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business statistics

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

Are inflows into stocks and bonds correlated? Is the correlation between net flow of money into stock mutual funds and into bond mutual funds significantly different from 0? Use the regression analysis you did in Exercise 10.30 part (b) to answer this question with no additional calculations.
Stocks and bonds. How is the flow of investors’ money into stock mutual funds related to the flow of money into bond mutual funds? Table 10.4 shows the net new money flowing into stock and bond mutual funds in the years 1984 to 2013, in millions of dollars.13 “Net” means that funds flowing
Correlation between the prevalences of adult binge drinking and underage drinking. A group of researchers compiled data on the prevalence of adult binge drinking and the prevalence of underage drinking in 42 states.12 A correlation of 0.32 was reported.(a) Use Table G to test the null hypothesis
Is the correlation significant? A study reports correlation r 5 20.42 based on a sample of size n 5 25.Another study reports the same correlation based on a sample of size n 5 15. For each, use Table G to test the null hypothesis that the population correlation 5 0 against the one-sided
T-bills and inflation. Exercises 10.6 through 10.8 interpret the part of the Excel output in Figure 10.10 (page 499) that concerns the slope, the rate at which T-bill returns increase as the rate of inflation increases. Use this output to answer questions about the intercept.(a) The intercept 0 in
Regression to the mean? Suppose a large population of test takers take the GMAT. You fear there may have been some cheating, so you ask those people who scored in the top 10% to take the exam again.(a) If their scores, on average, go down, is this evidence that there was cheating? Explain your
Was inference justified? You see from Figure 10.11 that the incomes of men at each age are(as expected) not Normal but right-skewed.(a) How is this apparent on the plot?(b) Nonetheless, your confidence interval in the previous exercise will be quite accurate even though it is based on Normal
Income increases with age. We see that older men do, on average, earn more than younger men, but the increase is not very rapid. (Note that the regression line describes many men of different ages—data on the same men over time might show a different pattern.)(a) We know even without looking at
Looking at age and income. The scatterplot in Figure 10.11 has a distinctive form.(a) Age is recorded as of the last birthday. How does this explain the vertical stacks in the scatterplot?(b) Give some reasons older men in this population might earn more than younger men. Give some reasons younger
Compare the analyses. In Exercises 10.15 and 10.21, you used two different explanatory variables to predict the tuition in 2013. Summarize the two analyses and compare the results. If you had to choose between the two, which explanatory variable would you choose?Give reasons for your answers.Age
Predicting public university tuition: 2000 versus 2013. Refer to Exercise 10.15. The data file also includes the in-state undergraduate tuition and required fees for the year 2000. Repeat parts (a) through (f) of Exercise 10.15 using these data in place of the data for the year 2008. TUIT
Incentive pay, continued. Refer to the previous exercise. PERPLAY(a) Now run the simple linear regression for the variables square root of rating and percent of salary from incentive payments.(b) Obtain the residuals and assess whether the assumptions for the linear regression analysis are
Incentive pay and job performance. In the National Football League (NFL), incentive bonuses now account for roughly 25% of player compensation.11 Does tying a player’s salary to performance bonuses result in better individual or team success on the field? Focusing on linebackers, let’s look at
The relationship between log income and education level for employees. Recall Case 10.1(pages 485–486). The researchers also looked at the relationship between education and log income for employees.An employee was defined as a person whose main employment status is a salaried job. Based on a
The timing of initial public offerings(IPOs). Initial public offerings (IPOs) have tended to group together in time and in sector of business. Some researchers hypothesize this is due to managers either speeding up or delaying the IPO process in hopes of taking advantage of a “hot” market,
More on public university tuition. Refer to the previous exercise. TUIT(a) Construct a 95% confidence interval for the slope.What does this interval tell you about the annual percent increase in tuition between 2008 and 2013?(b) What percent of the variability in 2013 tuition is explained by a
Public university tuition: 2008 versus 2013. Table 10.3 shows the in-state undergraduate tuition and required fees in 2008 and in-state tuition in 2013 for 33 public universities.9 TUIT(a) Plot the data with the 2008 tuition on the x axis and describe the relationship. Are there any outliers or
Assessment value versus sales price, continued.Refer to the previous exercise. Let’s consider linear regression analysis using just 34 properties. HSALES(a) Obtain the residuals and plot them versus assessed value. Is there anything unusual to report?If so, explain.(b) Do the residuals appear to
Assessment value versus sales price. Real estate is typically reassessed annually for property tax purposes. This assessed value, however, is not necessarily the same as the fair market value of the property. Table 10.2 summarizes an SRS of 35 properties recently sold in a midwestern county.8 Both
Two regressions. We have regressed the log income of entrepreneurs on their years of education, with the results appearing in Figures 10.5 and 10.6. Use software to regress years of education on log income for the same data.(a) What is the equation of the least-squares line for predicting years of
T-bills and inflation. We expect the interest rates on Treasury bills to rise when the rate of inflation rises and fall when inflation falls. That is, we expect a positive correlation between the return on T-bills and the inflation rate.(a) Find the sample correlation r for the 55 years in Table
Mediocrity triumphant? In the early 1930s, a man named Horace Secrist wrote a book titled The Triumph of Mediocrity in Business. Secrist found that businesses that did unusually well or unusually poorly in one year tended to be nearer the average in profitability at a later year. Why is it a
Hot funds? Explain carefully to a naive investor why the mutual funds that had the highest returns this year will as a group probably do less well relative to other funds next year.
