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The Practice Of Statistics For Business And Economics 4th Edition Layth C. Alwan, Bruce A. Craig - Solutions

Faculty salaries. Data on the salaries of a sample of professors in a business department at a large university are given below. The salaries are for the academic years 2014–2015 and 2015–2016. FACSAL 2014–2015 2015–2016 2014–2015 2015–2016 salary ($) salary ($) salary ($) salary
Look at the residuals. Refer to the previous exercise. Figure 2.25 is a plot of the residuals versus year. RAISES(a) Interpret the residual plot.(b) Explain how this plot highlights the deviations from the least-squares regression line that you can see in Figure 2.24.
Salaries and raises. For this exercise, we consider a hypothetical employee who starts working in Year 1 at a salary of $50,000. Each year her salary increases by approximately 5%. By Year 20, she is earning $126,000. The following table gives her salary for each year (in thousands of dollars):Year
Sales and production. Refer to the previous two exercises. MEIS(a) Make a scatterplot with sales as the response variable and production as the explanatory variable. Describe the relationship. Are there any outliers or influential observations?(b) Find the least-squares regression line and add it
Dwelling permits and production. Refer to the previous exercise. MEIS(a) Make a scatterplot with production as the response variable and permits issued for new dwellings as the explanatory variable. Describe the relationship. Are there any outliers or influential observations?(b) Find the
Dwelling permits and sales for 21 European countries. The Organization for Economic Cooperation and Development (OECD) collects data on Main Economic Indicators (MEIs) for many countries. Each variable is recorded as an index, with the year 2000 serving as a base year. This means that the variable
Residuals for companies of the world with logs. Refer to the previous exercise. INCCOM(a) Use a histogram to examine the distribution of the residuals.(b) Make a Normal quantile plot of the residuals.(c) Summarize the distribution of the residuals using the graphical displays that you created in
Companies of the world with logs. In Exercises 2.10 (page 72), 2.27 (page 78), and 2.58 (pages 95–96), you examined the relationship between the numbers of companies that are incorporated and are listed on their country’s stock exchange at the end of the year using data collected by the World
Find the table. Here are the row and column totals for a two-way table with two rows and two columns:a b 60 c d 60 70 50 120 Find two different sets of countsa, b,c, and d for the body of the table that give these same totals.This shows that the relationship between two variables cannot be obtained
Obesity and health. Recent studies have shown that earlier reports underestimated the health risks associated with being overweight. The error was due to lurking variables. In particular, smoking tends both to reduce weight and to lead to earlier death.Illustrate Simpson’s paradox by a simplified
Discrimination? Wabash Tech has two professional schools, business and law. Here are twoway tables of applicants to both schools, categorized by sex and admission decision. (Although these data are made up, similar situations occur in reality.)DISC Business Law Admit Deny Admit Deny Male 480 120
Demographics and new products—men.Refer to Exercises 2.113 and 2.114. Here are the corresponding counts for men:Marital status Never Age (years) married Married Widowed Divorced 18 to 24 13,509 1,245 6 63 25 to 39 12,685 16,029 78 1,790 40 to 64 6,869 34,650 760 6,647 $ 65 685 12,514 2,124 1,464
Demographics, continued. AGEGEN(a) Using the data in the previous exercise, compare the conditional distributions of marital status for women aged 18 to 24 and women aged 40 to 64. Briefly describe the most important differences between the two groups of women, and back up your description with
Demographics and new products. Companies planning to introduce a new product to the market must define the “target’’ for the product. Who do we hope to attract with our new product? Age and sex are two of the most important demographic variables. The following two-way table describes the age
Nonresponse in a survey of companies. A business school conducted a survey of companies in its state. It mailed a questionnaire to 200 small companies, 200 medium-sized companies, and 200 large companies. The rate of nonresponse is important in deciding how reliable survey results are. Here are the
Hiring practices. A company has been accused of age discrimination in hiring for operator positions.Lawyers for both sides look at data on applicants for the past three years. They compare hiring rates for applicants younger than 40 years and those 40 years or older. HIRING Age Hired Not hired
Class size and course level. College courses taught at lower levels often have larger class sizes. The following table gives the number of classes classified by course level and class size.22 For example, there were 202 first-year level courses with between one and nine students. CSIZE Class size
