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business statistics communicating

Business Analytics Communicating With Numbers 1st Edition Sanjiv Jaggia, Alison Kelly, Kevin Lertwachara, Leida Chen - Solutions

A government researcher is analyzing the relationship between retail sales (in $ millions) and the gross national product (GNP in $ billions). He also wonders whether there are significant differences in retail sales related to the quarters of the year. He collects 10 years of quarterly data. A
Consider a regression model that links a CEO’s compensation (in $ millions) with the total assets of the firm (in $ millions) and the firm’s industry. Dummy variables are used to represent four industries: Manufacturing Technology d1, Manufacturing Other d2, Financial Services d3, and
While the Federal Reserve controls short-term interest rates, long-term interest rates essentially depend on supply/demand dynamics, as well as longer-term interest rate expectations. In order to examine the relationship between short-term and long-term interest rates, monthly data were collected
Caterpillar, Inc., manufactures and sells heavy construction equipment worldwide. The performance of Caterpillar’s stock is likely to be strongly influenced by the economy. For example, during the Great Recession, the value of Caterpillar’s stock plunged dramatically. Monthly data for
It is generally believed that the wealthier a student’s family, the higher the student’s Scholastic Aptitude Test (SAT) score. Another commonly used predictor for SAT scores is the student’s grade point average (GPA). Consider the following portion of data collected on 24 students. a.
In order to determine if the homeownership rate in the U.S. is linked with income, state level data on the homeownership rate (Ownership in %) and median household income (Income in $) were collected. A portion of the data is shown in the accompanying table.a. Estimate and interpret the model
Is it defense or offense that wins football games? Consider the following portion of data, which includes a team’s winning record (Win in %), the average number of yards gained, and the average number of yards allowed during a recent NFL season. a. Compare two simple linear regression models
For a large restaurant chain, a financial analyst uses the following model to estimate a franchise’s net profit: y = β0 + β1x1 + β2x2 + ɛi, where y is net profit, x1 is counter sales, and x2 is drive-through sales. For a sample of 100 franchises, she finds that SSE = 4.4600 and SST =
The director of college admissions at a local university is trying to determine whether a student’s high school GPA or SAT score is a better predictor of the student’s subsequent college GPA. She formulates two models: Model 1. College GPA = β0 + β1 High School GPA + ε Model 2. College GPA =
American football is the highest-paying sport on a per-game basis. Given that the quarterback is considered the most important player on the team, he is typically well-compensated. A sports statistician examines the factors that influence a quarterback’s salary. He believes that a quarterback’s
A president of a large chain of fast-food restaurants collects data on 100 franchises.a. Estimate the model: y = β0 + β1x1 + β2x2 + ɛ where y is net profit, x1 is counter sales, and x2 is drive through sales. All variables are measured in millions of dollars.b. Interpret the coefficient
The consumption function, first developed by John Maynard Keynes, captures one of the key relationships in economics. It expresses consumption as a function of disposable income, where disposable income is income after taxes. The accompanying table shows a portion of quarterly data for average U.S.
A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows: Salary
Develop a predictive model for the price of a house in the college town of Ames, Iowa. Before evaluating various models, you first have to filter out the House Price data to get the appropriate subset of observations for selected variables. After you have obtained the preferred model, summarize
The data accompanying this exercise show the average monthly debt payments (Debt, in $) for residents of 26 metropolitan areas. a. State the null and the alternative hypotheses in order to test whether average monthly debt payments are greater than $900. b. What assumption regarding the
A police officer is concerned about speeds on a certain section of Interstate 90. The data accompanying this exercise show the speeds of 40 cars on a Saturday afternoon. a. The speed limit on this portion of Interstate 90 is 65 mph. Specify the competing hypotheses in order to determine if the
Based on the average predictions of 45 economists, the U.S. gross domestic product (GDP) will expand by 2.8% this year. Suppose the sample standard deviation of their predictions was 1%. At the 5% significance level, test if the mean forecast GDP of all economists is less than 1%.
