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Statistics For Business Decision Making And Analysis 2nd Edition Robert Stine, Dean Foster - Solutions

Which has larger standard deviation, the distribution of weekly allowances to 12-year-olds or the distribution of monthly household mortgage payments? Which would have the larger coefficient of variation?
Which has larger variance, the prices of items in a grocery or the prices of cars at a new car dealer? Which has the larger coefficient of variation?
In a study of how the environment affects spending, researchers varied the presence of music and scents in a shopping mall. Interviews with shoppers who made unplanned purchases revealed the following average purchase amounts. Each group has about 100 shoppers.18 Condition Mean Spending
The following table summarizes sales by day of the week at a convenience store operated by a major domestic gasoline retailer. The data cover about one year, with 52 values for each day of the week.(a) Which consecutive two-day period produces the highest total level of sales during the year? (b)
If a variable, such as income, is very right skewed, would you expect one-sixth of the values to be less than - s, or would you expect more than one-sixth?
Would you expect distributions of these variables to be uniform, unimodal, or bimodal? Symmetric or skewed? Explain why. (a) The number of songs that each student in your class has downloaded online (b) Cost of each order from a mail-order catalog for clothing (c) Weights of bags of M&Ms that are
Would you expect distributions of these variables to be uniform, unimodal or bimodal? Symmetric or skewed? Explain why. (a) Ages of shoppers in a convenience store near a university late Saturday night (b) Number of children of shoppers in a toy store (c) Amount of cash taken in by retail cashiers
This histogram shows the distribution of the amount of sales tax (as percentages) in the 50 states and District of Columbia.(a) About how many states charge between 4% and 5% sales tax? (b) Estimate the mean from the histogram. Attach the appropriate unit to your estimate. (c) Which do you think is
This histogram shows the average annual premium (in dollars) for homeowner€™s insurance paid in the 50 states and District of Columbia.19(a) Which holds more states, the interval from $600 to $700 or the interval from $700 to $800? (b) Estimate the mean and standard deviation of the rates
The following histogram and boxplot summarize the distribution of income for 1,000 households in Colorado.(a) Estimate the mean and median. How do you know that the mean is larger than the median for this distribution? (b) Estimate the interquartile range from the figure. (c) Which is larger, the
The following display summarizes the percentage of household income that goes to rent for 1,000 families that live in Denver, Colorado.(a) Estimate the mean and median from the fgure. (b) Estimate the IQR from the fgure. (c) What€™s the effect of the cluster of outliers on the right of
Price scanners at the checkout register sometimes make mistakes, charging either more or less than the labeled price.20 Suppose that a scanner is wrong 4% of the time, with half of the errors in favor of the store and half in favor of the customer. Assume that an error in favor of the store means
The Federal Reserve Survey of Consumer Finances reported that median household net worth was $91,700 and mean household net worth was $421,500 in 2001. Explain how it is possible for the median net worth to rise 5% from 2001 to 2009 (see the prior question) but mean net worth to rise by 14%.
This histogram shows the price in dollars of 218 used cars.(a) Suppose we converted the prices of these cars from dollars to euros, with an exchange rate of 1.2 dollars per euro. Describe the histogram of the prices if denominated in euros. (b) Cars are often sold with an additional dealer
(a) Convert the following summary values given in megabytes (MB) to seconds. Fill in the column for the times in seconds assuming that 1 MB of space provides 60 seconds of music.(b) If the size of each song were increased by 2 MB, how would the summary statistics given in MB change?(c) If we were
(a) The following table summarizes the prices of a collection of used cars. What are the comparable summary statistics when measured in euros?Fill in the column for the prices in euros if the exchange rate is $1.20 per euro.(b) If the price of each car were increased by $500, how would the summary
This figure shows the histogram of the annual tuition at 61 top undergraduate business schools, as rated by Business Week (May 8, 2006).(a) Estimate from the figure the center and spread of the data. Are the usual notions of center and spread useful for these data? (b) Describe the shape of the
This histogram shows the winning times in seconds for the Kentucky Derby since 1875.(a) Estimate the center and scale of these data from the histogram. Are the usual notions of center and spread useful summaries of these data? (b) Describe the shape of the distribution of these data. (c) What do
A column in this data file gives the engine displacement in liters of 509 vehicles sold in the United States. These vehicles are 2012 models, are not hybrids, have automatic transmissions, and lack turbochargers.(a) Produce a histogram of the engine displacements, with the interval widths set to
Another column in this data file cars gives the rated combined fuel economy (in miles per gallon) for 509 vehicles sold in the United States (see prior question). (a) Produce a histogram of these data. Describe and interpret the histogram. (b) Compare the histogram to the boxplot. What does the
Outliers have a dramatic effect on small data sets. For this exercise, the data consist of the sizes (in seconds and MB) of the 27 #1 hits on the Beatles’ album 1.(a) Generate the boxplot and histogram of the sizes of these songs.(b) Identify any outliers. What is the size of this song, in
Outliers affect more than the statistics that measure the center of a distribution. Outliers also affect statistics that measure the spread of the distribution. Use the sizes of the songs in Exercise 55 for this exercise.(a) Find the standard deviation and interquartile range of the sizes of the
