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The Practice Of Statistics For Business And Economics 3rd Edition David S. Moore, George P. McCabe, Layth C. Alwan, Bruce A. Craig, William M. Duckworth - Solutions
Squared correlation. SAS gives the squared correlation r 2 as “R-Square.” Howcan you obtain r 2 from theANOVAtable?Do this, and verify that your result agrees with R-Square.
The regression standard error. SAS labels the regression standard error s as “Root MSE.” How can you obtain s from the ANOVA table? Do this, and verify that your result agrees with Root MSE.
F versus t. How do the ANOVA F statistic and its Pvalue relate to the t statistic for the slope and its P-value? Identify these results on the output and verify their relationship (up to roundoff error).
Predicting profitability. A company not covered by the Fortune survey has reputation score x = 7. Will a 95% prediction interval for this company’s profitability be wider or narrower than the confidence interval found in the previous exercise? Explain why we should expect this. Then give the 95%
Predicting profitability. An additional calculation shows that the variance of the reputation scores for these 154 firms is s2 x= 0.8101. SAS labels the regression standard error s as “Root MSE.” Starting from these facts, give a 95% confidence interval for the mean profitability (return on
Estimating the slope. Explain clearly what the slope β1 of the population regression line tells us in this setting. Give a 99% confidence interval for this slope.
Significance in two senses.(a) Is there good evidence that reputation helps explain profitability?(State hypotheses, give a test statistic and P-value, and state a conclusion.)(b) What percent of the variation in profitability among these companies is explained by regression on reputation?(c) Use
Estimating the slope. The standard deviation of the S&P 500 returns for these years is 19.99%. From this and yourwork in the previous exercise, find the standard error for the least-squares slope b1. Give a 90% confidence interval for the slope β1 of the population regression line.Corporate
s and r2. What are the values of the regression standard error s and the squared correlation r 2?
The ANOVA table. Complete the analysis of variance table by filling in the “Residual Error” row and the other missing items in the DF, MS, and F columns.
ANOVA by-products.(a) The output gives r 2 = 0.5036. How can you obtain this from the ANOVA table?(b) The output gives the regression standard error as s = 1.8761. How can you obtain this from the ANOVA table?
The ANOVA table. Use the numerical results in the Excel output to verify each of these relationships.(a) The ANOVA equation for sums of squares.(b) How to obtain the total degrees of freedom and the residual degrees of freedom from the number of observations.(c) How to obtain each mean square from
A significant relationship? The output reports two tests of the null hypothesis that regressing on inflation does help to explain the return on T-bills. State the hypotheses carefully, give the two test statistics, show how they are related, and give the common P-value.
Predicting T-bill return. Figure 10.16 (page 554) uses statistical software to predict the return on Treasury bills in a year when the inflation rate is 3.7%. Let’s do this without specialized software. Figure 10.10 contains Excel regression output. Use a calculator or software to find the
T-bills and inflation. Figure 10.10 (page 541) gives the Excel output for regressing the annual return on Treasury bills on the annual rate of inflation. The data appear in Table 10.1 (page 540). Starting with the regression standard error s = 1.8761 from the output and the variance of the
Selling a large house. Among the houses for which we have data in Table 10.6, just four have floor areas of 1800 square feet or more. Give a 90% confidence interval for the mean selling price of houses with floor areas of 1800 square feet or more.
Beer and blood alcohol. Exercise 10.38 (page 550) gives data from measuring the blood alcohol content (BAC) of students 30 minutes after they drank an assigned number of cans of beer. Steve thinks he can drive legally 30 minutes after he drinks 5 beers. The legal limit is BAC = 0.08. Give a 90%
Size and selling price of houses. Table 10.6 (page 549)gives data on the size in square feet of a random sample of houses sold in a Midwest city along with their selling prices. DATADATA DATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA
Two confidence intervals. The data used for Exercise 10.49 include 195 men 30 years old. The mean income of these men is y = $49,880 and the standard deviation of these 195 incomes is sy = $38,250.(a) Use the one-sample t procedure to give a 95% confidence interval for the mean income μy of
T-bills and inflation. Figure 10.16 (page 554) gives part of a regression analysis of the data in Table 10.1 relating the return on Treasury bills to the rate of inflation. The output includes prediction of the T-bill return when the inflation rate is 3.7%.(a) Use the output to give a 90%
Predicting income from age, continued. Use the computer outputs in Figure 10.12 (page 548) and Exercise 10.49 to give a 99% confidence interval for the mean income of all 40-year-old men.