This past year, home prices in the Midwest increased by an average of 6.6%. A Realtor collects data on 36 recent home sales in the West. He finds an average increase in home prices of 7.5% with a standard deviation of 2%. Can he conclude that the average increase in home prices in the West is
In a survey of 1,116 adults, 47% approved of the job that President Trump was doing in handling the economy (Opinion Today, July 1, 2019). a. Compute the 90% confidence interval for the proportion of Americans who approved of President Trump’s handling of the economy. b. What is the
A survey of 1,026 people were asked about what they would do with an unexpected cash gift. Forty-seven percent responded that they would pay off debts. a. With 95% confidence, what is the margin of error? b. Construct the 95% confidence interval for the population proportion of people who
The monthly closing stock price for a large technology firm for the first six months of the year are reported in the following table. Month
Suppose that a study finds that 33% of teenagers text while driving. The study was based on 100 teen drivers. a. Discuss the sampling distribution of the sample proportion. b. What is the probability that the sample proportion is less than 0.30? c. What is the probability that the
A 2019 Pew Research study finds that the number of undocumented immigrants living in the United States has dropped to the level it was in 2004. While its share has declined, California still accounts for approximately 23% of the nation’s estimated 10.5 million undocumented immigrants. a. In
Suppose that the typical college student graduates with $28,650 in debt. Let debt among recent college graduates be normally distributed with a standard deviation of $7,000. a. What is the probability that the average debt of four recent college graduates is more than $25,000? b. What is
According to a 2018 paper released by the Economic Policy Institute, a nonprofit, nonpartisan think tank in Washington, D.C., income inequality continues to grow in the United States. Over the years, the rich have become richer while working-class wages have stagnated. A local Latino politician has
Researchers from leading universities have shown that divorces are contagious (Chicago Tribune, August 16, 2018). A split-up between immediate friends increases a person’s own chances of getting divorced from 36% to 63%, an increase of 75%. a. Compute the probability that more than half of
According to the Census Bureau projections, Hispanics will comprise 28.6% of the total population in 2060 (CNN, March 6, 2019). For comparison, they comprised just 18.1% of the total population in 2018. a. What is the expected value and the standard deviation of Hispanics in a random sample of
As of 2018, 30% of Americans have confidence in U.S. banks, which is still below the pre-recession level of 41% reported in June 2007 (www.gallup.com, June 28, 2018). a. What is the probability that fewer than half of four Americans in 2018 have confidence in U.S. banks? b. What would
Fraud detection has become an indispensable tool for banks and credit card companies to combat fraudulent credit card transactions. A fraud detection firm raises an alarm on 5% of all transactions and on 80% of fraudulent transactions. What is the probability that the transaction is fraudulent if
Professor Lang is a professor of economics at Salem State University. She has been teaching a course in Principles of Economics for over 25 years. Professor Lang has never graded on a curve because she believes that relative grading may unduly penalize or benefit a student in an unusually strong or
The accompanying data file shows the annual return (in %) for Fidelity’s Technology and Energy mutual funds from 1982 through 2018. a. Construct a boxplot for the Technology variable. Does the boxplot suggest that outliers exist? b. Use z-scores to determine if there are any outliers
The accompanying data file shows the average price of gas (Price in $ per gallon) for the 50 states during January 2019. a. Construct a boxplot for the Price variable. Does the boxplot suggest that outliers exist? b. Use z-scores to determine if there are any outliers for the Price
The accompanying data file shows the average monthly debt payments (Debt in $) for residents of 26 metropolitan areas. a. Construct a boxplot for the Debt variable. Does the boxplot suggest that outliers exist? b. Use z-scores to determine if there are any outliers for the Debt variable.
The accompanying data file shows the annual expenditures (Expenditures in $) for 100 Amazon Prime customers. a. Construct a boxplot for the Expenditures variable. Does the boxplot suggest that outliers exist? b. Use z-scores to determine if there are any outliers for the Expenditures
On average, an American professional football game lasts about three hours, even though the ball is actually in play only 11 minutes. Assume that game times follow a bell-shaped distribution and that the standard deviation is 0.4 hour. Use the empirical rule to answer the following
The historical returns on a portfolio had an average return of 8% and a standard deviation of 6%. Assume returns on the portfolio follow a bell-shaped distribution. Use the empirical rule to answer the following questions. a. Approximately what percentage of returns were between 2% and
A sample of the salaries of assistant professors on the business faculty at a local university revealed a mean income of $100,000 with a standard deviation of $10,000. Assume that salaries follow a bell-shaped distribution. Use the empirical rule to answer the following questions. a.
Consider the following five-point summary for a variable that was obtained using 500 observations a. Interpret Q1 and Q3.b. Calculate the interquartile range. Determine whether any outliers exist.c. Is the distribution symmetric? If not, comment on its skewness. Min 125 Q1
Consider the following boxplot.a. Does the boxplot indicate possible outliers in the data?b. Comment on the skewness of the underlying distribution 1.5 IQR 1.5 IQR
Consider the following boxplot.a. Does the boxplot indicate possible outliers in the data?b. Comment on the skewness of the underlying distribution. 1.5 IQR 1.5 IQR
Many attempts have been made to relate happiness with various factors. A 2018 study in the Journal of Happiness relates happiness with age and finds that holding everything else constant, people are least happy when they are in their mid-40s. The accompanying data file shows a respondent’s age
The accompanying data file shows life expectancies (in years) and obesity rates (in %) for the 50 states and the District of Columbia. Calculate and interpret the correlation coefficient.
