Managerial Statistics
Exam Solutions
Course Introduction
Managerial Statistics focuses on the application of statistical methods and analysis in the context of business decision-making. The course introduces students to fundamental concepts such as data collection, descriptive statistics, probability distributions, sampling, estimation, and hypothesis testing. Emphasis is placed on interpreting statistical findings, understanding variability, and making data-driven decisions in areas such as quality control, forecasting, market analysis, and performance evaluation. By the end of the course, students will be able to utilize statistical tools to assess business situations, solve real-world problems, and support managerial strategies with quantitative evidence.
Recommended Textbook
Statistics for Management and Economics 11th Edition by Gerald Keller
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Chapter 1: What Is Statistics
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Sample Questions
Q1) A company has developed a new engine whose average lifetime is unknown.In order to estimate this average,100 engines are randomly selected from a large production line and tested; their average lifetime is found to be 11 years.The 11 years represents a: A)parameter.
B)statistic.
C)sample.
D)population.
Answer: B
Q2) The Surgeon General wanted to study malpractice litigation in Chicago.A sample of 32,000 medical records was selected from all 3.5 million patients who were discharged during the year 2011.Using the information from the sample to make conclusions about malpractice litigation in Chicago is an example of doing ____________________ statistics.
Answer: inferential
Q3) A statistic is typically a known quantity while a parameter is typically an unknown quantity.
A)True
B)False
Answer: True
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Chapter 2: Graphical Descriptive Techniques 1
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Sample Questions
Q1) Data that contains information on two variables is called ____________________ data.
Answer: bivariate
Q2) {All-Nighters Narrative} There is a relationship between whether or not a student stayed up all night before the midterm,and how well they did on the midterm.Describe this relationship using percentages.
Answer: Of those who stayed up all night,60/200 = 30% did well and 70% did not.Of those who didn't stay up all night,120/200 = 60% did well and 40% did not.
Q3) In a pie chart,each slice is proportional to the ____________________ of individuals in that category.
Answer: percentage proportion relative frequency
Q4) {Car Buyers Narrative} Construct a pie chart of this data.Which car dealer offered the best overall service?
Answer: 11ea78b9_2dfb_7b3b_8379_e1279ec30069_TB4388_00 ContourMotors (C)received the most votes (35.0%).
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Chapter 3: Graphical Descriptive Techniques 2
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Sample Questions
Q1) Graphical excellence is a term usually applied to techniques that are informative and concise and that impart information clearly to their viewers.
A)True
B)False
Answer: True
Q2) Briefly discuss the difference between cross-sectional data and time-series data.
Answer: Data can be classified according to whether the observations are measured at the same time or whether they represent measurements at successive points in time.The former are called cross-sectional data and the latter,time-series data.
Q3) A popular method of creating distorted impressions with bar charts is to construct the bars so that their widths are proportional to their heights.
A)True
B)False
Answer: True
Q4) {Insurance Company Narrative} What proportion of homeowners had no claims in the last three years?
Answer: 9/64 = .14
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Chapter 4: Numerical Descriptive Techniques
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Sample Questions
Q1) Which of the following are measures of the linear relationship between two variables?
A)The covariance
B)The coefficient of correlation
C)The variance
D)Both a and b
Q2) {Ages of Workers Narrative} Compute and compare the coefficient of variation for the three samples.
Q3) {Longevity and Salary Narrative} Draw the scatter diagram and plot the least squares line.
Q4) In a positively skewed distribution,the percentage of data between the smallest observation and Q<sub>1</sub> is less than the percentage of data between Q<sub>3</sub> and the largest observation.
A)True
B)False
Q5) The median of a set of data is more representative than the mean when the mean is larger than most of the observations.
A)True
B)False
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Chapter 5: Data Collection and Sampling
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Q1) Selection bias occurs when researchers select biased questions to include on a survey.
A)True
B)False
Q2) Is it possible for a sample to yield better results than a census,from a practical standpoint? Explain.
Q3) A survey is an example of a(n)____________________ study.
Q4) Nonresponse error occurs when responses are not obtained from some members of the sample.
