?Exercises 16.146–16.149 address the question of what should governments do and not do

The term regression was originally used in 1885 bySir Francis Galton in his analysis of the relationship between the heights of children and parents. He formulated the “law of universal regression,” which specifies that “each peculiarity in a man is shared by his kinsmen, but on average in a less degree.” (Evidently, people spoke this way in 1885.) In 1903, two statisticians, K. Pearson and A. Lee, took a random sample of 1,078 father–son pairs to examine Galton’s law (“On the Laws of Inheritance in Man, I. Inheritance of Physical Characteristics,” Biometrika 2:457–462). Their sample regression line was Son’s height = 33.73 + .516 × Father’s height a. Interpret the coefficients. b. What does the regression line tell you about the heights of sons of tall fathers? c. What does the regression line tell you about the heights of sons of short fathers?

Xr16-02 Attempting to analyze the relationship between advertising and sales, the owner of a furniture store recorded the monthly advertising budget ($ thousands) and the sales ($ millions) for a sample of 12 months. The data are listed here. a. Draw a scatter diagram. Does it appear that advertising and sales are linearly related? b. Calculate the least squares line and interpret the coefficients.

Xr16-03 To determine how the number of housing starts is affected by mortgage rates an economist recorded the average mortgage rate and the number of housing starts in a large county for the past 10 years. These data are listed here. a. Determine the regression line. b. What do the coefficients of the regression line tell you about the relationship between mortgage rates and housing starts?

Xr16-04 Critics of television often refer to the detrimental effects that all the violence shown on television has on children. However, there may be another problem. It may be that watching television also reduces the amount of physical exercise, causing weight gains. A sample of 15 10-year-old children was taken. The number of pounds each child was overweight was recorded (a negative number indicates the child is underweight). In addition, the number of hours of television viewing per week was also recorded. These data are listed here. a. Draw the scatter diagram. b. Calculate the sample regression line and describe what the coefficients tell you about the relationship between the two variables.

Xr16-05 To help determine how many beers to stock the concession manager at Yankee Stadium wanted to know how the temperature affected beer sales. Accordingly, she took a sample of 10 games and recorded the number of beers sold and the temperature in the middle of the game. a. Compute the coefficients of the regression line. b. Interpret the coefficients.

The exercises that follow were created to allow you to see how regression analysis is used to solve realistic problems. As a result, most feature a large number of observations. We anticipate that most students will solve these problems using a computer and statistical software. However, for students without these resources, we have computed the means, variances, and covariances that will permit them to complete the calculations manually. (See Appendix A.) Xr16-06* In television’s early years, most commercials were 60 seconds long. Now, however, commercials can be any length. The objective of commercials remains the same—to have as many viewers as possible remember the product in a favorable way and eventually buy it. In an experiment to determine how the length of a commercial is related to people’s memory of it, 60 randomly selected people were asked to watch a 1-hour television program. In the middle of the show, a commercial advertising a brand of toothpaste appeared. Some viewers watched a commercial that lasted for 20 seconds, others watched one that lasted for 24 seconds, 28 seconds, . . . , 60 seconds. The essential content of the commercials was the same. After the show, each person was given a test to measure how much he or she remembered about the product. The commercial times and test scores (on a 30-point test) were recorded. a. Draw a scatter diagram of the data to determine whether a linear model appears to be appropriate. b. Determine the least squares line. c. Interpret the coefficients.

The exercises that follow were created to allow you to see how regression analysis is used to solve realistic problems. As a result, most feature a large number of observations. We anticipate that most students will solve these problems using a computer and statistical software. However, for students without these resources, we have computed the means, variances, and covariances that will permit them to complete the calculations manually. (See Appendix A.) Xr16-07 Florida condominiums are popular winter retreats for many North Americans. In recent years, the prices have steadily increased. A real estate agent wanted to know why prices of similar-sized apartments in the same building vary. A possible answer lies in the floor. It may be that the higher the floor, the greater the sale price of the apartment. He recorded the price (in $1,000s) of 1,200 sq. ft. condominiums in several buildings in the same location that have sold recently and the floor number of the condominium. a. Determine the regression line. b. What do the coefficients tell you about the relationship between the two variables?

The exercises that follow were created to allow you to see how regression analysis is used to solve realistic problems. As a result, most feature a large number of observations. We anticipate that most students will solve these problems using a computer and statistical software. However, for students without these resources, we have computed the means, variances, and covariances that will permit them to complete the calculations manually. (See Appendix A.) Xr16-08 In 2010, the United States conducted a census of the entire country. The census is completed by mail. To help ensure that the questions are understood, a random sample of Americans take the questionnaire before it is sent out. As part of their analysis, they record the amount of time and ages of the sample. Use the least squares method to analyze the relationship between the amount of time taken to complete the questionnaire and the age of the individual answering the questions. What do the coefficients tell you about the relationship between the two variables?

Retaining Workers Human resource managers are responsible for a variety of tasks within organizations. As we pointed out in the introduction in Chapter 1, personnel or human resource managers are involved with recruiting new workers, determining which applicants are most suitable to hire, and helping with various aspects of monitoring the workforce, including absenteeism and worker turnover. For many firms, worker turnover is a costly problem. First, there is the cost of recruiting and attracting qualified workers. The firm must advertise vacant positions and make certain that applicants are judged properly. Second, the cost of training hirees can be high, particularly in technical areas. Third, new employees are often not as productive and efficient as experienced employees. Consequently, it is in the interests of the firm to attract and keep the best workers. Any information that the personnel manager can obtain is likely to be useful. Xr16-09 The human resource manager of a telemarketing firm is concerned about the rapid turnover of the firm’s telemarketers. It appears that many telemarketers do not work very long before quitting. There may be a number of reasons, including relatively low pay, personal unsuitability for the work, and the low probability of advancement. Because of the high cost of hiring and training new workers, the manager decided to examine the factors that influence workers to quit. He reviewed the work history of a random sample of workers who have quit in the last year and recorded the number of weeks on the job before quitting and the age of each worker when originally hired. a. Use regression analysis to describe how the work period and age are related. b. Briefly discuss what the coefficients tell you.

Xr16-10 Besides their known long-term effects, do cigarettes also cause short-term illnesses such as colds? To help answer this question, a sample of smokers was drawn. Each person was asked to report the average number of cigarettes smoked per day and the number of days absent from work due to colds last year. a. Determine the regression line. b. What do the coefficients tell you about the relationship between smoking cigarettes and sick days because of colds?

Xr16-11 Fire damage in the United States amounts to billions of dollars, much of it insured. The time taken to arrive at the fire is critical. This raises the question, Should insurance companies lower premiums if the home to be insured is close to a fire station? To help make a decision, a study was undertaken wherein a number of fires were investigated. The distance to the nearest fire station (in miles) and the percentage of fire damage were recorded. Determine the least squares line and interpret the coefficients.