Predict what? The two 95% intervals for the income of 30-year-olds given in Exercise 10.49 are very different. Explain briefly to someone who knows no statistics why the second interval is so much wider than the first. Start by looking at 30-year-olds in Figure 10.11 (page 547).
Predicting income from age. Figures 10.11 and 10.12(pages 547 and 548) analyze data on the age and income of 5712 men between the ages of 25 and 65. Here is Minitab output predicting the income for ages 30, 40, 50, and 60 years:Predicted Values Fit StDev Fit 95.0% CI 95.0% PI 51638 948 (49780,
Is the price right? Refer to Exercise 10.33 (page 549), where the relationship between the size of a home and its selling price is examined.(a) Suppose that you have a client who is thinking about purchasing a home in this area that is 1500 square feet in size. The asking price is $140,000. What
Compare the estimates. Case 20 in Table 10.4 and Table 10.5 corresponds to the same watershed area. For this case the area is 54 km2 and the percent forest is 22%. A predicted index of biotic integrity based on area was computed in Exercise 10.45, while one based on percent forest was computed in
Predicting water quality from the percent of forested area. Refer to Exercise 10.20 (page 547). DATADATA DATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATA DATADATADATADATADATA DATA FILE IBI(a) Find
Predicting water quality from watershed area. Refer to Exercise 10.19 (page 546). DATADATA DATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATA DATADATADATADATADATA DATA FILE IBI(a) Find a 95%
More on assessment value versus sales price. Refer to Exercises 10.13 and 10.14 (pages 544 and 545). Suppose we’re interested in determining whether the population regression line differs from y = x. We’ll look at this three ways. DATADATA DATADATADATA DATADATADATADATADATA DATADATADATADATADATA
More on public university tuition. Refer to Exercise 10.15 (page 545). DATADATA DATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATA DATADATADATADATADATA DATA FILE TUITION(a) Construct a 95%
Predicting the return on Treasury bills. Table 10.1 (page 540) gives data on the rate of inflation and the percent return on Treasury bills for 51 years. Figures 10.9 and 10.10 analyze these data. You think that next year’s inflation rate will be 3.7%.Figure 10.16 displays part of the Minitab
Predicting stress level. In Example 10.8, software predicts the mean stress level of accountants with an LOC of 16 to be ˆy = 2.894.We also see that the standard error of this estimated mean is SEμˆ = 0.0722. These results come from data on 100 accountants.(a) Use these facts to verify by hand
Influence? Your scatterplot in Exercise 10.38 shows one unusual point: Student 3, who drank 9 beers.(a) Does Student 3 have the largest residual from the fitted line?(You can use the scatterplot to see this.) Is this observation extreme in the x direction, so that it may be influential?(b) Do the
Computer memory. The capacity (bits) of the largest DRAM (dynamic random access memory) chips commonly available at retail has increased as follows:17 DATADATA DATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA
Beer and blood alcohol. How well does the number of beers a student drinks predict his or her blood alcohol content(BAC)? Sixteen student volunteers at Ohio State University drank a randomly assigned number of 12-ounce cans of beer. Thirty minutes later, a police officer measured their BAC.Student
Influence? Your scatterplot in Exercise 10.33 shows one house whose selling price is quite high for its size. Rerun the analysis without this outlier. Does this one house influence r 2, the location of the least-squares line, or the t statistic for the slope in a way that would change your
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 10.34 to answer this question with no additional calculations.
Do larger houses have higher prices? We expect that there is a positive correlation between the sizes of houses in the same market and their selling prices. DATADATA DATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA
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 10.7 shows the net new money flowing into stock and bond mutual funds in the years 1985 to 2008, in billions of dollars.15 “Net” means that funds flowing
Size and selling price of houses. Table 10.6 describes a random sample of 30 houses sold in a Midwest city during a recent year.14 We will examine the relationship between size and price. DATADATA DATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA
Is this relationship significant? Refer to the previous exercise. Test the null hypothesis that the correlation between the binge-drinking rate and the average price for a bottle of beer within a two-mile radius of campus is zero.
Correlation between binge drinking and the average price of beer. Arecent study looked at 118 colleges to investigate the association between the binge-drinking rate and the average price for a bottle of beer at establishments within a two-mile radius of campus.13 A correlation of−0.36 was found.