Trust and honesty in the workplace. The students surveyed in the study described in the previous exercise were also asked whether they thought trust and honesty were essential in business and the workplace. Here are the counts classified by sex:Sex Trust and honesty are essential Male Female Agree
Lying to a teacher. One of the questions in a survey of high school students asked about lying to teachers.21 The accompanying table gives the numbers of students who said that they lied to a teacher about something significant at least once during the past year, classified by sex. LYING Sex Lied
Condition on age. Refer to the previous exercise. COLSTUD(a) For each age group, compute the percent of students who are full-time and the percent of students who are part-time.(b) Make a graphical display of the results that you found in part (a).(c) If you have the appropriate software, make a
Full-time and part-time college students.The Census Bureau provides estimates of numbers of people in the United States classified in various ways.20 Let’s look at college students. The following table gives us data to examine the relation between age and full-time or part-time status. The
Adequate sleep and exercise. Refer to the previous exercise. SLEEP(a) Find the distribution of exercise for those who get adequate sleep.(b) Do the same for those who do not get adequate sleep.(c) Write a short summary of the relationship between adequate sleep and exercise using the results of
Exercise and adequate sleep. A survey of 656 boys and girls, ages 13 to 18, asked about adequate sleep and other health-related behaviors. The recommended amount of sleep is six to eight hours per night.19 In the survey, 54% of the respondents reported that they got less than this amount of sleep
How does RDC vary across the country? The survey described in the previous exercise also classified community banks by region. Here is the 6 × 2 table of counts:Offer RDC Region Yes No Northeast 28 38 Southeast 57 61 Central 53 84 Midwest 63 181 Southwest 27 51 West 61 76 Summarize the results of
Remote deposit capture. The Federal Reserve has called remote deposit capture (RDC) “the most important development the [U.S.] banking industry has seen in years.’’ This service allows users to scan checks and to transmit the scanned images to a bank for posting.16 In its annual survey of
Patients in “poor’’ or “good’’ condition. Not all surgery cases are equally serious, however. Patients are classified as being in either “poor’’ or“good’’ condition before surgery. Here are the data broken down by patient condition.Check that the entries in the original
Which hospital is safer? Insurance companies and consumers are interested in the performance of hospitals. The government releases data about patient outcomes in hospitals that can be useful in making informed health care decisions.Here is a two-way table of data on the survival of patients after
Compare the two analytical approaches. In the previous two exercises, you examined the relationship between country and field of study in two different ways.(a) Compare these two approaches.(b) Which do you prefer? Give a reason for your answer.(c) What kinds of questions are most easily answered
Countries by fields of study for college students. Refer to the previous exercise. Answer the same questions for the conditional distribution of country for each field of study.
Fields of study by country for college students. In Exercise 2.93, you examined data on fields of study for graduating college students from seven countries.(a) Find the seven conditional distributions giving the distribution of graduates in the different fields of study for each country.(b)
Compare the conditional distributions. In Example 2.26, we found the distribution of sales by wine type when no music was playing. In Exercise 2.94, you found the distribution when French music was playing, and in Exercise 2.95, you found the distribution when Italian music was playing. Examine
Conditional distribution when Italian music was playing.(a) Write down the column of counts that you need to compute the conditional distribution of the type of wine sold when Italian music was playing.(b) Compute this conditional distribution.(c) Display this distribution graphically.(d) Compare
Conditional distribution when French music was playing.(a) Write down the column of counts that you need to compute the conditional distribution of the type of wine sold when French music was playing.(b) Compute this conditional distribution.(c) Display this distribution graphically.(d) Compare
Fields of study for college students. The following table gives the number of students (in thousands) graduating from college with degrees in several fields of study for seven countries:(a) Calculate the marginal totals, and add them to the table.(b) Find the marginal distribution of country, and
Construct a two-way table. Construct your own 2 × 3 table. Add the marginal totals and find the two marginal distributions.