Xr16-12* A real estate agent specializing in commercial real estate wanted a more precise method of judging the likely selling price (in $1,000s) of apartment buildings. As a first effort, she recorded the price of a number of apartment buildings sold recently and the number of square feet (in 1,000s) in the building. a. Calculate the regression line. b. What do the coefficients tell you about the relationship between price and square footage?

Xr16-13 Millions of boats are registered in the United States. As is the case with automobiles, there is an active used-boat market. Many of the boats purchased require bank financing, and, as a result, it is important for financial institutions to be capable of accurately estimating the price of boats. One variable that affects the price is the number of hours the engine has been run. To determine the effect of the hours on the price, a financial analyst recorded the price (in $1,000s) of a sample of 2007 24-foot Sea Ray cruisers (one of the most popular boats) and the number of hours they had been run. Determine the least squares line and explain what the coefficients tell you.

Xr03-62 (Exercise 3.62 revisited) In an attempt to determine the factors that affect the amount of energy used, 200 households were analyzed. In each, the number of occupants and the amount of electricity used were measured. Determine the regression line and interpret the results.

Xr16-15 An economist for the federal government is attempting to produce a better measure of poverty than is currently in use. To help acquire information, she recorded the annual household income (in $1,000s) and the amount of money spent on food during one week for a random sample of households. Determine the regression line and interpret the coefficients.

Xr16-16* An economist wanted to investigate the relationship between office rents (the dependent variable) and vacancy rates. Accordingly, he took a random sample of monthly office rents and the percentage of vacant office space in 30 different cities. a. Determine the regression line. b. Interpret the coefficients.

Xr03-64 (Exercise 3.64 revisited) One general belief held by observers of the business world is that taller men earn more money than shorter men. In a University of Pittsburgh study, 250 MBA graduates, all about 30 years old, were polled and asked to report their height (in inches) and their annual income (to the nearest $1,000). a. Determine the regression line. b. What do the coefficients tell you?

Testing Job Applicants The recruitment process at many firms involves tests to determine the suitability of candidates. The tests may be written to determine whether the applicant has sufficient knowledge in his or her area of expertise to perform well on the job. There may be oral tests to determine whether the applicant’s personality matches the needs of the job. Manual or technical skills can be tested through a variety of physical tests. The test results contribute to the decision to hire. In some cases, the test result is the only criterion to hire. Consequently, it is vital to ensure that the test is a reliable predictor of job performance. If the tests are poor predictors, they should be discontinued. Statistical analyses allow personnel managers to examine the link between the test results and job performance. Xr16-18 Although a large number of tasks in the computer industry are robotic, many operations require human workers. Some jobs require a great deal of dexterity to properly position components into place. A large North American computer maker routinely tests applicants for these jobs by giving a dexterity test that involves a number of intricate finger and hand movements. The tests are scored on a 100-point scale. Only those who have scored above 70 are hired. To determine whether the tests are valid predictors of job performance, the personnel manager drew a random sample of 45 workers who were hired 2 months ago. He recorded their test scores and the percentage of nondefective computers they produced in the last week. Determine the regression line and interpret the coefficients.

Describe what the required conditions mean in Exercise 16.6. If the conditions are satisfied, what can you say about the distribution of memory test scores?

What are the required conditions for Exercise 16.8? Do these seem reasonable?

Assuming that the required conditions are satisfied in Exercise 16.13, what does this tell you about the distribution of used boat prices?

Use a 5% significance level for all tests of hypotheses. You have been given the following data: x 1 3 4 6 9 8 10 y 1 8 15 33 75 70 95 a. Draw the scatter diagram. Does it appear that x and y are related? If so, how? b. Test to determine whether there is evidence of a linear relationship.

Use a 5% significance level for all tests of hypotheses. Suppose that you have the following data: x 3 5 2 6 1 4 y 25 110 9 250 3 71 a. Draw the scatter diagram. Does it appear that x and y are related? If so, how? b. Test to determine whether there is evidence of a linear relationship.

Use a 5% significance level for all tests of hypotheses. Refer to Exercise 16.2. a. Determine the standard error of estimate. b. Is there evidence of a linear relationship between advertising and sales? c. Estimate \(\beta_{1}\) with 95% confidence. d. Compute the coefficient of determination and interpret this value. e. Briefly summarize what you have learned in parts (a) through (d). Text Transcription: beta_1

Use a 5% significance level for all tests of hypotheses. Calculate the coefficient of determination and conduct a test to determine whether a linear relationship exists between housing starts and mortgage interest in Exercise 16.3.

Use a 5% significance level for all tests of hypotheses. Is there evidence of a linear relationship between the number of hours of television viewing and how overweight the child is in Exercise 16.4?

Use a 5% significance level for all tests of hypotheses. Determine whether there is evidence of a negative linear relationship between temperature and the number of beers sold at Yankee Stadium in Exercise 16.5.

Exercises 16.28–16.44 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Refer to Exercise 16.6. a. What is the standard error of estimate? Interpret its value. b. Describe how well the memory test scores and length of television commercial are linearly related. c. Are the memory test scores and length of commercial linearly related? Test using a 5% significance level. d. Estimate the slope coefficient with 90% confidence.

Exercises 16.28–16.44 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Refer to Exercise 16.7. Apply the three methods of assessing the model to determine how well the linear model fits.

Exercises 16.28–16.44 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Is there enough evidence to infer that age and the amount of time needed to complete the questionnaire are linearly related in Exercise 16.8?

Exercises 16.28–16.44 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Refer to Exercise 16.9. Use two statistics to measure the strength of the linear association. What do these statistics tell you?

Exercises 16.28–16.44 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Is there evidence of a linear relationship between number of cigarettes smoked and number of sick days in Exercise 16.10?

Exercises 16.28–16.44 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Refer to Exercise 16.11. a. Test to determine whether there is evidence of a linear relationship between distance to the nearest fire station and percentage of damage. b. Estimate the slope coefficient with 95% confidence. c. Determine the coefficient of determination. What does this statistic tell you about the relationship?

Exercises 16.28–16.44 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Refer to Exercise 16.12. a. Determine the standard error of estimate, and describe what this statistic tells you about the regression line. b. Can we conclude that the size and price of the apartment building are linearly related? c. Determine the coefficient of determination and discuss what its value tells you about the two variables.

Exercises 16.28–16.44 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Is there enough evidence to infer that as the number of hours of engine use increases, the price decreases in Exercise 16.13?

Exercises 16.28–16.44 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Assess fit of the regression line in Exercise 16.14.

Exercises 16.28–16.44 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Refer to Exercise 16.15. a. Determine the coefficient of determination and describe what it tells you. b. Conduct a test to determine whether there is evidence of a linear relationship between household income and food budget.

Exercises 16.28–16.44 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Can we infer that office rents and vacancy rates are linearly related in Exercise 16.16?

