Relationships
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Sample Questions
Q1) Which of the following is a quadratic regression equation?
A) y = <sub>0</sub> +
B) y = <sub>0</sub> + <sub>1</sub>x +
C) y = <sub>0</sub> + <sub>1</sub>x + <sub>2</sub>x<sup>2</sup>+
D) y = <sub>0</sub> + <sub>1</sub>x + <sub>2</sub>x<sup>2</sup> + <sub>3</sub>x<sup>3</sup> +
Q2) Which of the following is not a semi-log regression model?
A) Logarithmic
B) Exponential
C) Quadratic
D) None of these choices are correct.
Q3) An inverted U-shaped curve is also known as ________.
A) concave
B) convex
C) opaque
D) hyperbola
Q4) The regression model ln(y) = <sub>0</sub> + <sub>1</sub>ln(x) + is called a log-log model.
A)True
B)False
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Chapter 17: Regression Models With Dummy Variables
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Sample Questions
Q1) A model formulated as y = <sub>0</sub> + <sub>1</sub>x + = P(y = 1) + is called a(n) ________ probability model.
Q2) In the model y = <sub>0</sub> + <sub>1</sub>x + <sub>2</sub>d + <sub>3</sub>xd + , when d changes from 0 to 1 how does the intercept of the corresponding lines change?
A) From b<sub>0</sub> to b<sub>0</sub> + b<sub>1</sub> <sub>
B) </sub>From b<sub>0</sub> to b<sub>0</sub> + b<sub>2</sub>
C)<sub> </sub>From b<sub>0</sub> to b<sub>0</sub> + b<sub>3</sub>
D)<sub> </sub>From b<sub>0</sub> to b<sub>0</sub> + b<sub>1</sub> + b<sub>2</sub>
Q3) A model y = <sub>0</sub> + <sub>1</sub>x + , in which y is a binary variable, is called a linear probability model. A)True B)False
Q4) The logit model cannot be estimated with standard ________ least squares procedures.
Q5) A logit model ensures that the predicted probability of the binary response variable falls between ________.
Q6) Gender is an example of ________ variable.
Page 19
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Chapter 18: Time Series and Forecasting
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Sample Questions
Q1) Which of the following models is considered for a quarterly time series that seems to change on average by a fixed amount and seems to have seasonality?
A) ln(y<sub>t</sub>) = <sub>0</sub> + <sub>1</sub>d<sub>1</sub> + <sub>2</sub>d<sub>2</sub> + <sub>3</sub>d<sub>3</sub> + <sub>4</sub>t + <sub>t</sub>
B) y<sub>t</sub> = <sub>0</sub> + <sub>1</sub>d<sub>1</sub> + <sub>2</sub>d<sub>2</sub> + <sub>3</sub>d<sub>3</sub> + <sub>4</sub>t + <sub>t</sub>
C)<sub> </sub>ln(y<sub>t</sub>) = <sub>0</sub> + <sub>1</sub>d<sub>1</sub> + <sub>2</sub>d<sub>2</sub> + <sub>3</sub>d<sub>3</sub> + <sub>4</sub>d<sub>4</sub> + <sub>5</sub>t + <sub>t</sub>
D)<sub> </sub>y<sub>t</sub> = <sub>0</sub> + <sub>1</sub>d<sub>1</sub> + <sub>2</sub>d<sub>2</sub> + <sub>3</sub>d<sub>3</sub> + <sub>4</sub>d<sub>4</sub> + <sub>5</sub>t + <sub>t</sub>
Q2) The optimal value of the speed of decline in the exponential smoothing procedure is determined by a(n) ________ method.
Q3) A linear trend can be estimated using ________ technique.
Q4) The seasonal component typically represents repetitions over a ________ period.
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Page 20
Chapter 19: Returns, Index Numbers, and Inflation
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Sample Questions
Q1) The weighted aggregate price index assigns a lower weight to the items that are sold in higher quantities.
A)True
B)False
Q2) Emily Myers purchased a share of company X at $700 one year ago and earned a dividend of $50 during the year. The share is trading now at $850. Calculate Emily's return from investment if she sells her share at $850.
A) 7.14%
B) 21.43%
C) 28.57%
D) 14.29%
Q3) Which of the following is true about the comparison between the CPI and the PPI?
A) Both indices are based on the same basket of goods and services.
B) Sales and excise taxes are included in the PPI, but they are not included in the CPI.
C) The PPI is more commonly used to adjust wages for changes in the cost of living than the CPI.
D) Unlike the CPI that uses prices people pay, the PPI uses the prices measured at the wholesale level.
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Chapter 20: Nonparametric Tests
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Sample Questions
Q1) A trading magazine wants to determine the number of hours stockbrokers work each week. In particular, the trading magazine wants to determine if the median numbers worked per week differs from 100 hours. The magazine samples 18 traders. For the Wilcoxon signed-rank test, the value of the test statistic is T = T<sup>+</sup> = 153. Which of the following are the competing hypotheses to determine if the median number of hours worked per week differs from 100 hours?
A) H<sub>0</sub>: m 100; H<sub>A</sub>: m > 100
B) H<sub>0</sub>: m 100; H<sub>A</sub>: m < 100
C) H<sub>0</sub>: m 100; H<sub>A</sub>: m = 100
D) H<sub>0</sub>: m = 100; H<sub>A</sub>: m 100
Q2) A research analyst believes that a positive relationship exists between a firm's advertising expenditures and its sales. For 65 firms, she collects data on each firm's yearly advertising expenditures and its sales. She calculates a Spearman rank correlation coefficient of 0.45. The value of the test statistic and p-value are ________, respectively.
A) 3.60 and 0.0002
B) 3.60 and 0.0004
C) 3.63 and 0.0002
D) 3.63 and 0.0004
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