Is the correlation significant? A study reports correlation r = −0.5 based on a sample of size n = 20. Another study reports the same correlation based on a sample of size n = 10. For each, use Table G to test the null hypothesis that the population correlation ρ = 0 against the one-sided
T-bills and inflation. Exercises 10.6 to 10.8 interpret the part of the Excel output in Figure 10.10 (page 541) 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 β0 in the
Stress level for an extreme internal locus of control.The intercept β0 of the population regression line of job stress among accountants on locus of control measures the job stress felt by an accountant who feels his or her fate is completely in his or her own hands. Use the Excel output in Figure
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 the 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 why older men in this population might earn more than younger men. Give some reasons why
An outlier can destroy statistical significance. Consider the data in Table 10.4 and the relationship between IBI andwatershed area. The relationship between these two variables is statistically significant. Demonstrate the potential effect of an outlier on statistical significance by changing the
Using the other explanatory variable. Refer to Exercise 10.20. Using the questions in the previous exercise as a guide, use the correlation to analyze the relationship between IBI and percent of watershed area that was forest.
Using the correlation to describe the results. Refer to Exercise 10.19. Find the correlation and test the null hypothesis that the corresponding population correlation is zero versus the two-sided alternative. Is the correlation a good numerical measure to describe these data? Compare the results
Comparing the analyses. In Exercises 10.19 and 10.20 you used two different explanatory variables to predict IBI. Summarize the two analyses and compare the results. If you had to choose between the two, which one would you prefer? Give reasons for your answer.
Predicting water quality using a different explanatory variable. The researchers who conducted the study described in the previous exercise also recorded the percent of the watershed area that was forest for each of the streams. The data are given in Table 10.5. Analyze these data using the
Predicting water quality. Pollution of water resources is a serious problem that can require substantial efforts to improve.To determine the financial resources required, the extent of the problem needs to be assessed. The index of biotic integrity (IBI)is a measure of thewater quality in streams
Incentive pay, continued. Refer to the previous exercise.DATADATA DATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATA DATADATADATADATADATA DATA FILE LINEBACKERS(a) Now run the simple linear
Incentive pay and job performance. Tying compensation to performance is typically an efficient method of motivating employees. In the National Football League (NFL), incentive bonuses now account for roughly 25% of player compensation.10 Does tying a player’s salary to performance bonuses result
More on public university tuition. Refer to the previous exercise.(a) Construct a 95% confidence interval for the slope. What does this interval tell you about the annual percent increase in tuition between 2000 and 2008?(b) What percent of the variability in 2008 tuition is explained by a linear
Public university tuition: 2000 versus 2008. Table 10.3 shows the in-state undergraduate tuition and required fees for 33 public universities in 2000 and 2008.9 DATADATA DATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA
Assessment value versus sales price, continued. Refer to the previous exercise. DATADATA DATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATA DATADATADATADATADATA DATA FILE HOMESALES(a) Calculate the
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 30 properties recently sold in a midwestern city.8 Both
Two regressions. We have regressed perceived stress level of accountants on their locus of control, with the results appearing in Figures 10.5 and 10.6(pages 534 and 535). Use software to regress locus of control on stress level for the same data.(a) What is the equation of the least-squares line
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 51 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 fallacy
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 β1 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
Is there a relationship? What are the slope b1 of the fitted line and its standard error? Use these numbers to calculate by hand the t statistic for testing the hypothesis that there is no straight-line relationship between inflation rate and T-bill return against the alternative that the return on
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 2003 to 2007:Year: 2003 2004 2005 2006 2007 Spending (billions of dollars): 40.1 43.3 45.8
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) Which parameter in your
Domestic and foreign stock markets. 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 μy = 100.35 − 5.8x and standard deviation σ = 3.2.(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
Predict the level of job stress. In Case 10.1, the third accountant had an LOC of 3 and a stress level of 2.68. Using the least-squares regression equation in Example 10.1, find the predicted stress level and the residual for this individual.