Exercises 16.28–16.44 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Are height and income in Exercise 16.17 positively linearly related?

Exercises 16.28–16.44 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Refer to Exercise 16.18. a. Compute the coefficient of determination and describe what it tells you. b. Can we infer that aptitude test scores and percentages of non defectives are linearly related?

Exercises 16.28–16.44 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Repeat Exercise 16.13 using the t-test of the coefficient of correlation to determine whether there is a negative linear relationship between the number of hours of engine use and the selling price of the used boats.

Exercises 16.28–16.44 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Repeat Exercise 16.6 using the t-test of the coefficient of correlation. Is this result identical to the one you produced in Exercise 16.6?

Exercises 16.28–16.44 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Are food budget and household income in Exercise 16.15 linearly related? Employ the t-test of the coefficient of correlation to answer the question.

Exercises 16.28–16.44 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Refer to Exercise 16.10. Use the t-test of the coefficient of correlation to determine whether there is evidence of a positive linear relationship between number of cigarettes smoked and the number of sick days.

Xr16-45 Do more educated people spend more time watching or news on the Internet? To help answer the question, a statistics practitioner undertook a survey that asked a random sample of people how many years of education they had and the amount of time they spend in a typical day watching or reading news on the Internet? a. Determine whether there is enough evidence to infer that a linear relationship exists between the two variables. b. If there is a linear relationship estimate with 95% confidence the marginal increase in the time watching or reading news on the Internet for each additional year of education.

Xr03-70 Refer to Exercise 3.70 where we looked at the relationship between the grade of a particular coin (Canadian 1925 nickel) and its auction selling price. a. Is there sufficient evidence to conclude that the two variables are linearly related? b. Compute the coefficient of determination and briefly explain what it tells you.

Xr16-47 National news on television features commercials describing pharmaceutical drugs that treat ailments that plague older people. Apparently, the major networks believe that older people tend to watch national newscasts. The marketing manager of a drug company conducted a survey that took a random sample of people older than 60 years of age and recorded their age and the number of days they watched national on television in a typical week. a. Test to determine whether there is enough evidence to conclude that there is a linear relationship between age and number of days watching national news. b. Calculate the coefficient of determination and briefly describe what it tells you.

Xr16-48 In most presidential elections in the United States, the voter turnout is quite low, often in the neighborhood of 50%. Political workers would like to be able to predict who is likely to vote. Thus, it is important to know which variables are related to intention to vote. A political pollster took a random sample of registered voters 3 months before an election. Each respondent was asked the following question, “How definite is your intention to vote or not?” The results were recorded as 1 = Definitely will not vote; 2, 3, 4, 5, 6, 7, 8, 9, 10 = Definitely will vote. Also recorded was the age of the respondent. Is there sufficient evidence to infer that age (AGE) and intention to vote (DEFINITE) are linearly related?

Xr03-71 Refer to Exercise 3.71 wherein we looked at the relationship between temperature and distance that golf balls travel. a. Conduct a regression analysis to determine whether there is enough evidence of a positive linear relationship b. Interpret the slope coefficient. c. Determine the coefficient of determination and describe the information it provides.

Excel users: You must delete rows containing empty cells. Use a 5% significance level for all tests. GSS2014* Does one’s income (RINCOME) affect his or her position on the question, Should the government reduce income differences between rich and poor (EQWLTH: 1 = Government should reduce income differences; 2, 3, 4, 5, 6, 7 = No government action)? Answer the question by testing the relationship between the two variables.

Excel users: You must delete rows containing empty cells. Use a 5% significance level for all tests. GSS2014* Conduct an analysis of the relationship between income (RINCOME) and age (AGE). Estimate with 95% confidence the average increase in income for each additional year of age.

Excel users: You must delete rows containing empty cells. Use a 5% significance level for all tests. GSS2014* Does television appeal to the lowest common denominator? If so, we would expect more educated people to watch less television. Is there sufficient evidence to conclude that more educated people (EDUC) watch less television (TVHOURS)?

Excel users: You must delete rows containing empty cells. Use a 5% significance level for all tests. GSS2014* It seems rather obvious that the longer one works the more one earns. The question is how much more one earns annually for each additional hour of work. Conduct an analysis of annual income (INCOME) and number of hours per week of work (HRS1). a. Test to determine whether there is a positive linear relationship. b. Estimate with 95% confidence the increase in annual income for each additional hour of work per week.

Excel users: You must delete rows containing empty cells. Use a 5% significance level for all tests. GSS2014* Is there a linear relationship between age (AGE) and how many hours per week one works (HRS1)? Conduct a test to answer the question.

Excel users: You must delete rows containing empty cells. Use a 5% significance level for all tests. GSS2014* Television advertisers always want to know who is watching their televised advertising. Do older people watch more television than do younger people? Do the data provide sufficient evidence to infer that there is a positive linear relationship between age (AGE) and television watched (TVHOURS)?

Excel users: You must delete rows containing empty cells. Use a 5% significance level for all tests. GSS2014* How does having more family members earning income (EARNRS) affect total family income (INCOME)? Conduct an analysis to determine whether there is a positive linear relationship between the two variables, and, if so, estimate with 95% confidence the average increase in total family income for each additional of earners.

Excel users: You must delete rows containing empty cells. Use a 5% significance level for all tests. GSS2014* Are more educated (EDUC) people more likely to support government action to reduce income differences across the country differences (EQWLTH: 1 = Government should reduce income differences; 2, 3, 4, 5, 6, 7 = No government action)? Conduct a test to answer the question.

Excel users: You must delete rows containing empty cells. Use a 5% significance level for all tests. GSS2014* Do more educated people tend to marry individuals with similar educational experience? Test to determine whether a married person’s years of education (EDUC) are positively linearly related to his or her spouse’s level of education (SPEDUC).

Excel users: You must delete rows containing empty cells. Use a 5% significance level for all tests. GSS2014* An economic theory suggests that as people become richer they tend to have more children. Analyze the relationship between income (INCOME) and number of children (CHILDS) to test the theory.

Excel users: You must delete rows containing empty cells. Use a 5% significance level for all tests. GSS2014* If one spouse works longer hours does this mean that the other spouse also works longer hours? Test the relationship between HRS1 and SPHRS1 to answer the question.

Excel users: You must delete rows containing empty cells. Use a 5% significance level for all tests. GSS2014* Does staying in university longer mean that postpone having children? If so, we would expect a positive linear relationship between years of education (EDUC) and the age when one has his or her first child (AGEKDBORN). Test to determine whether there is sufficient statistical evidence of this relationship.

Excel users: You must delete rows containing empty cells. Use a 5% significance level for all tests. GSS2014* Refer to Exercise 16.61. We would expect that more educated people would have fewer children. Analyze the relationship between education (EDUC) and number of children (CHILDS).

Excel users: You must delete rows containing empty cells. Use a 5% significance level for all tests. GSS2014* Does the amount of education that one completes influence the amount of education his son or daughter completes? Test the relationship between a person’s education (EDUC) and his or her father’s education (PAEDUC).