This data table includes several characteristics of 428 companies classified as being in the information industry in 2010. One column gives the total revenue of the company, in millions of dollars. (a) Find the median, mean, and standard deviation of the total revenue of these companies. What units
Using the data from Exercise 57, consider the total revenue per employee. Revenue is in millions of dollars, and the count of employees is given in the data table. (a) Why are there fewer than 428 observations available for making a histogram? (b) Find the median, mean, and standard deviation of
These data give the monthly returns on stocks in three technology companies: Dell, IBM, and Microsoft. For each month from January 1990 through the end of 2005 (192 months), the data give the return earned by owning a share of stock in each company. The return is the percentage change in the price,
These data give monthly returns for stocks of three familiar companies: Disney, Exxon, and McDonald’s from January 1990 through December 2005.(a) Describe and contrast histograms of the three companies. Be sure to use common axes to scale the histograms to make the comparison easier and more
Some investors use the Sharpe ratio as a way of comparing the benefits of owning shares of stock in a company to the risks. The Sharpe ratio of a stock is defined as the ratio of the difference between the mean return on the stock and the mean return on government bonds (called the risk-free rate
(See Exercise 60 regarding the data, and Exercise 61 for the Sharpe ratio.)(a) Find the Sharpe ratio of stock in these three companies. Which looks best from this investment point of view?(b) Form a new column by subtracting rf from the return each month on Exxon. Next divide this column of
Companies vary greatly in size. This variation can hide how well a company is performing. A retailer, for instance, reports $500 million in profits for the past year. That would be a good year for Foot Locker stores, but not for Wal-Mart whose profit was $16 billion in 2010. Rather than look at the
When a customer asks to borrow money, many banks check their credit score before giving them a loan. The credit score estimates the risk associated with making a loan to the customer. Credit scores are based on how well an individual has handled past debts. Customers that have made regular payments
1. Table of cross-classified counts 2. Counts cases that match values of two categorical variables 3. Shown in the bar chart of a categorical variable 4. Shown in a stacked bar chart 5. Measure of association that grows with increased sample size 6. Measure of association that lies between 0 and
1. We can fill in the cells of the contingency table from the marginal counts if the two categorical variables are not associated. 2. We can see association between two categorical variables by comparing their bar charts. 3. The percentages of cases in the first column within each row of a
1. The value of chi-squared depends on which variable defines the rows and which defines the columns of the contingency table. 2. If variable X is associated with variable Y, then Y is caused by X. 3. If the categorical variable that identifies the supervising manager is associated with the
This table shows counts from a consumer satisfaction survey of 2,000 customers who called a credit card company to dispute a charge. One thousand customers were retired and the remaining were employed.(a) What would it mean to find association between these variables?(b) Does the table show
This table summarizes the status of 1,000 loans made by a bank. Each loan either ended in default or was repaid. Loans were divided into large (more than $50,000) or small size.(a) What would it mean to find association between these variables?(b) Does the table show association? (You
A marketing study asked potential customers for their preferences for two attributes of a new product, the color and the packaging. The color of the final product is to be chosen by one manager and the packaging by another. Is this division of labor simpler if the two variables are associated or if
This chart summarizes explanations given for missing work. The data are the explanations given for 100 absences by employees on the assembly line, administration, and supervising managers. The explanations are classified as medical, family emergency, or other.(a) For which group are absences due to
The following chart summarizes the complaints received at a catalog sales call center by day of the week. The chart shows percentages for each day. The complaints are classified as related to delivery (the order has not arrived), fulfillment (an item was missing from an order or not what was
The mosaic plot on the next page shows the sales of cigarettes by the three leading manufacturers, divided into six international regions. (Total sales in 2006 were approximately 2 trillion.)(a) In which region are total cigarette sales the largest?(b) In which two regions does British-American
The following table compares market shares of several companies in the computer industry as reported by Gartner, an industry monitor. The table gives the number of computer systems shipped during each quarter, in thousands.(a) Summarize these data using both a stacked bar chart (of market share)
A chain of stores suspects that coupons will increase sales to customers in its frequent shopper program. To test this theory, the chain mails some customers coupons and does not send these coupons to others. A manager builds a contingency table of two variables: whether the customer was sent a
Among other services, Standard and Poor’s (S&P) rates the risk of default for corporate bonds. AAA bonds are top rated (smallest chance of default), followed by AA, A, BBB, BB, B, CCC, CC, and last D. In a table of bond ratings crossed with the presence or absence of default, would you expect to
Numerous epidemiological studies associate a history of smoking with the presence of lung cancer. If a study finds association (cancer rates are higher among smokers), does this mean that smoking causes cancer?