Estimating the slope. Using Excel’s values for b1 and its standard error, find a 95% confidence interval for the slope 1 of the population regression line. Compare your result with Excel’s 95% confidence interval. What does the confidence interval tell you about the change in the T-bill return
Is there a relationship? What are the slope b1 of the fitted line and its standard error? Use these numbers to test by hand the hypothesis that there is no straight-line relationship between inflation rate and T-bill return against the alternative that the return on T-bills increases as the rate of
Look at the data. Give a brief description of the form, direction, and strength of the relationship between the inflation rate and the return on Treasury bills. What is the equation of the least-squares regression line for predicting T-bill return?
Research and development spending. The National Science Foundation collects data on the research and development spending by universities and colleges in the United States.3 Here are the data for the years 2008–2011:Year 2008 2009 2010 2011 Spending (billions of dollars) 51.9 54.9 58.4 62.0(a)
Fixed and variable costs. In some mass production settings, there is a linear relationship between the number x of units of a product in a production run and the total cost y of making these x units.(a) Write a population regression model to describe this relationship.(b) The fixed cost is the
U.S. versus overseas stock returns. Returns on common stocks in the United States and overseas appear to be growing more closely correlated as economies become more interdependent. Suppose that the following population regression line connects the total annual returns (in percent) on two indexes of
Understanding a linear regression model. Consider a linear regression model with y 5 26.35 1 3.4x and standard deviation 5 4.1.(a) What is the slope of the population regression line?(b) Explain clearly what this slope says about the change in the mean of y for a unit change in x.(c) What is the
Predict the log income. In Case 10.1, Entrepreneur 3 has an EDUC of 14 years and a log income of 10.9475. Using the least-squares regression equation in Example 10.1, find the predicted log income and the residual for this individual.
Suspicious results? An instructor who assigned an exercise similar to the one described in the previous exercise received homework from a student who reported a P-value of 0.999. The instructor suspected that the student did not use the computer for the assignment but just made up some numbers for
More on goodness of fit to the uniform distribution. Refer to the previous exercise.(a) Use software to generate your own sample of 800 uniform random variables on the interval from 0 to 1, and perform the goodness-of-fit test using the intervals from the previous exercise.(b) Choose a different
Goodness of fit to the uniform distribution. Computer software generated 500 random numbers that should look as if they are from the uniform distribution on the interval 0 to 1 (see page 213). They are categorized into five groups: (1) less than or equal to 0.2, (2) greater than 0.2 and less than
More on the goodness of fit to a standard Normal distribution. Refer to the previous exercise.(a) Use software to generate your own sample of 800 standard Normal random variables, and perform the goodness-of-fit test using the intervals from the previous exercise.(b) Choose a different set of
Goodness of fit to a standard Normal distribution. Computer software generated 500 random numbers that should look as if they are from the standard Normal distribution. They are categorized into five groups: (1) less than or equal to 20.6, (2) greater than 20.6 and less than or equal to 20.1, (3)
Titanic! In 1912, the luxury liner Titanic, on its first voyage, struck an iceberg and sank. Some passengers got off the ship in lifeboats, but many died. Think of the Titanic disaster as an experiment in how the people of that time behaved when faced with death in a situation where only some can
Computations for RDC and bank size. Refer to the 3 3 2 table of data for bank asset size and remote deposit capture offering in Exercise 9.27 (page 477).(a) Compute the expected count for each cell in the table.(b) Compute the X2 test statistic.(c) What are the degrees of freedom for this
Which model? This exercise concerns the material in Section 9.1 on models for two-way tables.Look at Exercises 9.27, 9.31, 9.42, and 9.47. For each exercise, state whether you are comparing several populations based on separate samples from each population (the first model for two-way tables) or
Employee performance appraisal. A major issue that arises in RIFs like that in the previous exercise is the extent to which employees in various groups are similar.If, for example, employees over 40 receive generally lower performance ratings than younger workers, that might explain why more older
A reduction in force. In economic downturns or to improve their competitiveness, corporations may undertake a reduction in force (RIF), in which substantial numbers of employees are laid off. Federal and state laws require that employees be treated equally regardless of their age. In particular,
Students explain statistical data. The National Survey of Student Engagement conducts surveys to study various aspects of undergraduate education.20 In a recent survey, students were asked if they needed to explain the meaning of numerical or statistical data in a written assignment. Among the
Jury selection. Exercise 8.93 (page 453)concerns Casteneda v. Partida, the case in which the Supreme Court decision used the phrase “two or three standard deviations” as a criterion for statistical significance. There were 181,535 persons eligible for jury duty, of whom 143,611 were Mexican
Construct a table. Construct a 3 3 2 table of counts where there is no apparent association between the row and column variables.