Marginal distribution for type of music. Find the marginal distribution for the type of music. Display the distribution using a graph.
Do power lines cause cancer? It has been suggested that electromagnetic fields of the kind present near power lines can cause leukemia in children. Experiments with children and power lines are not ethical. Careful studies have found no association between exposure to electromagnetic fields and
Education and income. There is a strong positive correlation between years of schooling completed x and lifetime earnings y for American men. One possible reason for this association is causation: more education leads to higher-paying jobs. But lurking variables may explain some of the correlation.
Does your product help nursing-home residents? A group of college students believes that herbal tea has remarkable powers. To test this belief, they make weekly visits to a local nursing home, where they visit with the residents and serve them herbal tea. The nursing-home staff reports that, after
Does your product have an undesirable side effect? People who use artificial sweeteners in place of sugar tend to be heavier than people who use sugar.Does this mean that artificial sweeteners cause weight gain? Give a more plausible explanation for this association.
Sales at a farmers’ market. You sell fruits and vegetables at your local farmers’ market, and you keep track of your weekly sales. A plot of the data from May through August suggests a increase over time that is approximately linear, so you calculate the leastsquares regression line. Your
Marital status and income. Data show that married, divorced, and widowed men earn quite a bit more than men the same age who have never been married. This does not mean that a man can raise his income by getting married because men who have never been married are different from married men in many
Older workers and income. The effect of a lurking variable can be surprising when cases are divided into groups. Explain how, as a nation’s population grows older, mean income can go down for workers in each age group but still go up for all workers.
Predict the sales. You analyzed the past 10 years of sales data for your company, and the data fit a straight line very well. Do you think the equation you found would be useful for predicting next year’s sales? Would your answer change if the prediction was for sales five years from now? Give
What’s wrong? Each of the following statements contains an error. Describe each error and explain why the statement is wrong.(a) An outlier will always have a large residual.(b) If we have data at values of x equal to 1, 2, 3, 4, and 5, and we try to predict the value of y at x = 2.5 using a
What’s wrong? Each of the following statements contains an error. Describe each error and explain why the statement is wrong.(a) A negative relationship is always due to causation.(b) A lurking variable is always a quantitative variable.(c) If the residuals are all negative, this implies that
Do firefighters make fires worse? Someone says, “There is a strong positive correlation between the number of firefighters at a fire and the amount of damage the fire does. So sending lots of firefighters just causes more damage.’’Explain why this reasoning is wrong.
Are big hospitals bad for you? A study shows that there is a positive correlation between the size of a hospital (measured by its number of beds x) and the median number of days y that patients remain in the hospital. Does this mean that you can shorten a hospital stay by choosing a small hospital?