Incidences of flu are much more prevalent in the winter months than in the summer. Does this association between respiratory illness and outside temperature imply that cold weather causes the flu?
(a) What is Cramer€™s V for this contingency table, which shows choices for paint colors and finishes at a hardware store? (You should not need to do any calculations.)(b) What is the value of Cramer€™s V for this contingency table, which reverses the order of the counts in the
(a) What is the value of Cramer€™s V for this contingency table? (You should not need to do any calculations.)(b) What is the value of Cramer€™s V for this contingency table, which reverses the position of the nonzero values? (c) What is the implication of the association
A service station near an interstate highway sells three grades of gasoline: regular, plus, and premium. During the last week, the manager counted the number of cars that purchased these types of gasoline. He kept the counts separate for weekdays and the weekend. The data table has two categorical
A men’s clothing retailer stocks a variety of men’s shirts. The data for this question record the type of sales during the last three months, indicating shirt style and size. (You should recognize these data!)(a) Find the contingency table defined by the size and type of shirt. Include the
The contingency table in Exercise 39 shows counts of the types of gasoline bought during the week and during weekends.(a) Find the value of chi-squared and Cramer’s V for this table.(b) Interpret these values. What do these tell you about the association in the table?
The contingency table in Exercise 40 shows counts of the sizes of shirts bought in three styles in a retail store.(a) Find the value of chi-squared and Cramer’s V for this table.(b) Interpret these values. What do these tell you about the association in the table?
A marketing survey of car owners was presented in two ways.11 One wording asked the customer whether he was satisfied with his car. The other asked the customer whether he was dissatisfied. The data table has two variables, one indicating the wording of the question and one giving the level of
After the collapse of the stock market in October 1987, Business Week polled its readers and asked whether they expected another big drop in the market during the next 12 months.12 The data table for this question has two variables. One indicates whether the reader owns stock and the other gives
Exercise 43 compares the responses of customers in a survey depending on how a question about their satisfaction with their car was phrased.(a) Quantify the amount of association between the type of question and the degree of satisfaction.(b) Combine the counts of very satisfied with somewhat
Exercise 44 summarizes results from a survey of stockholders following the October 1987 stock market crash.(a) Quantify the amount of association between the respondents’ stock ownership and expectation about the chance for another big drop in stock prices.(b) Reduce the table by combining the
This table shows percentages of men and women employed in four industries.13(a) Is there association between the gender of the employee and the industry? How can you tell?(b) Interpret the association (or lack thereof).(c) Find the chi-squared statistic and Cramer€™s V if these data were
The best-known credit rating for consumers in the United States is the FICO score (named for the company Fair Isaac). The score ranges from 300 to 850, with higher scores indicating that the consumer is a better credit risk. For the following table, consumers with scores below 620 are labeled
The National Opinion Research Center at the University of Chicago reported the following results of a survey in fall of 2004. The survey asked 2,812 adults to state how much they trust different figures in the news. This table summarizes the amount of confidence the public puts in each group.(a)
Business Week magazine asked a sample of investors in the United States and other nations which stock market they expected to produce the best percentage gains over the next 12 months.14 This table shows the percentage of American and foreign investors who picked each country as offering the best
Does the fact that medical researchers get money from drug manufacturers affect their results? The New England Journal of Medicine published a paper that included the following results.15 The table at the top of the next page summarizes the tone of articles published by 69 authors during
To gauge the reactions of possible customers, the manufacturer of a new type of cellular telephone displayed the product at a kiosk in a busy shopping mall. The following table summarizes the results for the customers who stopped to look at the phone:(a) Is the reaction to the new phone associated
These data compare the on-time arrival performance of United and US Airways. The table shows the status of 13,511 arrivals during January 2006.(a) On the basis of this initial summary, find the percentages (row or column) that are appropriate for comparing the on-time arrival rates of the two