A)True
B)False
Q5) When responses are not obtained from some members of the sample,bias is introduced.
A)True B)False
Q6) Sampling error refers to the difference between the sample and the population that exists only because of the observations that happened to be selected for the sample.
A)True
B)False
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Chapter 6: Probability
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Q1) There are situations where we witness a particular event and we need to compute the probability of one of its possible causes.____________________ is the technique we use to do this.
Q2) Suppose P(A)= 0.30,P(B)= 0.50,and P(B|A)= 0.60.
a.Find P(A and B).
b.Find P(A or B).
c.Find P(A|B).
Q3) The union of events A and B is the event that occurs when either A or B occurs but not both.
A)True
B)False
Q4) If P(A|B)= P(A)then events A and B are ____________________.
Q5) {GPA and Class Narrative} If the GPA of the student selected is over 3.0,what is the probability that the student is in the lower class?
Q6) {Equity Loan Rates Narrative} What approach was used in estimating the probabilities for the interest rates?
Q7) {Club Members Narrative} What is the probability that a subscriber owns both a car and a house?
Q8) {Cysts Narrative} What is the probability that the patient will test positive?
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Chapter 7: Random Variables and Discrete Probability
Distributions
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Sample Questions
Q1) {Shopping Outlet Narrative} Use the laws of expected value to calculate the mean of Y from the probability distribution of X.
Q2) {Mobile Phones Sales Narrative} Compute the variance of the number of Blackberries sold daily.
Q3) If X has a binomial distribution with n = 4 and p = 0.3,find the probability that X is at least one.
Q4) The covariance can be negative but the coefficient of correlation cannot. A)True B)False
Q5) {Golfing Store Narrative} Calculate E(XY).
Q6) {Gym Visits Narrative} Find the mean and the standard deviation of Y = 2X 1.
Q7) {Elizabeth's Portfolio Narrative} Find the expected mean of the portfolio.
Q8) {Shopping Outlet Narrative} Use the laws of variance to calculate the variance and standard deviation of Y from the probability distribution of X.
Q9) {Stress Narrative} Find the probability distribution of X.
Q10) The variance of the sum always equals the sum of the variances. A)True B)False Page 9
Q11) {Retries Narrative} What is the standard deviation of the number of retries?
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Chapter 8: Continuous Probability Distributions
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Sample Questions
Q1) The value of a chi-squared distribution with 8 degrees of freedom such that the area to its left is 0.95 is 2.73.
A)True
B)False
Q2) If the parameter of an exponential distribution is 1,then which of the following is true?
A)The density function is e x for x 0.
B)The mean is equal to 1.
C)The standard deviation and variance are both equal to 1.
D)All of these choices are true.
Q3) Which of the following distributions can take on negative values?
A)Student t
B) <sup>2</sup>
C)F
D)None of these choices.
Q4) The variance of a Student t distribution approaches ____________________ as the degrees of freedom increase to infinity.
Q5) {Waiting Time Narrative} What is the probability that a patient would have to wait between one and two hours?
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Chapter 9: Sampling Distributions
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Sample Questions
Q1) Consider an infinite population with a mean of 160 and a standard deviation of 25.A random sample of size 64 is taken from this population.The standard deviation of the sample mean equals:
A)25
B)25/64
C)25/ 64
D)None of these choices.
Q2) {Retirees Narrative} What is the probability that the mean age is at most 73 years?
Q3) A CPA knows from past history that the average accounts receivable for a company is $521.72 with a standard deviation of $584.64.If the auditor takes a simple random sample of 100 accounts,what is the probability that the mean of the sample is within $120 of the population mean?
Q4) {Barack Obama Narrative} What is the probability that the number of voters in the sample who will vote for Barack Obama in the year 2012 is between 340 and 350?
Q5) Because the value of the ____________________ varies randomly from sample to sample,we can regard it as a new random variable created by sampling.
Q6) {CFO's Salary Narrative} Find the standard error of the sample mean difference.
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Chapter 10: Introduction to Estimation
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Sample Questions
Q1) It is ____________________ to say that a 95% confidence interval means there is a 95% chance that the parameter lies in that confidence interval.