How’s your self-esteem? People who do well tend to feel good about themselves.Perhaps helping people feel good about themselves will help them do better in their jobs and in life. For a time, raising self-esteem became a goal in many schools and companies. Can you think of explanations for the
Education and income. There is a strong positive correlation between years of education and income for economists employed by business firms. In particular, economists with a doctorate earn more than economists with only a bachelor’s degree. There is also a strong positive correlation between
Always plot your data! Four sets of data prepared by the statistician Frank Anscombe illustrate the dangers of calculating without first plotting the data.11(a) Without making scatterplots, find the correlation and the least-squares regression line for all four data sets.What do you notice? Use the
Employee absenteeism and raises. Data on number of days of work missed and annual salary increase for a company’s employees show that, in general, employees who missed more days of work during the year received smaller raises than those who missed fewer days. Number of days missed explained 49%
Influence in regression. As in the previous exercise, create a group of 12 points in the lowerleft corner of the scatterplot with a strong straight-line pattern (correlation at least 0.9). Click the “Show least-squares line’’ box to display the regression line.(a) Add one point at the upper
Influence on correlation. The Correlation and Regression applet at the text website allows you to create a scatterplot and to move points by dragging with the mouse. Click to create a group of 12 points in the lower-left corner of the scatterplot with a strong straight-line pattern (correlation
Add a different outlier. Refer to the previous two exercises. Add an additional case with y = 60 and x = 18 to the original data set.(a) Repeat the analysis that you performed in the first exercise and summarize your results, paying particular attention to the effect of this outlier.(b) In this
Add an outlier. Refer to the previous exercise. Add an additional case with y = 60 and x = 32 to the data set.Repeat the analysis that you performed in the previous exercise and summarize your results, paying particular attention to the effect of this outlier.
Data generated by software. The following 20 observations on y and x were generated by a computer program.y x y x 34.38 22.06 27.07 17.75 30.38 19.88 31.17 19.96 26.13 18.83 27.74 17.87 31.85 22.09 30.01 20.20 26.77 17.19 29.61 20.65 29.00 20.72 31.78 20.32 28.92 18.10 32.93 21.37 26.30 18.01 30.29
Monitoring the water quality near a manufacturing plant. Manufacturing companies(and the Environmental Protection Agency) monitor the quality of the water near manufacturing plants.Measurements of pollutants in water are indirect—a typical analysis involves forming a dye by a chemical reaction
Carbohydrates and alcohol in beer revisited.Refer to Exercise 2.65. The data that you used to compute the least-squares regression line includes a beer with a very low alcohol content that might be considered to be an outlier.(a) Remove this case and recompute the least-squares regression line.(b)
Predicted values and residuals. Refer to the previous two exercises.(a) Make a plot of the residuals versus percent alcohol.(b) Interpret the plot. Is there any systematic pattern?Explain your answer.(c) Examine the plot carefully and determine the approximate location of New Belgium Fat Tire. Is
Predicted values and residuals. Refer to the previous exercise.(a) New Belgium Fat Tire is 5.2 percent alcohol and has 160 calories per 12 ounces. Find the predicted calories for New Belgium Fat Tire.(b) Find the residual for New Belgium Fat Tire.
Predict one characteristic of a product using another characteristic. In Exercise 2.12 (page 72), you used a scatterplot to examine the relationship between calories per 12 ounces and percent alcohol in 175 domestic brands of beer. In Exercise 2.31(page 79), you calculated the correlation between
Consider the fuel type. Refer to the previous two exercises and to Figure 2.6 (page 71), where different colors are used to distinguish four different types of fuels used by these vehicles. In Exercise 2.38, you examined the relationship between Highway MPG and City MPG for each of the four
Fuel efficiency and CO2 emissions. Refer to the previous exercise.(a) Make a scatterplot of the data with highway MPG as the response variable and city MPG as the explanatory variable. Include the least-squares regression line on the plot. There is an unusual pattern for the vehicles with high city
Fuel efficiency and CO2 emissions. In Exercise 2.37 (page 79), you examined the relationship between highway MPG and city MPG for 1067 vehicles for the model year 2014.(a) Use the city MPG to predict the highway MPG. Give the equation of the least-squares regression line.(b) The Lexus 350h AWD gets