The accompanying table shows a portion of the annual returns (in %) for a technology mutual fund and an energy mutual fund from 1982 through 2018.a. Which fund had the higher average return?b. Which fund was riskier over this time period?c. Given a risk-free rate of 2%, which fund had the higher
The accompanying data file shows midterm and final grades for 32 students. Calculate and interpret the correlation coefficient.
The accompanying table shows a portion of the annual returns (in %) for a mutual fund focusing on investments in Latin America and a mutual fund focusing on investments in Canada from 1994 through 2018.a. Which fund had the higher reward over this time period? Explain.b. Which fund was riskier over
Refer to the previous exercise for a description of the data. a. The skewness and (excess) kurtosis coefficients for the Latin America fund are 0.3215 and −0.7026, respectively. Interpret these values. b. The skewness and (excess) kurtosis coefficients for the Canada fund are −0.2531
Monthly stock prices (in $) for Firm A and Firm B are collected for five years. A portion of the data is shown in the accompanying table. a. Calculate the mean, the variance, and the standard deviation for each firm’s stock price. b. Which firm had the higher average stock price over
Many environmental groups and politicians are suggesting a return to the federal 55-mile-per-hour (mph) speed limit on America’s highways. They argue that not only will a lower national speed limit reduce greenhouse emissions, it will also increase traffic safety. A researcher believes that a
Refer to the previous exercise for a description of the data. a. The skewness and (excess) kurtosis coefficients for monthly rent are 1.0198 and 0.4790, respectively. Interpret these values. b. The skewness and (excess) kurtosis coefficients for square footage are 3.0573 and 12.3484,
The following table shows a portion of the monthly rent and square footage for 40 rentals in a large college town.a. Calculate the mean and the standard deviation for monthly rent.b. Calculate the mean and the standard deviation for square footage.
The following table lists a portion of the average price (in $) for a gallon of gas for the 50 states and the District of Columbia as reported by AAA Gas Prices on January 2, 2019. a. Find the mean and the median for gas price. b. Calculate and interpret the first quartile and the third
The accompanying table shows a portion of the annual expenditures (in $) for 100 Amazon Prime customers. a. Find the mean and the median of annual expenditures. b. Calculate and interpret the first quartile and the third quartile for annual expenditures. Customer
Annual revenues (in $ millions) for Home Depot and Lowe’s Corporation are collected for 13 years. A portion of the data is shown in the accompanying table. a. For each company, calculate the mean and the median revenues for this time period. Which company had higher average revenues? b.
The accompanying table shows a portion of life expectancies (in years) and obesity rates (in %) for the 50 states and the District of Columbia. Construct a scatterplot of Life Expectancy against Obesity. Describe the relationship. State Alabama Alaska I Wyoming Life
The accompanying table shows a portion of quarterly data for average U.S. annual consumption (Consumption in $) and disposable income (Income in $) for the years 2000–2016. Construct a scatterplot of Consumption against Income. Describe the relationship. Date Q1, 2000 Q2, 2000 Q4,
In order to diversify risk, investors are often encouraged to invest in assets whose returns have either a negative relationship or no relationship. The accompanying table shows a portion of the annual return data (in %) on two assets. Construct a scatterplot of Return B against Return A. In order
Healthy living has always been an important goal for any society. Most would agree that a diet that is rich in fruits and vegetables (FV) and regular exercise have a positive effect on health, while smoking has a negative effect on health. The accompanying table shows a portion of the percentage of
A financial analyst wants to compare the performance of the stocks of two Internet companies, Amazon (AMZN) and Google (GOOG). She records the average closing prices of the two stocks for the years 2010 through 2016. A portion of the data is shown in the accompanying table. Construct a line chart
The accompanying table shows a portion of data consisting of the price, the age, and the mileage for 20 used sedans. a. Construct a scatterplot of Price against Age. Describe the relationship. b. Construct a scatterplot of Price against Mileage. Describe the relationship. Price Age
It is believed that India will overtake China to become the world’s most populous nation much sooner than previously thought (CNN, June 19, 2019). The accompanying data file, compiled by the World Bank, contains the population data, in millions, for India and China from 1960 to 2017. Construct a
The accompanying table shows a portion of the average SAT math score (Math), the average SAT writing score (Writing), the number of test takers (Test Taker),and whether the school is a private or public school (Type) for 25 high schools in a major metropolitan area.a. Construct a bubble plot that
A company that sells unisex t-shirts is interested in finding out the color and size of its best-selling t-shirt. The accompanying data file contains the size, color, and quantity of t-shirts that were ordered during the last 1,000 transactions. A portion of the data is shown in the accompanying