Excel users: You must delete rows containing empty cells. Use a 5% significance level for all tests. GSS2014* Refer to Exercise 16.63. Is there sufficient evidence of a positive linear relationship between the years of education (EDUC) and the years of education of one’s mother (MAEDUC)?

Excel users: You must delete rows containing empty cells. Use a 5% significance level for all tests. GSS2014* Are harder-working Americans more likely to urge to want government to reduce income differences? Test to determine whether there is sufficient evidence of a positive linear relationship between hours of work per week (HRS1) and position on whether government should reduce income differences (EQWLTH: 1 = Government should reduce income differences; 2, 3, 4, 5, 6, 7 = No government action).

SCF2013:\MC* We who educate would like to believe that people who have more education are more likely to do well professionally and financially. Fortunately, we have a number of surveys with real data to confirm our beliefs. Analyze the relationship between years of education (EDUC) of the head of middle-class households and income (INCOME). a. Is there enough evidence to conclude that more education is related to more income? b. Estimate the marginal change in income for each additional year of education.

SCF2013:\MC* How does education (EDUC) affect financial success among the heads of middle-class households? Conduct a regression analysis and determine the following. a. Is there evidence of a positive linear relationship between education and total financial assets (FIN)? b. Estimate with 95% confidence the marginal increase in total financial assets for each additional year of education. c. Find the coefficient of determination and describe its value.

SCF2013:\MC* Do you need more years of education to get further into debt? This question can be answered by determining the relationship between number of years of education (EDUC) and household debt (DEBT). Undertake a regression analysis to determine the following. a. Is there sufficient evidence to infer a linear relationship between the two variables? b. Interpret the slope coefficient. c. Calculate the coefficient of determination and describe what this statistic tells you about the linear relationship.

SCF2013:\MC* An increasing number of people are attending colleges and universities. The effect of this trend is that younger people will be more educated than older people. Conduct a test to determine whether age (AGE) and years of education (EDUC) are negatively linearly related among the heads of middle-class households. Report the p-value of the test.

SCF2013:\MC* It seems obvious that for people who take out student loans more years of education lead to larger student debt. a. Conduct a test to determine whether there is a positive linear relationship between years of education (EDUC) and total value of student loans (EDN_INST). b. Estimate the marginal increase in student debt for each additional year of education.

SCF2013:\MC* Are younger middle-class people more likely to eat out at restaurants than older people? Conduct a test to determine whether there is sufficient evidence to infer that age (AGE) and amount spent on food away from home (FOODAWAY) are negatively related?

SCF2013:\MC* Another way to interpret the results of Exercise 16.71 is that older people spend less on all food because their families are smaller (children have left home) or that they eat less expensive meals. If so, then we would expect that age (AGE) and amount spent on food at home FOODHOME) are also negatively related. Conduct a test to determine whether this is true. What is the p-value of the test?

SCF2013:\MC* It takes many years to build up capital gains. Use a statistical analysis to determine whether there is enough evidence to conclude that as one grows older one increases unrealized capital gains (AGE, KGTOTAL). What is the p-value of the test?

SCF2013:\MC* How much more do households have to spend on food when there are children living at home? a. Conduct a test to determine whether there is evidence of a positive linear relationship between total annual amount spent on food at home (FOODHOME) and number of children in the household (KIDS). b. Estimate the amount spent for each additional child.

SCF2013:\MC* Repeat Exercise 16.74 for amount spent on food away from home (FOODAWAY).

Briefly describe the difference between predicting a value of y and estimating the expected value of y.

Will the prediction interval always be wider than the estimation interval for the same value of the independent variable? Briefly explain.

Use the regression equation in Exercise 16.2 to predict with 90% confidence the sales when the advertising budget is $80,000.

Estimate with 90% confidence the mean monthly number of housing starts when the mortgage interest rate is 7% in Exercise 16.3.

Refer to Exercise 16.4. a. Predict with 90% confidence the number of pounds overweight for a child who watches 35 hours of television per week. b. Estimate with 90% confidence the mean number of pounds overweight for children who watch 35 hours of television per week.

Refer to Exercise 16.5. Predict with 90% confidence the number of beers to be sold when the temperature is 75 degrees.

Exercises 16.82–16.94 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Refer to Exercise 16.6. a. Predict with 95% confidence the memory test score of a viewer who watches a 30-second commercial. b. Estimate with 95% confidence the mean memory test score of people who watch 30-second commercials.

Exercises 16.82–16.94 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Refer to Exercise 16.7. a. Predict with 95% confidence the selling price of a 1,200 sq.ft. condominium on the 20 th floor. b. Estimate with 99% confidence the average selling price of a 1,200 sq.ft. condominium on the 15th floor.

Exercises 16.82–16.94 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Refer to Exercise 16.8. Estimate with 90% confidence the mean amount of time for 40-year-old Americans to complete the census.

Exercises 16.82–16.94 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Refer to Exercise 16.9. The company has just hired a 22-year-old telemarketer. Predict with 95% confidence how long he will stay with the company.

Exercises 16.82–16.94 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Refer to Exercise 16.10. Predict with 95% confidence the number of sick days for individuals who smoke on average 40 cigarettes per day.

Exercises 16.82–16.94 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Refer to Exercise 16.11. a. Predict with 95% confidence the percentage loss due to fire for a house that is 8 miles away from the nearest fire station. b. Estimate with 95% confidence the average percentage loss due to fire for houses that are 5 miles away from the nearest fire station.

Exercises 16.82–16.94 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Refer to Exercise 16.12. Estimate with 95% confidence the mean price of 60,000 sq.ft. apartment buildings.

Exercises 16.82–16.94 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Refer to Exercise 16.13. Predict with 99% confidence the price of a 1999 24-ft. Sea Ray cruiser with 400 hours of engine use.

Exercises 16.82–16.94 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Refer to Exercise 16.14. Estimate with 90% confidence the mean electricity consumption for households with four occupants.

Exercises 16.82–16.94 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Refer to Exercise 16.15. Predict the food budget of a family whose household income is $60,000. Use a 90% confidence level.

Exercises 16.82–16.94 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Refer to Exercise 16.16. Predict with 95% confidence the monthly office rent in a city when the vacancy rate is 8%.

Exercises 16.82–16.94 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Refer to Exercise 16.17. a. Estimate with 95% confidence the mean annual income of 6’2” (74 inches)-tall men. b. Suppose that an individual is 5’8” (68 inches). Predict with 95% confidence his annual income.

Exercises 16.82–16.94 require the use of a computer and software. The answers may be calculated manually. See Appendix A for the sample statistics. Refer to Exercise 16.18. Estimate with 95% confidence the mean percentage of defectives for workers who score 80 on the dexterity test.