Use a log for the radioactive decay. Refer to the previous exercise. Also see Exercise 2.18 (page 73), where you transformed the counts with a logarithm, and Exercise 2.30 (pages 78–79), where you found the correlation between time and the log of the counts.Answer parts (a) to (e) of the previous
A product for lab experiments. In Exercise 2.17(page 73), you described the relationship between time and count for an experiment examining the decay of barium. In Exercise 2.29 (page 78), you found the correlation between these two variables.(a) Find the least-squares regression equation for
Companies of the world. Refer to the previous exercise and to Exercise 2.11 (page 72). Answer parts (a), (b), and (c) of the previous exercise for 2012 and 1992. Compare the results you found in the previous exercise with the ones you found in this exercise. Explain your findings in a short
Companies of the world. Refer to Exercise 1.118(page 61), where we examined data collected by the World Bank on the numbers of companies that are incorporated and listed on their country’s stock exchange at the end of the year. In Exercise 2.10, you examined the relationship between these numbers
Compare the cell phone payment plans. A cellular telephone company offers two plans. Plan A charges $30 a month for up to 120 minutes of airtime and $0.55 per minute above 120 minutes. Plan B charges $35 a month for up to 200 minutes and $0.50 per minute above 200 minutes.(a) Draw a graph of the
Inventory of Blu-Ray players. A local consumer electronics store sells exactly eight Blu-Ray players of a particular model each week. The store expects no more shipments of this particular model, and they have 96 such units in their current inventory.(a) Give an equation for the number of Blu-Ray
Production costs for cell phone batteries. A company manufactures batteries for cell phones. The overhead expenses of keeping the factory operational for a month—even if no batteries are made—total$500,000. Batteries are manufactured in lots (1000 batteries per lot) costing $7000 to make. In
What is the equation for the selling price? You buy items at a cost of x and sell them for y. Assume that your selling price includes a profit of 12% plus a fixed cost of $25.00. Give an equation that can be used to determine y from x.
The influence of Texas. Make a plot similar to Figure 2.16 giving regression lines with and without Texas. Summarize what this plot describes.
Identify the four states. In Figure 2.13, four states are identified by name:California, Texas, Florida, and New York. The dashed lines in the plot represent the residuals.(a) Sketch a version of Figure 2.14 or generate your own plot using the EDSPEND data file. Write in the names of the states
Sum the education spending residuals. The residuals in the EDSPEND data file have been rounded to two places after the decimal. Find the sum of these residuals. Is the sum exactly zero? If not, explain why.
Residual for Texas. Refer to Example 2.16 (page 89). Texas spent $90.5 million on education and has a population of 26.8 million people.(a) Find the predicted education spending for Texas.(b) Find the residual for Texas.(c) Which state, California or Texas, has a greater deviation from the
Is regression useful? In Exercise 2.39 (pages 79–80), you used the Correlation and Regression applet to create three scatterplots having correlation about r = 0.7 between the horizontal variable x and the vertical variable y. Create three similar scatterplots again, after clicking the “Show
The “January effect.’’ Some people think that the behavior of the stock market in January predicts its behavior for the rest of the year. Take the explanatory variable x to be the percent change in a stock market index in January and the response variable y to be the change in the index for
Predicted values for GDP and assets. Refer to the world financial markets data in Example 2.9.(a) Use software to compute the coefficients of the regression equation. Indicate where to find the slope and the intercept on the output, and report these values.(b) Make a scatterplot of the data with
A regression line. A regression equation is y = 15 + 30x.(a) What is the slope of the regression line?(b) What is the intercept of the regression line?(c) Find the predicted values of y for x = 10, for x = 20, and for x = 30.(d) Plot the regression line for values of x between 0 and 50.
Positive and negative prediction errors. Examine Figure 2.9 carefully.How many of the prediction errors are positive? How many are negative?
Find a prediction error. Use Figure 2.9 to estimate the net assets per capita for a country that has a GDP per capita of $40,000. If the actual net assets per capita are $170,000, find the prediction error.