The local police department is performing a crime analysis to find out which crimes are most likely to occur at which locations. The accompanying data file contains the types of crimes (CrimeType) that occurred at various locations (Location) in the city over the past five years. A portion of the
Monthly stock prices (in $) for Corporation A and Corporation B are collected for five years. A portion of the data is shown in the accompanying table.a. Calculate the mean and the standard deviation for each corporation’s stock price. b. Which corporation had the higher average stock price
The accompanying table shows a portion of midterm and final grades for 32 students. Construct a scatterplot of Final against Midterm. Describe the relationship. Final 86 94 ⠀ 91 Midterm 78 97 : 47
A report suggests that business majors spend the least amount of time on course work compared to all other college students (The Washington Post, January 28, 2017). A provost of a university conducts a survey on 270 students. Students are asked their major (business or nonbusiness) and if they
Amazon Prime is a $119-per-year service that gives the company’s customers free two-day shipping and discounted rates on overnight delivery. Prime customers also get other perks, such as free e-books. The accompanying table shows a portion of the annual expenditures (in $) for 100 Prime
The following histogram summarizes the salaries (in $100,000s) for the 30 highest-paid portfolio managers at a large investment firm over the past year. a. Is the distribution symmetric? If not, is it positively or negatively skewed?b. How many of the portfolio managers earned between
The accompanying table shows a portion of the daily price index for the Dow Jones Industrial Average (DJIA) for the first half of 2019. a. Construct the frequency distribution and the histogram for the DJIA. Use five intervals with widths of 22,000 < x ≤ 23,000; 23,000 < x ≤ 24,000;
The following histogram summarizes Apple Inc.’s monthly stock price for the years 2014 through 2018.a. Is the distribution symmetric? If not, is it positively or negatively skewed?b. Over this five-year period, approximate the minimum monthly stock price and the maximum monthly stock
The following table lists a portion of median house values (in $) for the 50 states as reported by the U.S. Census Bureau in 2010. a. Construct the frequency distribution and the histogram for the median house values. Use six intervals with widths of 0 < x ≤ 100,000; 100,000 < x ≤
The manager at a water park constructed the following frequency distribution to summarize attendance in July and August.a. Construct the relative frequency distribution. What proportion of the time was attendance at least 1,750 but less than 2,000? What proportion of the time was attendance less
Consider the following relative frequency distribution that summarizes the returns (in %) for 500 small cap stocks.a. Construct the frequency distribution. How many of the stocks had a return of at least 10% but less than 20%? b. Construct a histogram. Comment on the shape of the distribution.
Fifty cities provided information on vacancy rates (in %) in local apartments in the following frequency distribution. a. Construct the frequency distribution. How many of the cities had a vacancy rate of at least 6% but less than 9%? How many of the cities had a vacancy rate of at least
A 2014 Religious Landscape Study by the Pew Research Center found that 35% of Millennials (Americans born between 1981 and 1996) identified themselves as not religious. A researcher wonders if this finding is consistent today. She surveys 600 Millennials and asks them to rate their faith. Possible
A researcher conducts a mileage economy test involving 80 cars. The frequency distribution describing average miles per gallon (mpg) appears in the following table.a. Construct the relative frequency distribution. What proportion of the cars got at least 20 mpg but less than 25 mpg? What proportion
A recent poll of 3,057 individuals asked: “What’s the longest vacation you plan to take this summer?” The following relative frequency distribution summarizes the results. a. Construct the frequency distribution. How many people are going to take a one-week vacation this summer?b.
In 2018, the U.S. Census Bureau provided the following frequency distribution for the number of people (in 1,000s) who live below the poverty level by region. a. Construct the relative frequency distribution. What proportion of people who live below the poverty level live in the Midwest?b.
Patients at North Shore Family Practice are required to fill out a questionnaire that gives the doctor an overall idea of each patient’s health. The first question is: “In general, what is the quality of your health?” The patient chooses Excellent, Good, Fair, or Poor. A portion of the
A local restaurant is committed to providing its patrons with the best dining experience possible. On a recent survey, the restaurant asked patrons to rate the quality of their entrées. The responses ranged from 1 to 5, where 1 indicated a disappointing entrée and 5 indicated an exceptional
The following frequency distribution shows the counts of sales of men’s shirts at an online retailer over the weekend.a. Construct the relative frequency distribution. What proportion of sales were for a medium-sized shirt?b. Construct a bar chart. Comment on the findings.