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 3×2 table of data for bank asset size and remote deposit capture offering in Exercise 9.10 (page 513).(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
Computations for exercise and adequate sleep. Refer to the 2 × 2 table of data for exercise and adequate sleep in Exercise 9.12 (page 513).(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 statistic?(d) Sketch
Which model? This exercise concerns the optional material in Section 9.2 on models for two-way tables. Look at Exercises 9.10, 9.12, 9.16, 9.28, and 9.30. For each exercise, state whether you are comparing several populations based on separate samples from each population (the first model for
Jury selection. Exercise 8.107 (page 489) 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
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
Areduction 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
Students explain statistical data. The National Survey of Student Engagement conducts surveys to study various aspects of undergraduate education.27 In a recent survey, students were asked if they needed to explain the meaning of numerical or statistical data in a written assignment. For first-year
Internet references in prominent journals. The World Wide Web has led to an enormous increase in the amount of information that is easily available to anyone with Internet access.References to Internet pages are becoming quite common in the scientific literature. One study examined Internet
Hummingbirds in Santa Lucia. E. jugularis is a type of hummingbird that lives in the forest preserves of the Caribbean island of Santa Lucia. The males and the females of this species have bills that are shaped somewhat differently. Researchers who study these birds thought that the bill shape
Air pollution from a steel mill. One possible effect of air pollution is genetic damage. A study designed to examine this problem exposed one group of mice to air near a steel mill and another group to air in a rural area and compared the numbers of mutations in each group.24 Here are the data for
Student athletes and gambling. A survey of student athletes that asked questions about gambling behavior classified students according to the National Collegiate Athletic Association(NCAA) division.23 For male student athletes, the percent who reported wagering on collegiate sports are given here
Identity theft and college students. A study of identity theft looked at how well consumers protect themselves from this increasingly prevalent crime. The behaviors of 61 college students were compared with the behaviors of 59 nonstudents. One of the questions was “When asked to create a
Intended readership of ads with sexual imagery. The ads in the study described in the previous exercise were also classified according to the age group of the intended readership. Here is a summary of the data:Magazine Readership Age Group Model dress Young adult Mature adult Not sexual (percent)
Sexual imagery in magazine ads. In what ways do advertisers in magazines use sexual imagery to appeal to youth? One study classified each of 1509 full-page or larger ads as “not sexual”or “sexual,” according to the amount and style of the dress of the male or female model in the ad. The ads
Class size and departments. A university classifies its classes as either “small” (fewer than 40 students) or “large.”A dean sees that 62% of Department A’s classes are small, while Department B has only 40% small classes. She wonders if she should cut Department A’s budget and insist
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 4 × 3
Construct a table. Construct a 3×3 table of counts where there is no apparent association between the row and column variables.
What’s wrong? Explain what is wrong with each of the following:(a) A chi-square test was used to test the null hypothesis that there is an association between two categorical variables.(b) The P-value for a chi-square significance test was 1.05.(c) Expected cell counts are computed under the
Other funding for Canadian students in private career colleges? Refer to the previous exercise. Another major source of funding was parents, family, or spouse. The table below gives the survey percents of Canadian private students who relied on these sources classified by field of study:Field of
Government loans for Canadian students in private career colleges. Refer to the previous exercise. The survey also asked about how these college students paid for their education.A major source of funding was government loans. Here are the survey percents of Canadian private students who used
When do Canadian students enter private career colleges? A survey of Canadian students who enrolled in private career colleges was conducted to understand student participation in the private postsecondary educational system.20 In one part of the survey, students were asked about their field of
Class attendance and DFW rates. One study that looked at DFW rates surveyed 719 students who were enrolled in one or more of seven gateway courses in business, mathematics, and science.19 If a student was enrolled in more than one course, then a single course was randomly selected for analysis. In
DFW rates. Colleges and universities want the students that they admit to graduate. Studies indicate that a key issue in retaining students is their performance in so-called gateway courses.17 These are courses that serve as prerequisites for other key courses that are essential for student
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 $68
Switching from dial-up to broadband. A Pew survey asked dial-up users about their interest in switching to broadband.14 Here is the summary given in the report:Date of survey: October February December May 2002 2004 2005 2008 Interested in switch: 38% 40% 39% 36%(a) The percents reported in the
How robust are the conclusions? Refer to Exercise 9.21 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 9.21 against the
What about dial-up? Refer to the previous exercise. The same surveys provided data on access to the Internet using dialup.Here are the data:Date of survey: April 2001 April 2004 March 2007 April 2008 Homes with dial-up: 41% 30% 16% 12%(a) to (c) Answer the questions given in the previous exercise
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