Sloppy writing about correlation. Each of the following statements contains a blunder. Explain in each case what is wrong.(a) “The correlation between y and x is r = 0.5 but the correlation between x and y is r = −0.5.’’(b) “There is a high correlation between the color of a smartphone
Investment reports and correlations. Investment reports often include correlations. Following a table of correlations among mutual funds, a report adds, “Two funds can have perfect correlation, yet different levels of risk. For example, Fund A and Fund B may be perfectly correlated, yet Fund A
CEO compensation and stock market performance. An academic study concludes, “The evidence indicates that the correlation between the compensation of corporate CEOs and the performance of their company’s stock is close to zero.’’ A business magazine reports this as “A new study shows that
Stretching a scatterplot. Changing the units of measurement can greatly alter the appearance of a scatterplot.Consider the following data:x −4 −4 −3 3 4 4 y 0.5 −0.6 −0.5 0.5 0.5 −0.6(a) Draw x and y axes each extending from −6 to 6. Plot the data on these axes.(b) Calculate the
Match the correlation. The Correlation and Regression applet at the text website allows you to create a scatterplot by clicking and dragging with the mouse. The applet calculates and displays the correlation as you change the plot. You will use this applet to make scatterplots with 10 points that
Consider the fuel type. Refer to the previous exercise and to Figure 2.6 (page 71), where different colors are used to distinguish four different types of fuels used by these vehicles. CANFUEL(a) Make a figure similar to Figure 2.6 that allows us to see the categorical variable, type of fuel, in
Fuel efficiency and CO2 emissions. In Example 2.7 (pages 70–71), we examined the relationship between highway MPG and CO2 emissions for 1067 vehicles for the model year 2014. Let’s examine the relationship between the two measures of fuel efficiency in the data set, highway MPG and city
Are they outliers? Refer to the previous exercise. Delete the four states with high values.EDSPEND(a) Find the correlation between spending on education and population for the remaining 46 states.(b) Do the same for these variables expressed as logs.(c) Compare your results in parts (a) and (b)
Education spending and population with logs. In Example 2.3 (page 66), we examined the relationship between spending on education and population, and in Exercise 2.23 (page 75), you found the correlation between these two variables. In Example 2.6 (page 69), we examined the relationship between the
Nunavut. Refer to the previous exercise.CANADAP(a) Do you think that Nunavut is an outlier? Explain your answer.(b) Find the correlation without Nunavut. Using your work from the previous exercise, summarize the effect of Nunavut on the correlation.
Marketing in Canada. In Exercise 2.14(page 73), you examined the relationship between the percent of the population over 65 and the percent under 15 for the 13 Canadian provinces and territories.CANADAP(a) Make a scatterplot of the two variables if you do not have your work from Exercise 2.14.(b)
Alcohol and carbohydrates in beer revisited.Refer to the previous exercise. Delete any outliers that you identified in Exercise 2.12. BEER(a) Recompute the correlation without the outliers.(b) Write a short paragraph about the possible effects of outliers on the correlation, using this example to
Brand-to-brand variation in a product. In Exercise 2.12 (page 73), you examined the relationship between percent alcohol and calories per 12 ounces for 175 domestic brands of beer. BEER(a) Compute the correlation between these two variables.(b) Do you think that the correlation you computed gives a
Use a log for the radioactive decay. Refer to the previous exercise and to Exercise 2.18 (page 73), where you transformed the counts with a logarithm.DECAY(a) Is the relationship between time and the log of the counts strong? Explain your answer.(b) Find the correlation between time and the log of
A product for lab experiments. In Exercise 2.17 (page 73), you described the relationship between time and count for an experiment examining the decay of barium. DECAY(a) Is the relationship between these two variables strong? Explain your answer.(b) Find the correlation.(c) Do you think that the
Companies of the world. Refer to the previous exercise and to Exercise 2.11 (page 72). Answer parts(a) and (b) for 2012 and 1992. Compare the correlation you found in the previous exercise with the one you found in this exercise. Why do they differ in this way?
Companies of the world. Refer to Exercise 1.118 (page 61), where we examined data collected by the World Bank on the numbers of companies that are incorporated and are listed on their country’s stock exchange at the end of the year. In Exercise 2.10(page 72), you examined the relationship between

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