Xr16-45 Refer to Exercise 16.45. Estimate with 95% confidence the mean time spent watching or reading news on the Internet for the population of people who have completed 12 years of education.

Xr03-70 Refer to Exercise 16.46. Use a prediction interval with 90% confidence to predict the auction selling price of one Canada 1925 nickel with a grade of 40.

Xr16-47 Refer to Exercise 16.47. Estimate with 90% confidence the mean number of days watching the national news on television for the population of 70-year-olds.

Xr16-48 Refer to Exercise 16.48. Predict with 90% confidence how definite is the intention to vote for one 50-year-old.

Xr03-71 Refer to Exercise 16.49. The temperature is 80 degrees. Predict with 95% confidence how far the golfer’s next drive will travel.

Pick any one of the previous five exercises and briefly describe why the intervals are so wide.

For Exercises 16.101 to 16.111, construct a prediction interval and a confidence interval estimate of the expected value of the dependent variable for the given value of the independent variable. Use a 95% confidence level. GSS2014* Refer to Exercise 16.51. Annual income of someone who is 45 years old.

For Exercises 16.101 to 16.111, construct a prediction interval and a confidence interval estimate of the expected value of the dependent variable for the given value of the independent variable. Use a 95% confidence level. GSS2014* Refer to Exercise 16.52. Number of hours of television watching per day for people with 12 years of education.

For Exercises 16.101 to 16.111, construct a prediction interval and a confidence interval estimate of the expected value of the dependent variable for the given value of the independent variable. Use a 95% confidence level. GSS2014* Refer to Exercise 16.53. Income of someone who works 40 hours per week.

For Exercises 16.101 to 16.111, construct a prediction interval and a confidence interval estimate of the expected value of the dependent variable for the given value of the independent variable. Use a 95% confidence level. GSS2014* Refer to Exercise 16.54. Number of hours of t work per week for some who is 60 years old.

For Exercises 16.101 to 16.111, construct a prediction interval and a confidence interval estimate of the expected value of the dependent variable for the given value of the independent variable. Use a 95% confidence level. GSS2014* Refer to Exercise 16.55. Number of hours of television per day of a 65-year-old.

For Exercises 16.101 to 16.111, construct a prediction interval and a confidence interval estimate of the expected value of the dependent variable for the given value of the independent variable. Use a 95% confidence level. GSS2014* Refer to Exercise 16.56. Total family income of a family with four earners.

For Exercises 16.101 to 16.111, construct a prediction interval and a confidence interval estimate of the expected value of the dependent variable for the given value of the independent variable. Use a 95% confidence level. GSS2014* Refer to Exercise 16.59. Income of someone with one child.

For Exercises 16.101 to 16.111, construct a prediction interval and a confidence interval estimate of the expected value of the dependent variable for the given value of the independent variable. Use a 95% confidence level. GSS2014* Refer to Exercise 16.62. Number of children of a person with 11 years of education.

For Exercises 16.101 to 16.111, construct a prediction interval and a confidence interval estimate of the expected value of the dependent variable for the given value of the independent variable. Use a 95% confidence level. GSS2014* Refer to Exercise 16.63. Number of years of education of a person whose father had 15 years of education.

For Exercises 16.101 to 16.111, construct a prediction interval and a confidence interval estimate of the expected value of the dependent variable for the given value of the independent variable. Use a 95% confidence level. GSS2014* Refer to Exercise 16.64. Number of years of education of a person whose mother had 20 years of education.

For Exercises 16.101 to 16.111, construct a prediction interval and a confidence interval estimate of the expected value of the dependent variable for the given value of the independent variable. Use a 95% confidence level. GSS2014* Refer to Exercise 16.65. Position on the issue of whether government should reduce income differences of someone who works 50 hours per week.

Pick any 1 (or more) of the 11 exercises above and briefly describe why the prediction interval is so wide.

You are given the following six points: x ?5 ?2 0 3 4 7 y 15 9 7 6 4 1 a. Determine the regression equation. b. Use the regression equation to determine the predicted values of y. c. Use the predicted and actual values of y to calculate the residuals. d. Compute the standardized residuals. e. Identify possible outliers.

Refer to Exercise 16.2. Calculate the residuals and the predicted values of y.

Calculate the residuals and predicted values of y in Exercise 16.3.

Refer to Exercise 16.4. a. Calculate the residuals. b. Calculate the predicted values of y. c. Plot the residuals (on the vertical axis) and the predicted values of y.

Calculate and plot the residuals and predicted values of y for Exercise 16.5.

The following exercises require the use of a computer and software. Refer to Exercise 16.6. a. Determine the residuals and the standardized residuals. b. Draw the histogram of the residuals. Does it appear that the errors are normally distributed? Explain. c. Identify possible outliers. d. Plot the residuals versus the predicted values of y. Does it appear that heteroscedasticity is a problem? Explain.

The following exercises require the use of a computer and software. Refer to Exercise 16.7. a. Does it appear that the errors are normally distributed? Explain. b. Does it appear that heteroscedasticity is a problem? Explain.

The following exercises require the use of a computer and software. Are the required conditions satisfied in Exercise 16.8?

The following exercises require the use of a computer and software. Refer to Exercise 16.9. a. Determine the residuals and the standardized residuals. b. Draw the histogram of the residuals. Does it appear that the errors are normally distributed? Explain. c. Identify possible outliers. d. Plot the residuals versus the predicted values of y. Does it appear that heteroscedasticity is a problem? Explain.

The following exercises require the use of a computer and software. Refer to Exercise 16.10. Are the required conditions satisfied?

The following exercises require the use of a computer and software. Refer to Exercise 16.11. a. Determine the residuals and the standardized residuals. b. Draw the histogram of the residuals. Does it appear that the errors are normally distributed? Explain. c. Identify possible outliers. d. Plot the residuals versus the predicted values of y. Does it appear that heteroscedasticity is a problem? Explain.

The following exercises require the use of a computer and software. Check the required conditions for Exercise 16.12.

The following exercises require the use of a computer and software. Refer to Exercise 16.13. Are the required conditions satisfied?

The following exercises require the use of a computer and software. Refer to Exercise 16.14. a. Determine the residuals and the standardized residuals. b. Draw the histogram of the residuals. Does it appear that the errors are normally distributed? Explain. c. Identify possible outliers. d. Plot the residuals versus the predicted values of y. Does it appear that heteroscedasticity is a problem? Explain.

The following exercises require the use of a computer and software. Are the required conditions satisfied for Exercise 16.15?

The following exercises require the use of a computer and software. Check to ensure that the required conditions for Exercise 16.16 are satisfied.

The following exercises require the use of a computer and software. Are the required conditions satisfied for Exercise 16.17?

The following exercises require the use of a computer and software. Perform a complete diagnostic analysis for Exercise 16.18 to determine whether the required conditions are satisfied.