These data compare the on-time arrival performance of fights on American and Delta. The table shows the status of 17,064 arrivals during January 2006.(a) On the basis of this initial summary, find the percentages (row or column) that are appropriate for comparing the on-time arrival rates of the
Contingency tables appear frequently in legal cases, such as those that allege that a company has discriminated against a protected class. The following table gives the number of employees of different ages who were laid off when a company anticipated a decline in business:16Several long-time
One effort to improve the efficiency of the health care system provides patients and doctors with more information about the quality of care delivered by hospitals. The idea is to help consumers find the best hospital to treat their illness.These data describe patients with breast cancer. Breast
Match the description to the scatterplot.(a) Negative direction, linear, moderate variation around line(b) Positive direction, linear, small variation around line(c) No pattern. A plot of scrambled pairs would look the same(d) Negative then positive direction, valley-shaped curve, moderate
1. If net revenue at a firm is about 10% of gross sales, then a scatterplot of net revenue versus gross sales would show a nonlinear pattern rather than a line. 2. If two variables are linearly associated, the peak in the histogram of the explanatory variable will line up with the peak in the
1. A report gives the covariance between the number of employees at an assembly factory and the total number of items produced daily. The covariance would be larger if these data were aggregated to monthly totals. 2. The correlation between sales and advertising when both are measured in millions
Match the description to the scatterplot.(a) No pattern. A plot of scrambled pairs would look the same(b) Negative direction, linear, small variation around line(c) Positive direction, but bending with small variation around curving pattern(d) Positive direction, linear, large variation around line
Suppose you collect data for each of the following pairs of variables. You want to make a scatterplot. Identify the response and explanatory variables. What would you expect to see in the scatterplot? Discuss the direction, curvature, and variation. (a) Sales receipts: number of items, total
Suppose you collect data for each of the following pairs of variables. You want to make a scatterplot. Identify the response and explanatory variables. What would you expect to see in the scatterplot? Discuss the likely direction, curvature, and variation. (a) Winter electricity: kilowatts,
States in the United States are allowed to set their own rates for sales taxes as well as taxes on services, such as telephone calls. The scatterplot below graphs the state and local taxes charged for wireless phone calls (as a percentage) versus the state sales tax (also as a percentage).(a)
The Organization for Economic Cooperation and Development (OECD) is a loose affiliation of 30 nations. The data in this scatterplot show the percentage of disposable income for a single citizen that remains after paying taxes versus the top personal income tax rate (also a percentage).(a) Describe
Management of a sales force has noticed that there is a positive linear association (r = 0.6) between sales produced by company representatives in adjacent months. If a sales representative does really well this month (say, her z-score is +2), why should we expect her z-score to be lower next month?
Match the value of the correlation to the data in the scatterplot.(a) r = 0(b) r = 0.5(c) r = 0.8 (d) r = -0.6
The human resources department at a company noticed that there is a linear association between the number of days that an employee is absent from year to year, with correlation 0.4. The correlation of absences this year with the number of absences last year is 0.4. Managers claim that an award
The following time plot shows the values of two indices of the economy in the United States: inflation (left axis, in red, measured as the year-over-year percentage change in the Consumer Price Index) and the Survey of Consumer Sentiment (right axis, in blue, from the University of Michigan). Both
The scatterplot that follows shows monthly values of consumer sentiment plotted versus inflation (see Exercise 31 for the definition of these variables). For this plot, we€™ve shown the full history of the consumer survey back to January 1978. The subset of the points in black shows data
Which do you think produces a larger correlation between the weight and the price of diamonds: using a collection of gems of various cuts, colors, and clarities or a collection of stones that have the same cut, color, and clarity?
To measure the association between the number of employees and the number of items produced on a small assembly line, a company recorded the number of employees each day (from 5 to 10) and the number of items produced. To make a nicer plot, a manager found the average number of items produced when
The correlation measures the strength of linear dependence. Does Cramer’s V (Chapter 5) only measure linear dependence?