Population estimates. Refer to the previous exercise. One reason to do an audit such as this is to estimate the number of claims that would not be allowed if all claims in a population were examined by experts.We have estimates of the proportions of such claims from each stratum based on our
Health care fraud. Most errors in billing insurance providers for health care services involve honest mistakes by patients, physicians, or others involved in the health care system. However, fraud is a serious problem. The National Health Care Anti-fraud Association estimates that approximately
Find the P-value. For each of the following situations, give the degrees of freedom and an appropriate bound on the P-value (give the exact value if you have software available) for the X2 statistic for testing the null hypothesis of no association between the row and column variables.(a) A 2 3 3
How robust are the conclusions? Refer to Exercise 9.38 on the use of broadband to access the Internet. In that exercise, the percents were read from a graph, and we assumed that the sample size was 2250 for all the surveys. Investigate the robustness of your conclusions in Exercise 9.38 against the
Can dial-up compete? Refer to the previous exercise. The same surveys provided data on access to the Internet using dial-up. Here are the data:Date of survey 2001 2005 2009 2013 Homes with dial-up 41% 28% 7% 3%(a) to (c) Answer the questions given in the previous exercise for these data.(d) Write a
Trends in broadband market. The Pew Internet and American Life Project collects data about the impact of the Internet on various aspects of American life.16 One set of surveys has tracked the use of broadband in homes over a period of several years.17 Here are some data on the percent of homes that
Plot the test statistic and the P-values. Here is a 2 3 2 two-way table of counts. The two categorical variables are U and V, and the possible values for each of these variables are 0 and 1.U V 0 1 0 5 5 1 7 3(a) Find the percent of zeros for V when U 5 0. Do the same for the case where U 5 1. Find
Plot the test statistic and the P-values. Here is a 2 3 2 two-way table of counts. The two categorical variables are U and V, and the possible values for each of these variables are 0 and 1. Notice that the second row depends upon a quantity that we calla. For this exercise, you will examine how
What’s wrong? Explain what is wrong with each of the following:(a) The P-value for a chi-square significance test was 20.05.(b) Expected cell counts are computed under the assumption that the alternative hypothesis is true.(c) A chi-square test was used to test the alternative hypothesis that
Discrimination? Wabash Tech has two professional schools, business and law. Here are two-way tables of applicants to both schools, categorized by gender and admission decision.(Although these data are made up, similar situations occur in reality.)Business Law Admit Deny Admit Deny Male 480 120 Male
Obesity and health. Recent studies have shown that earlier reports underestimated the health risks associated with being overweight. The error was due to overlooking lurking variables. In particular, smoking tends both to reduce weight and to lead to earlier death.Note that you answered part (a) of
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.Age Hired Not hired Younger than
Nonresponse in a survey. A business school conducted a survey of companies in its state. It mailed a questionnaire to 200 small companies, 200 mediumsized companies, and 200 large companies. The rate of nonresponse is important in deciding how reliable survey results are. Here are the data on
Lying to a teacher. The students surveyed in the study described in the previous exercise were also asked about lying to teachers. The following table gives the numbers of students who said that they lied to a teacher at least once during the past year, classified by gender.Gender Lied at least
Trust and honesty in the workplace. One of the questions in a survey of high school students asked about trust and honesty in the workplace.15 Specifically, they were asked whether they thought trust and honesty were essential in business and the workplace. Here are the counts classified by
How does RDC vary across the country? The survey described in the previous exercise also classified community banks by region.14 Here is the 6 3 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(a) Summarize the results
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.12 In its annual survey of
Compare the college presidents with the general public. Refer to Exercise 9.24. Another Pew Internet survey asked the general public about their opinions on the value of online courses. Of the 2142 people who participated in the survey, 621 responded Yes to the question, “Do you believe that
Do the answers depend upon institution type?Refer to the previous exercise. You want to examine whether or not the data provide evidence that the belief that online and classroom courses offer equal educational value varies with the type of institution of the president.(a) Formulate this question
The value of online courses. A Pew Internet survey asked college presidents whether or not they believed that online courses offer an equal educational value when compared with courses taken in the classroom. The presidents were classified by the type of educational institution. Here are the
Compare the brands. Refer to the previous three exercises. Compare the results that you found for the three brands. Be sure to indicate similarities and differences in the way that these brands are viewed.