Q2) The librarian at the New York City Public Library has asked her assistant for an interval estimate of the mean number of books checked out each day.The assistant took a sample and found the mean to be 880 books.She provides the librarian with an interval estimate of between 790 and 970 books checked out per day.An efficient,unbiased point estimate of the number of books checked out each day at the New York City Public Library is:
A)790
B)880
C)90
D)None of these choices.
Q3) ____________________ estimators reflect the effects of larger sample sizes,but ____________________ estimators do not.
Q4) A point estimator is defined as:
A)a range of values that estimates an unknown population parameter.
B)a single value that estimates an unknown population parameter.
C)a range of values that estimates an unknown sample statistic.
D)a single value that estimates an unknown sample statistic.
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Chapter 11: Introduction to Hypothesis Testing
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Sample Questions
Q1) If your p-value is greater than 0.900 you should reject H<sub>0</sub> at the 0.10 level.
A)True
B)False
Q2) A Type II error is defined as:
A)rejecting a true null hypothesis.
B)rejecting a false null hypothesis.
C)not rejecting a true null hypothesis.
D)not rejecting a false null hypothesis.
Q3) {Rechargeable Batteries Narrative} Calculate the power of the test when = 1000 and = 0.10.
Q4) If a researcher rejects a false null hypothesis,she has made a(n)____________________ decision.
Q5) In a two-tail test for the population mean,if the null hypothesis is rejected when the alternative hypothesis is true:
A)a Type I error is committed.
B)a Type II error is committed.
C)a correct decision is made.
D)a one-tail test should be used instead of a two-tail test.
Q6) {Marathon Runners Narrative} Compute the p-value.
Page 14
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Chapter 12: Inference About a Population
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Sample Questions
Q1) A robust estimator is one that is:
A)unbiased and symmetrical about zero.
B)consistent and is also mound-shaped.
C)efficient and less spread out.
D)not sensitive to moderate nonnormality.
Q2) During a natural gas shortage,a gas company randomly sampled residential gas meters in order to monitor daily gas consumption.On a particular day,a sample of 100 meters showed a sample mean of 250 cubic feet and a sample standard deviation of 50 cubic feet.Provide a 90% confidence interval estimate of the mean gas consumption for the population.
Q3) {Science Quiz Scores Narrative} Estimate the population variance with 90% confidence.
Q4) {Sinus Drug Narrative} Compute the p-value of the test.
Q5) {Socialist Voters Narrative} Test the hypotheses at the 5% significance level.
Q6) {Single Mothers' Ages Narrative} Test to determine if we can infer at the 5% significance level that the population mean is not equal to 20.
Q7) {Concert Tickets Narrative} Estimate the population mean with 90% confidence.
Q8) {Applicants' Grades Narrative} Compute the sample variance.
Q9) {Healthy Foods Narrative} Interpret the confidence interval of p.
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Chapter 13: Inference About Comparing Two Populations
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Sample Questions
Q1) {Promotional Campaigns Narrative} Can they infer at the 5% significance level that sales increase during the campaign?
Q2) {Antioxidants Narrative} Determine the rejection region for testing the equality of the two population variances at = .05.
Q3) {Starting Salary Narrative} Estimate with 95% confidence the difference between the two population means.
Q4) For testing the difference between two population proportions,the pooled proportion estimate is found by taking:
A)the proportion of successes from sample 1 plus the proportion of successes from sample 2.
B)the total number of successes in both samples divided by the total of both sample sizes.
C)the difference between the proportion of successes in each sample.
D)None of these choices.
Q5) The variance of the difference in sample proportions equals the difference of their population variances.
A)True
B)False
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Chapter 14: Analysis of Variance
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Sample Questions
Q1) Conducting t-tests for each pair or population means is statistically equivalent to conducting one F-test comparing all the population means.
A)True
B)False
Q2) Which of the following is true regarding SSB?
A)SSB stands for sum of squares for blocks.
B)SSB can help to reduce SSE.
C)SSB can help make it easier to determine whether differences exist between the treatment means.