The following exercises require the use of a computer and software.The answers to some of the questions may be calculated manually. See Appendix A for the sample statistics. Conduct all tests of hypotheses at the 5% significance level. Xr16-131 The manager of Colonial Furniture has been reviewing weekly advertising expenditures. During the past 6 months, all advertisements for the store have appeared in the local newspaper. The number of ads per week has varied from one to seven. The store’s sales staff has been tracking the number of customers who enter the store each week. The number of ads and the number of customers per week for the past 26 weeks were recorded. a. Determine the sample regression line. b. Interpret the coefficients. c. Can the manager infer that the larger the number of ads, the larger the number of customers? d. Find and interpret the coefficient of determination. e. In your opinion, is it a worthwhile exercise to use the regression equation to predict the number of customers who will enter the store, given that Colonial intends to advertise five times in the newspaper? If so, find a 95% prediction interval. If not, explain why not.

The following exercises require the use of a computer and software.The answers to some of the questions may be calculated manually. See Appendix A for the sample statistics. Conduct all tests of hypotheses at the 5% significance level. Xr16-132 The president of a company that manufactures car seats has been concerned about the number and cost of machine breakdowns. The problem is that the machines are old and becoming quite unreliable. However, the cost of replacing them is quite high, and the president is not certain that the cost can be made up in today’s slow economy. To help make a decision about replacement, he gathered data about last month’s costs for repairs and the ages (in months) of the plant’s 20 welding machines. a. Find the sample regression line. b. Interpret the coefficients. c. Determine the coefficient of determination, and discuss what this statistic tells you. d. Conduct a test to determine whether the age of a machine and its monthly cost of repair are linearly related. e. Is the fit of the simple linear model goodenough to allow the president to predict the monthly repair cost of a welding machine that is 120 months old? If so, find a 95% prediction interval. If not, explain why not.

The following exercises require the use of a computer and software.The answers to some of the questions may be calculated manually. See Appendix A for the sample statistics. Conduct all tests of hypotheses at the 5% significance level. Xr16-133 An agronomist wanted to investigate the factors that determine crop yield. Accordingly, she undertook an experiment wherein a farm was divided into 30 one-acre plots. The amount of fertilizer applied to each plot was varied. Corn was then planted, and the amount of corn harvested at the end of the season was recorded. a. Find the sample regression line, and interpret the coefficients. b. Can the agronomist conclude that there is a linear relationship between the amount of fertilizer and the crop yield? c. Find the coefficient of determination, and interpret its value. d. Does the simple linear model appear to be a useful tool in predicting crop yield from the amount of fertilizer applied? If so, produce a 95% prediction interval of the crop yield when 300 pounds of fertilizer are applied. If not, explain why not.

The following exercises require the use of a computer and software.The answers to some of the questions may be calculated manually. See Appendix A for the sample statistics. Conduct all tests of hypotheses at the 5% significance level. Xr16-134 Every year, the U.S. Federal TradeCommission rates cigarette brands according to their levels of tar and nicotine, substances that are hazardous to smokers’ health. Additionally, the commission includes the amount of carbon monoxide, which is a by-product of burning tobacco that seriously affects the heart. A random sample of 25 brands was taken. a. Are the levels of tar and nicotine linearly related? b. Are the levels of nicotine and carbon monoxide linearly related?

The following exercises require the use of a computer and software.The answers to some of the questions may be calculated manually. See Appendix A for the sample statistics. Conduct all tests of hypotheses at the 5% significance level. Xr16-135 Some critics of television complain that the amount of violence shown on television contributes to violence in our society. Others point out that television also contributes to the high level of obesity among children. We may have to add financial problems to the list. A sociologist theorized that people who watch television frequently are exposed to many commercials, which in turn leads them to buy more, finally resulting in increasing debt. To test this belief, a sample of 430 families was drawn. For each, the total debt and the number of hours the television is turned on per week were recorded. Perform a statistical procedure to help test the theory.

The following exercises require the use of a computer and software.The answers to some of the questions may be calculated manually. See Appendix A for the sample statistics. Conduct all tests of hypotheses at the 5% significance level. Xr16-136 The analysis that the human resources manager performed in Exercise 16.18 indicated that the dexterity test is not a predictor of job performance. However, before discontinuing the test, he decided that the problem is that the statistical analysis was flawed because it examined the relationship between test score and job performance only for those who scored well in the test. (Recall that only those who scored above 70 were hired; applicants who achieved scores below 70 were not hired.) The manager decided to perform another statistical analysis. A sample of 50 job applicants who scored above 50 were hired, and as before the workers’ performance was measured. The test scores and percentages of nondefective computers produced were recorded. On the basis of these data, should the manager discontinue the dexterity tests?

The following exercises require the use of a computer and software.The answers to some of the questions may be calculated manually. See Appendix A for the sample statistics. Conduct all tests of hypotheses at the 5% significance level. Xr16-137 Mutual funds minimize risks by diversifying the investments they make. There are mutual funds that specialize in particular types of investments. For example, the TD Precious Metal Mutual Fund buys shares in gold mining companies. The value of this mutual fund depends on a number of factors related to the companies in which the fund invests as well as on the price of gold. To investigate the relationship between the value of the fund and the price of gold, an MBA student gathered the daily fund price and the daily price of gold for a 28-day period. Can we infer from these data that there is a positive linear relationship between the value of the fund and the price of gold? (The authors are grateful to Jim Wheat for writing this exercise.)

The following exercises require the use of a computer and software.The answers to some of the questions may be calculated manually. See Appendix A for the sample statistics. Conduct all tests of hypotheses at the 5% significance level. Xr03-67 (Exercise 3.67 revisited) A very large contribution to profits for a movie theater is the sale of popcorn, soft drinks, and candy. A movie theater manager speculated that the longer the time between showings of a movie, the greater the sales of concessions. To acquire more information the manager conducted an experiment. For a month he varied the amount of time between movie showings and calculated the sales. Can the manager conclude that when the times between movies increase so do sales?

The following exercises require the use of a computer and software.The answers to some of the questions may be calculated manually. See Appendix A for the sample statistics. Conduct all tests of hypotheses at the 5% significance level. Xr16-139* A computer dating service typically asks for various pieces of information such as height, weight, income, and so on. One such service requested the length of index fingers. The only plausible reason for this request is to act as a proxy on height. Women have often complained that men lie about their heights. If there is a strong relationship between heights and index fingers, the information can be used to “correct” false claims about heights. To test the relationship between the two variables researchers gathered the heights and lengths of index fingers (in centimeters) of 121 students. a. Graph the relationship between the two variables. b. Is there sufficient evidence to infer that height and length of index fingers are linearly related? c. Predict with 95% confidence the height of someone whose index finger is 6.5 cm long. Is this prediction likely to be useful? Explain. (The authors would like to thank Howard Waner for supplying the problem and data.)