Brands and sex-typed portraits: H&M. Refer to the previous two exercises. Another brand studied was H&M, one of the brands described as an androgynous brand. Here are the data.Portrait Intensity Female Male High 167 16 Low 27 61 Analyze these data. Write a short summary of your results that
Brands and sex-typed portraits: Audi. Refer to the previous exercise. Another brand studied was Audi, one of the brands described as a highly masculine brand.Here are the data.Portrait Intensity Female Male High 15 217 Low 9 28 Analyze these data. Write a short summary of your results that includes
Brands and sex-typed portraits: Nivea. In a study of brand personality, subjects were shown four portraits: a highly feminine female, a less feminine female, a highly masculine male, and a less masculine male. They were then asked to classify brands to one of these four sex-typed portraits.10 We
Evaluating the price and math anxiety.Subjects in a study were asked to arrange for the rental of two tents, each for two weeks. They were offered two options for the price: (A) $40 per day per tent with a discount of $50 per tent per week, or (B) $40 per day per tent with a discount of 20%. The
To tip or not to tip: women customers. Refer to the previous exercise. Here are the data for the 304 female customers who participated in the study.Shirt color Tip Black White Red Yellow Blue Green Yes 18 16 15 19 16 18 No 33 32 38 31 31 37 Using the questions for the previous exercise as a guide,
To tip or not to tip. A study of tipping behaviors examined the relationship between the color of the shirt worn by the server and whether or not the customer left a tip.8 Here are the data for 418 male customers who participated in the study.Shirt color Tip Black White Red Yellow Blue Green Yes 22
Is the coin fair? In Exercise 5.78 (page 284) we learned that the South African statistician John Kerrich tossed a coin 10,000 times while imprisoned by the Germans during World War II. The coin came up heads 5067 times.(a) Formulate the question about whether or not the coin was fair as a
Distribution of M&M colors. M&M Mars Company has varied the mix of colors for M&M’S Plain Chocolate Candies over the years. These changes in color blends are the result of consumer preference tests. Most recently, the color distribution is reported to be 13% brown, 14% yellow, 13% red, 20%
Compute the chi-square statistic. For each of the other five states, compute the contribution to the chi-square statistic using the method illustrated for Arizona in Example 9.13. Use the expected counts that you calculated in Exercise 9.13 for these calculations. Show that the sum of these values
Calculate the expected counts. Refer to Example 9.12. Find the expected counts for the other five states. Report your results with three places after the decimal as we did for Arizona.
Why is the sum 1567.01? Refer to the table of expected counts in Example 9.12. Explain why the sum of the expected counts is 1567.01 and not 1567.
Social media in the supply chain. Sample proportions from Example 9.1 and the two-way table in Example 9.2 (page 456) report the same information in different ways. We saw in Example 8.9 (pages 442–443) that the z statistic for the hypothesis of equal population proportions is z 5 4.87 with P ,
The P-value. A test for association gives X2 5 15.07 with df 5 8. How would you report the P-value for this problem? Use Table F in the back of the book. Illustrate your solution with a sketch.
Degrees of freedom. A chi-square significance test is performed to examine the association between two categorical variables in a 5 3 3 table. What are the degrees of freedom associated with the test statistic?
An alternative view. Refer to Figure 9.1. Verify that you can obtain the expected count for the highly competitive by adaptive flexibility cell by multiplying the number of highly competitive companies by the percent of companies that use adaptive flexibility. Explain your calculations in words.