D)All of these choices are true.
Q3) {Food Irradiation Narrative} Set up the ANOVA Table.Use = 0.01 to determine the critical values.
Q4) To test for interaction between factors A and B in a two-factor ANOVA,you use the F statistic that equals ____________________ divided by
Q5) Number of observation for a particular combination of treatments is called a replicate.
A)True B)False
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Chapter 15: Chi-Squared Tests
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Sample
Questions
Q1) How do you calculate the expected frequency for one cell in a goodness-of-fit test?
A)The expected frequency is equal to the proportion specified in H<sub>0</sub> for that cell.
B)Use the total number of observations divided by the number of categories.
C)Multiply the specified proportion for that cell (found in H<sub>0</sub>)by the total sample size.
D)None of these choices.
Q2) The expected frequency for the cell in row i and column j is the row i total plus the row j total,all divided by n.
A)True
B)False
Q3) A large value of a chi-squared test statistic in a test of a contingency table leads you to conclude the two variables are ____________________.
Q4) If we use the chi-squared method of analysis we must first check that there are at least 5 observations in each cell of the contingency table.
A)True
B)False
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Chapter 16: Simple Linear Regression and Correlation
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Sample Questions
Q1) {Game Winnings & Education Narrative} Estimate with 95% confidence the average winnings of all contestants who have 10 years of education.
Q2) {Oil Quality and Price Narrative} Does it appear that the errors are normally distributed? Explain.
Q3) If an estimated regression line has a y-intercept of 10 and a slope of 4,then when x = 2 the actual value of y is:
A)18
B)15
C)14
D)unknown.
Q4) Which of the following assumptions concerning the probability distribution of the random error term is stated incorrectly?
A)The distribution is normal.
B)The mean of the distribution is 0.
C)The variance of the distribution increases as x increases.
D)The errors are independent from one value of y to the next.
Q5) {Theatre Revenues Narrative} Determine the least squares regression line.
Q6) SSE stands for ____________________ of squares for ____________________.
Page 19
Q7) We check for normality by drawing a(n)____________________ of the residuals.
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Chapter 17: Multiple Regression
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Sample Questions
Q1) {Student's Final Grade Narrative} What is the adjusted coefficient of determination? What does this statistic tell you?
Q2) Multicollinearity is present when there is a high degree of correlation between the independent variables included in the regression model.
A)True
B)False
Q3) {Real Estate Builder Narrative} What minimum annual income would an individual with a family size of 9 and 10 years of education need to attain a predicted 5,000 square foot home?
Q4) In a multiple regression model,the value of the coefficient of determination has to fall between
A) 1 and +1.
B)0 and +1.
C) 1 and 0.
D)None of these choices.
Q5) To use the Durbin-Watson test to test for negative first-order autocorrelation,the null hypothesis will be H<sub>0</sub>: ____________________ (there is/there is no)first-order autocorrelation.
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Chapter 18: Model Building
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Sample Questions
Q1) An indicator variable is a variable that can assume:
A)one of two values (usually 0 and 1).
B)one of three values (usually 0,1,and 2).
C)any number of values.
D)None of these choices.
Q2) In explaining students' test scores,which of the following independent variables would not best be represented with indicator variables?
A)Gender
B)Race
C)Number of hours studying for the test
D)Marital status
Q3) {Hockey Teams Narrative} Test to determine at the 10% significance level if the x<sup>2</sup> term should be retained.
Q4) {Computer Training Narrative} Use the quadratic model to predict the value of y when x = 45.
Q5) {Incomes of Physicians Narrative} Estimate the annual income for a psychiatrist with 15 years of experience.
Q6) An indicator variable is a nominal variable that can assume _______________ possible values.
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Chapter 19: Nonparametric Statistics
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Sample Questions
Q1) Statistical methods that require,among other assumptions,that the populations be normally distributed are known as:
A)distribution-free techniques.
B)nonparametric techniques.
C)parametric techniques.
D)both a and b are correct.
Q2) {Keyboard Speed Narrative} Perform the sign test to determine if these data provide enough evidence at the 5% significance level to infer that the brands differ with respect to keyboard speed.