The following exercises require the use of a computer and software.The answers to some of the questions may be calculated manually. See Appendix A for the sample statistics. Conduct all tests of hypotheses at the 5% significance level. The following exercises employ data files associated with two previous exercises. Xr12-31* In addition to the data recorded forExercises 12.31 and 13.227, we recorded the grade point average of the students who held down part time jobs. Determine whether there is evidence of a linear relationship between the hours spent at part time jobs and the grade point averages.

The following exercises require the use of a computer and software.The answers to some of the questions may be calculated manually. See Appendix A for the sample statistics. Conduct all tests of hypotheses at the 5% significance level. The following exercises employ data files associated with two previous exercises. Xr13-19* Exercise 13.19 described a survey that asked people between 18 and 34 years of age and 35 to 50 years of age how much time they spent listening to FM radio each day. Also recorded were the amounts spent on music throughout the year. Can we infer that a linear relationship exists between listening times and amounts spent on music?

If we interpret the responses to POLVIEWS (1 = Extremely liberal,2 = Liberal, 3 = Slightly liberal, 4 = Moderate, 5 = Slightly conservative, 6 = Conservative, 7 = Extremely conservative) as an interval variable we can acquire useful information about where people stand on the liberal–conservative spectrum. Discuss what assumption(s) is necessary to make the POLVIEWS spectrum responses an interval variable.

If we interpret the responses to POLVIEWS (1 = Extremely liberal,2 = Liberal, 3 = Slightly liberal, 4 = Moderate, 5 = Slightly conservative, 6 = Conservative, 7 = Extremely conservative) as an interval variable we can acquire useful information about where people stand on the liberal–conservative spectrum. GSS2014* As people grow older do they become more conservative? If so, there should be a positive linear relationship between age (AGE) and political philosophy (POLVIEWS). Use an appropriate statistical procedure to determine whether there is enough evidence to infer that as people grow older they become more conservative. Report the p-value of the test.

If we interpret the responses to POLVIEWS (1 = Extremely liberal,2 = Liberal, 3 = Slightly liberal, 4 = Moderate, 5 = Slightly conservative, 6 = Conservative, 7 = Extremely conservative) as an interval variable we can acquire useful information about where people stand on the liberal–conservative spectrum. GSS2014* Is there sufficient evidence to conclude that as income (RINCOME) rises people grow more conservative (POLVIEWS)? What is the p-value?

If we interpret the responses to POLVIEWS (1 = Extremely liberal,2 = Liberal, 3 = Slightly liberal, 4 = Moderate, 5 = Slightly conservative, 6 = Conservative, 7 = Extremely conservative) as an interval variable we can acquire useful information about where people stand on the liberal–conservative spectrum. GSS2014* Do more educated individuals lean to the liberal end of the political philosophy spectrum? Conduct a test to determine whether there is enough evidence to conclude that as education (EDUC) increases the political philosophy score (POLVIEWS) decreases. Briefly describe what the p-value of the test tells you.

Exercises 16.146–16.149 address the question of what should governments do and not do. For each question determine whether there is enough evidence to infer that individuals on the liberal end of the political philosophy (POLVIEWS) would choose government action and those on the conservative end would choose no government action. Report the p-value of each test and the coefficient of determination. Briefly describe what the p-value of the coefficient of determination tells you about the linear relationship. GSS2014* EQWLTH: Should government reduce income differences between rich and poor? (1 = Government should reduce differences; 2, 3, 4, 5, 6, 7 = No government action.)

Exercises 16.146–16.149 address the question of what should governments do and not do. For each question determine whether there is enough evidence to infer that individuals on the liberal end of the political philosophy (POLVIEWS) would choose government action and those on the conservative end would choose no government action. Report the p-value of each test and the coefficient of determination. Briefly describe what the p-value of the coefficient of determination tells you about the linear relationship. GSS2014* HELPPOOR: Should government improve standard of living of poor people? (1 = Government act; 2, 3, 4, 5 = People should help themselves.)

Exercises 16.146–16.149 address the question of what should governments do and not do. For each question determine whether there is enough evidence to infer that individuals on the liberal end of the political philosophy (POLVIEWS) would choose government action and those on the conservative end would choose no government action. Report the p-value of each test and the coefficient of determination. Briefly describe what the p-value of the coefficient of determination tells you about the linear relationship. GSS2014* HELPNOT: Should government do more or less to solve country’s problems? (1 = Government should do more; 2, 3, 4, 5 = Government does too much.)

Exercises 16.146–16.149 address the question of what should governments do and not do. For each question determine whether there is enough evidence to infer that individuals on the liberal end of the political philosophy (POLVIEWS) would choose government action and those on the conservative end would choose no government action. Report the p-value of each test and the coefficient of determination. Briefly describe what the p-value of the coefficient of determination tells you about the linear relationship. GSS2014* HELPSICK: Is it government’s responsibility to help pay for doctor and hospital bills? (1 = Government should help, 2, 3, 4, 5 = People should help themselves.)

Exercises 16.146–16.149 address the question of what should governments do and not do. For each question determine whether there is enough evidence to infer that individuals on the liberal end of the political philosophy (POLVIEWS) would choose government action and those on the conservative end would choose no government action. Report the p-value of each test and the coefficient of determination. Briefly describe what the p-value of the coefficient of determination tells you about the linear relationship. Summarize what you have discovered about the relationship between political philosophy and preference for government action in Exercises 16.146–16.149. In particular, discuss the coefficients of determination.

XrA16-01 In the last decade, society in general and the judicial system in particular have altered their opinions on the seriousness of drunken driving. In most jurisdictions, driving an automobile with a blood alcohol level in excess of .08 is a felony. Because of a number of factors, it is difficult to provide guidelines for when it is safe for someone who has consumed alcohol to drive a car. In an experiment to examine the relationship between blood alcohol level and the weight of a drinker, 50 men of varying weights were each given three beers to drink, and 1 hour later their blood alcohol levels were measured. If we assume that the two variables are normally distributed, can we conclude that blood alcohol level and weight are related?

XrA16-02 An article in the journal Appetite(December 2003) described an experiment to determine the effect that breakfast meals have on school children. A sample of 29 children was tested on four successive days, having a different breakfast each day. The breakfast meals were 1. Cereal (Cheerios) 2. Cereal (Shreddies) 3. A glucose drink 4. No breakfast The order of breakfast meals was randomly assigned. A computerized test of working memory was conducted prior to breakfast and again 2 hours later. The decrease in scores was recorded. Do these data allow us to infer that there are differences in the decrease depending on the type of breakfast?

Do cell phones cause cancer? This is a multibillion-dollar question. Currently, dozens of lawsuits are pending that claim cell phone use has caused cancer. To help shed light on the issue, several scientific research projects have been undertaken. One such project was conducted by Danish researchers The 13-year study examined 420,000 Danish cell phone users. The scientists determined the number of Danes who would be expected to contract various forms of cancer. The expected number and the actual number of cell phone users who developed each type of cancer are listed here. a. Can we infer from these data that there is a relationship between cell phone use and cancer? b. Discuss the results, including whether the data are observational or experimental. Provide several interpretations of the statistics. In particular, indicate whether you can infer that cell phone use causes cancer.