Expected counts. We want to calculate the expected count of companies that use adaptive flexibility and are highly competitive. From Figure 9.1(pages 459–460), how many companies use adaptive flexibility? What proportion of all companies are highly competitive? Explain in words why, if there is
A reduction in force. Refer to Exercise 9.2 (page 458) where you summarized data regarding a reduction in force. Make a graphical display of the data.Give reasons for the choices of what information to include in your plot.
Gender and commercial preference. Refer to Exercise 9.1 (page 458)where you created a 2 3 2 table of counts for the commercial preferences of women and men. Make a graphical display of the data. Give reasons for the choices of what information to include in your plot.
Read the output. Look at Figure 9.1. What type of flexibility characterizes the largest percent of companies? What is this percent?
Read the output. Look at Figure 9.1. What percent of companies are highly competitive? What percent of highly competitive companies are classified as parallel for flexibility?
A reduction in force. A human resources manager wants to assess the impact of a planned reduction in force (RIF) on employees over the age of 40.(Various laws state that discrimination against this group is illegal.) The company has 850 employees over 40 and 675 who are 40 years of age or less. The
Gender and commercial preference. In Exercise 8.52 (page 439) we analyzed data from a study where women and men were asked to express a preference for one of two commercials, A or B. For the women, 44 out of 100 women preferred Commercial A. For the men, 79 out of 140 preferred Commercial A.(a) For
Should you bet on Punxsutawney Phil? There is a gathering every year on February 2 at Gobbler’s Knob in Punxsutawney, Pennsylvania. A groundhog, always named Phil, is the center of attraction. If Phil sees his shadow when he emerges from his burrow, tradition says that there will be six more
Where do you get your news? A report produced by the Pew Research Center’s Project for Excellence in Journalism summarized the results of a survey on how people get their news. Of the 2342 people in the survey who own a desktop or laptop, 1639 reported that they get their news from the desktop or
The future of gamification as a marketing tool.Gamification is an interactive design that includes rewards such as points, payments, and gifts. A Pew survey of 1021 technology stakeholders and critics was conducted to predict the future of gamification. A report on the survey said that 42% of those
Statistics and the law. Casteneda v. Partida is an important court case in which statistical methods were used as part of a legal argument. When reviewing this case, the Supreme Court used the phrase “two or three standard deviations” as a criterion for statistical significance. This Supreme
Students change their majors. In a random sample of 890 students from a large public university, it was found that 404 of the students changed majors during their college years.(a) Give a 99% confidence interval for the proportion of students at this university who change majors.(b) Express your
Unequal sample sizes. You are planning a survey in which a 95% confidence interval for the difference between two proportions will present the results. You will use the conservative guessed value 0.5 for p⁄1 and p⁄2 in your planning. You would like the margin of error of the confidence interval
Choosing sample sizes, continued. As the previous exercise noted, using the guessed value 0.5 for both p⁄1 and p⁄2 gives a conservative margin of error in confidence intervals for the difference between two population proportions. You are planning a survey and will calculate a 95% confidence
Choosing sample sizes. For a single proportion, the margin of error of a confidence interval is largest for any given sample size n and confidence level C when p⁄5 0.5. This led us to use p* 5 0.5 for planning purposes. A similar result is true for the two-sample problem. The margin of error of
How much is the improvement? In the setting of the previous exercise, give a 95% confidence interval for the proportion of nonconforming items for the modified process. Then, taking p0 5 0.12 to be the old proportion and p the proportion for the modified process, give a 95% confidence interval for
Does the new process give a better product?Twelve percent of the products produced by an industrial process over the past several months fail to conform to the specifications. The company modifies the process in an attempt to reduce the rate of nonconformities. In a trial run, the modified process
The parrot effect: how to increase your tips, continued. Refer to the previous exercise.(a) The study was performed in a restaurant in The Netherlands. Two waitresses performed the tasks. How do these facts relate to the type of conclusions that can be drawn from this study? Do you think that the
The parrot effect: how to increase your tips.An experiment examined the relationship between tips and server behavior in a restaurant.21 In one condition, the server repeated the customer’s order word for word, while in the other condition, the orders were not repeated. Tips were received in 47
What would the margin of error be? Refer to the previous exercise. Using the sample sizes for the two groups that you found there, what would you expect the 95% margin of error to be for the estimated difference between the two proportions? For your calculations, assume that the sample proportions

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