Each month, the Department of Commerce releases its estimate of construction activity. A key measure is the percentage change in the number of new homes under construction. Are changes in home construction associated with changes in the stock market? These data show the percentage change in the
Match the value of the correlation to the data in the scatterplot.(a) r = 0(b) r = -0.9(c) r = 1(d) r = 0.4
These data give the median dollar value in 2009 of homes in the 50 states and District of Columbia along with the average annual premium for homeowners’ insurance (from the Statistical Abstract of the United States). (a) Would you expect these variables to be dependent or independent? What would
The slope for the correlation line when expressed in z-scores is r. Hence when formulated in z-scores, the absolute value of the slope is less than 1 unless the data lie along a single line. The data in this example are productivity measures used to grade 15 employees who work on an assembly line.
These data give the times in minutes for cyclists who competed in the 2010 Tour de France and raced in both time trial events. In a time trial, each cyclist individually rides a set course. The rider with the shortest time wins the event. The courses in the 2010 tour varied in length. The frst time
How many mistakes get made during data entry? The following table gives the number of mistakes made by 15 data entry clerks who enter medical data from case report forms. These forms are submitted by doctors who participate in studies of the performance of drugs for treating various illnesses. The
The Minnesota Department of Transportation would like to measure the weights of commercial trucks on its highways without the expense of maintaining weigh stations along the highway. Weigh stations are expensive to operate, delay shipments, and aggravate truckers. To see if a proposed remote weight
These data report characteristics of 196 types of cars sold in the United States in 2012. One column gives the official mileage (combined MPG), and an-other gives the rated horsepower. (a) Make a scatterplot of these two columns. Which variable makes the most sense to put on the x-axis, and which
These data are described in Exercise 45. In exercise 45: These data report characteristics of 196 types of cars sold in the United States in 2012. One column gives the official mileage (combined MPG), and an-other gives the rated horsepower. (a) Make a scatterplot of weight and highway mile-age.
These data describe housing prices in the Philadelphia area. Each of the 110 rows of this data table describes a region of the metropolitan area. (Several make up the city of Philadelphia.) One column, labeled Selling Price, gives the median price for homes sold in that area during 1999 in
These data describe 506 census tracts in the Boston area. These data were assembled in the 1970s and used to build a famous model in economics, known as a hedonic pricing model.13 The column Median Value is the median value of owner-occupied homes in the tract (in thousands of dollars back in the
There€™s a special situation in which you can measure dependence using either the correlation or Cramer€™s V (Chapter 5). Suppose both variables indicate group membership. One variable might distinguish male from female customers, and the other whether the customer uses a credit card, as in
1. The explanatory variable defines the x-axis in a scatterplot. 2. In a plot of income (the response) versus education (the explanatory variable) for managers, managers with the lowest levels of education are at the right-hand side of the figure. 3. The presence of a pattern in a scatterplot means
A scatterplot is not so useful for numerical data when the data include many copies. In Exercise 49, there are 50 cases of male customers who paid with cash. That’s 50 pairs of values with Sex = 1 and Cash = 1.(a) What does the scatterplot of Cash versus Sex look like?(b) Suggest a method for
The Bureau of Labor Statistics monitors characteristics of the United States economy. Several of these time series are in the data table for this question. These time series are quarterly and span the time period from 1980 through the third quarter of 2011. For example, the bureau monitors
The government wants consumers to have money to spend to keep the economy moving, so it watches the national level of personal disposable income. The Federal Reserve wants to make sure that these same consumers do not get into too much debt. The variable Disposable Income tracks the money available
If the airline fight that you are on is 20 minutes late departing, can you expect the pilot to make these minutes up by, say, fying faster than usual? These data summarize the status of a sample of 984 fights during August 2006. (Like the data used to illustrate Simpson’s paradox in Chapter 5,
These data give the amount of CO2 produced in 40 nations along with the level of economic activity, both in 2009. CO2 emissions are given in millions of metric tons. Economic activity is given by the gross domestic product (GDP), a summary of overall economic output. Both variables are from the
Apple, Dell, IBM, and Microsoft are well known in the computer industry. If the computer industry is doing well, then we might expect the stocks of all four to increase in value. If the industry goes down, we’d expect all four to go down as well. How strong is the association among these
Companies that manufacture products that conform to a unique specifcation for each order need help in estimating their own costs. Because each order is unique, it can be hard to know for sure just how much it will cost to manufacture. Plus, the company often needs to quote a price when the customer

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