An investor currently owns real estate in the college town of Blacksburg, Virginia—home to the Virginia Tech Hokies. He would like to expand his holdings by purchasing similar rental property in either Athens, Georgia, or Chapel Hill, North Carolina. As a preliminary step, he would like
The following frequency distribution summarizes the counts of purchases by day of the week for a major domestic retailera. Construct the relative frequency distribution. What proportion of the purchases occurred on Wednesday?b. Construct a bar chart using relative frequencies. Comment on the
Refer to Exercise 2.46 for a description of the problem and data set. a. The variable Satisfaction contains five ordered categories: Very Dissatisfied, Dissatisfied, Neutral, Satisfied, and Very Satisfied. Replace the category names with scores ranging from 1 (Very Dissatisfied) to 5 (Very
Refer to Exercise 2.48 for a description of the problem and data set. a. The variable Race contains five unordered categories: American Indian, Asian/Pacific Islander, Hispanic, Non Hispanic Black, and Non-Hispanic White. Reduce the number of categories to four by combining the two least
Refer to Exercise 2.47 for a description of the problem and data set. a. The variable Personality contains four unordered personality types: Analyst, Diplomat, Explorer, and Sentinel. To facilitate subsequent analyses, Erin needs to convert this variable into dummy variables. How many dummy
After each thunderstorm, a technician is assigned to do a check on cellular towers in his or her service area. For each visit, the technician records in a database the tower number (Tower), the unit model (Model: A or B), and the extent of the damage to the unit (Damage: None, Minor, Partial,
A manager of a local package delivery store believes that too many of the packages were damaged or lost. She extracts a sample of 75 packages with the following variables: the package number (Package), the status of the package (Status: Delivered, Damaged, or Lost), the delivery type (Delivery:
Consider the following portion of data that includes information about home loan applications. Variables on each application include the application number (Application), whether the application is conventional or subsidized by the federal housing administration (LoanType), whether the property is
The following table has three variables and six observations. a. Convert Sex into dummy variables. Use the most frequent category as the reference category. Which category is the reference category? b. Transform Decision into dummy variables. Use the most frequent category as the
Jerry Stevenson is the manager of a medical clinic in Scottsdale, AZ. He wants to analyze patient data to identify high-risk patients for cardiovascular diseases. From medical literature, he learned that the risk of cardiovascular diseases is influenced by a patient’s age, body mass index (BMI),
Erin Thomas, an HR manager of an engineering firm, wants to perform an analysis on the data about the company’s engineers. The variables included in the data are date of birth (BirthDate), personality type according to the Myers-Briggs Personality assessment (Personality), annual salary (Salary),
The accompanying data set contains three variables, x1, x2, and x3. a. The variable x1 contains 3 categories: S, M, and L. Convert the category names into category scores (i.e., S = 1, M = 2, and L = 3). How many observations have a category score of 3? b. Transform x2 into an appropriate
Greg Metcalf works for a national credit card company, and he is performing a customer value analysis on a subset of credit card customers. In order to perform the RFM analysis on the customers, Greg has compiled a data set that contains the dates of the last transaction (LastTransactionDate),
The accompanying data set contains two variables, x1 and x2. a. The variable x1 contains three categories ranging from “Low” to “High.” Convert the category names into category scores (i.e., 1 = “Low”, 2 = “Medium”, and 3 = “High”). How many observations have a category
TurboX is a online video game company that makes three types of video games: action, role play, and sports. It is interested in understanding its millennial customers. By combining the data from its customer database and a customer survey, TurboX compiled a data set that has the following
The accompanying data set contains two variables, Birthdate and LoanDecision. a. LoanDecision contains three unordered categories. To facilitate subsequent analyses, we need to convert LoanDecision into dummy variables. How many dummy variables should be created? Create the dummy variables
The accompanying data set contains three variables, x1, x2, and x3. a. The variable x1 contains 6 categories ranging from “A” to “F.” Reduce the number of categories to five by combining the two least-frequent categories. Name the new category “Other.” How many observations are in
Refer to the previous exercise for a description of the data set. a. Create a new variable called “Difference” that contains the difference between the 2018 population and the 2017 population for each state (i.e., 2018 population - 2017 population). What is the average difference? b.
The U.S. Census Bureau records the population for the 50 states each year. The accompanying table shows a portion of these data for the years 2010 to 2018.a. Bin the 2017 population values into four equal-size groups. Label the groups using numbers 1 (lowest values) to 4 (highest values). How many

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