Q3) If the test statistic F<sub>r</sub> for the Friedman test is ____________________,we do not reject H<sub>0</sub>.
Q4) In a Kruskal-Wallis test,there are four samples and the value of the test statistic is calculated as H = 8.79.The most accurate statement that can be made about the p-value is that:
A)it is greater than 0.10.
B)it is greater than 0.05 but smaller than 0.10.
C)it is greater than 0.05.
D)it is greater than 0.025 but smaller than 0.05.
Q5) {Campaign Commercials Narrative} Which test is appropriate for this situation?
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Chapter 20: Time-Series Analytics and Forecasting
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Sample Questions
Q1) In determining monthly seasonal indexes for gas consumption,the sum of the 12 means for gas consumption as a percentage of the moving average is 1150.To get the seasonal indexes,each of the 12 monthly means is to be multiplied by:
A)1150 / 1200
B)(1200 + 1150)/ 12
C)(1150 + 12)/ 1200
D)1200 / 1150
Q2) In determining monthly seasonal indexes,the first step is to construct a centered moving average with a period of
A)24 months
B)12 months
C)6 months
D)3 months
Q3) Cyclical variation,one of the four different components of a time series,is more likely to exhibit business cycles that record periods of economic recession and inflation.
A)True
B)False
Q4) {Hotel Occupancy Narrative} Find the regression trend line.
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Chapter 21: Statistical Process Control
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Q1) Describe the three essential parts of a control chart.
Q2) What are the null and alternative hypotheses used to determine whether or not a process is in control?
Q3) Discuss what we mean by assignable variation in a process and give an example.
Q4) If a control chart finds six increasing or six decreasing points in a row,this is an example of assignable cause variation called a(n)____________________.
Q5) If you change the control limits from ±3 standard errors from the centerline to ±2 standard deviations from the centerline,this ____________________ the probability of a Type I error and ____________________ the probability of a Type II error.
Q6) The process capability index measures the capability of the process to produce units whose dimensions fall outside the specification limits. A)True B)False
Q7) Describe what a Type I error is,and what its impact is,in terms of a production process.
Q8) To construct a p chart,draw samples of size n,and for each sample calculate the sample ____________________ of defective units.
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Chapter 22: Decision Analysis
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Q1) {Demolition Company Narrative} Determine the EMV decision.
Q2) {Car Audio Store Narrative} What is the expected value of perfect information?
Q3) {Power Company Narrative} What is the expected value of perfect information?
Q4) A surgeon is involved in a $3 million malpractice suit.He can either settle out of court for $750,000 or go to court.If he goes to court and loses,he must pay $2,500,000 plus $500,000 in court costs.If he wins in court the plaintiffs pay the court costs.Identify the actions of this decision-making problem.
A)Two choices: (1)go to court and (2)settle out of court.
B)Two choices: (1)win the case in court and (2)lose the case in court.
C)Four consequences resulting from Go/Settle and Win/Lose combinations.
D)The amount of money paid by the doctor.
Q5) {Demolition Company Narrative} Determine the EOL decision.
Q6) {Dishwasher Designs Narrative} Convert the payoff table to an opportunity loss table.
Q7) In general,the branches of a decision tree represent acts and states of nature.
A)True
B)False
Q8) {Gross Profits Narrative} If the probability of s<sub>1</sub> is 0.5,then the optimal alternative using EMV is ____________________.
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Chapter 23: Conclusion
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Sample Questions
Q1) A larger sample increases the confidence level of a confidence interval.
A)True
B)False
Q2) The width of a confidence interval ____________________ when more data is collected.
Q3) We can use analysis of variance (ANOVA)in place of the t-test when comparing two population means.
A)True
B)False
Q4) Which of the following is NOT a type of data?
A)Parameter data
B)Nominal data
C)Ordinal data
D)Interval data
Q5) Which of the following is an example of ordinal data?
A)The weight of a newborn baby.
B)The gender of a baby.
C)The number of siblings a baby has.
D)Your order of preference of three baby names.
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