XrA16-04 A new antiflu vaccine designed to reduce the duration of symptoms has been developed. However, the effect of the drug varies from person to person. To examine the effect of age on the effectiveness of the drug, a sample of 140 flu sufferers was drawn. Each person reported how long the symptoms of the flu persisted and his or her age. Do these data provide sufficient evidence to infer that the older the patient, the longer it takes for the symptoms to disappear?

XrA16-05 Several years ago we heard about the“Mommy Track,” the phenomenon of women being underpaid in the corporate world because of what is seen as their divided loyalties between home and office. There may also be a “Daddy Differential,” which refers to the situation where men whose wives stay at home earn more than men whose wives work. It is argued that the differential occurs because bosses reward their male employees if they come from “traditional families.” Linda Stroh of Loyola University of Chicago studied a random sample of 348 male managers employed by 20 Fortune 500 companies. Each manager reported whether his wife stayed at home to care for their children or worked outside the home, and his annual income. The incomes (in thousands of dollars) were recorded. The incomes of the managers whose wives stay at home are stored in column 1. Column 2 contains the incomes of managers whose wives work outside the home. a. Can we conclude that men whose wives stay at home earn more than men whose wives work outside the home? b. If your answer in part (a) is affirmative, does this establish a case for discrimination? Can you think of another cause-and-effect scenario? Explain.

XrA16-06 There are enormous differences between health-care systems in the United States and Canada. In a study to examine one dimension of these differences, 300 heart attack victims in each country were randomly selected. (Results of the study conducted by Dr. Daniel Mark of Duke University Medical Center, Dr. David Naylor of Sunnybrook Hospital in Toronto, and Dr. Paul Armstrong of the University of Alberta were published in the Toronto Sun, October 27, 1994.) Each patient was asked the following questions regarding the effect of his or her treatment: 1. How many days did it take you to return to work? 2. Do you still have chest pain? (This question was asked 1 month, 6 months, and 12 months after the patients’ heart attacks.) The responses were recorded in the following way: Column 1: Code representing nationality: 1 = U.S.; 2 = Canada Column 2: Responses to question 1 Column 3: Responses to question 2–1 month after heart attack: 2 = yes; 1 = no Column 4: Responses to question 2–6 months after heart attack: 2 = yes; 1 = no Column 5: Responses to question 2–12 months after heart attack: 2 = yes; 1 = no Can we conclude that recovery is faster in the United States?

XrA16-07 Betting on the results of NationalFootball League games is a popular NorthAmerican activity. In some states and provinces, it is legal to do so provided that wagers are made through a government-authorized betting organization. In the province of Ontario, Pro-Line serves that function. Bettors can choose any team on which to wager, and Pro-Line sets the odds, which determine the winning payoffs. It is also possible to bet that in any game a tie will be the result. (A tie is defined as a game in which the winning margin is 3 or fewer points. A win occurs when the winning margin is greater than 3.) To assist bettors, Pro-Line lists the favorite for each game and predicts the point spread between the two teams. To judge how well Pro-Line predicts outcomes, the Creative Statistics Company tracked the results of a recent season. It recorded whether a team was favored by (1) 3 or fewer points, (2) 3.5 to 7 points, (3) 7.5 to 11 points, or (4) 11.5 or more points. It also recorded whether the favored team (1) won, (2) lost, or (3) tied. These data are recorded in columns 1 (Pro-Line’s predictions) and 2 (game results). Can we conclude that Pro-Line’s forecasts are useful for bettors?

XrA16-08 As all baseball fans know, first base is the only base that the base runner may overrun. At both second and third base, the runner may be tagged out if he runs past the base. Consequently, on close plays at second and third base, the runner will slide, enabling him to stop at the base. In recent years, however, several players have chosen to slide headfirst when approaching first base, claiming that this is faster than simply running over the base. In an experiment to test this claim, 25 players on one National League team were recruited. Each player ran to first base with and without sliding, and the times to reach the base were recorded. Can we conclude that sliding is slower than not sliding?

XrA16-09 How does mental outlook affect a person’s health? The answer to this question may allow physicians to care more effectively for their patients. In an experiment to examine the relationship between attitude and physical health, Dr. Daniel Mark, a heart specialist at Duke University, studied 1,719 men and women who had recently undergone a heart catheterization, a procedure that checks for clogged arteries. Patients undergo this procedure when heart disease results in chest pain. All of the patients in the experiment were in about the same condition. In interviews, 14% of the patients doubted that they would recover sufficiently to resume their daily routines. Dr. Mark identified these individuals as pessimists; the others were (by default) optimists. After one year, Dr. Mark recorded how many patients were still alive. The data are stored in columns 1 11 = optimist, 2 = pessimist2 and 2 12 = alive, 1 = dead2 . Do these data allow us to infer that pessimists are less likely to survive than optimists with similar physical ailments?

XrA16-10 Physicians have been recommending more exercise for their patients, particularly those who are overweight. One benefit of regular exercise appears to be a reduction in cholesterol, a substance associated with heart disease. To study the relationship more carefully, a physician took a random sample of 50 patients who do not exercise and measured their cholesterol levels. He then started them on regular exercise programs. After 4 months, he asked each patient how many minutes per week (on average) he or she exercised; he also measured their cholesterol levels. Column 1 = weekly exercise in minutes, column 2 = cholesterol level before exercise program, and column 3 = cholesterol level after exercise program. a. Do these data allow us to infer that the amount of exercise and the reduction in cholesterol levels are related? b. Produce a 95% interval of the amount of cholesterol reduction for someone who exercises for 100 minutes per week. c. Produce a 95% interval for the average cholesterol reduction for people who exercise for 120 minutes per week.

XrA16-11 An economist working for a state university wanted to acquire information about salaries in publicly funded and private colleges and universities. She conducted a survey of 623 public-university faculty members and 592 private-university faculty members asking each to report his or her rank (instructor = 1, assistant professor = 2, associate professor = 3, and professor = 4) and current salary ($1,000). a. Conduct a test to determine whether public colleges and universities and private colleges and universities pay different salaries when all ranks are combined. b. For each rank, determine whether there is enough evidence to infer that the private college and university salaries differ from that of publicly funded colleges and universities. c. If the answers to parts (a) and (b) differ, suggest a cause. d. Conduct a test to determine whether your suggested cause is valid.

XrA16-12 Millions of people suffer from migraine headaches. The costs in work days lost, medication, and treatment are measured in the billions of dollars. A study reported in the Journal of the American Medical Association (2005, 203: 2118–2125) described an experiment that examined whether acupuncture is an effective procedure in treating migraines. A random sample of 302 migraine patients was selected and divided into three groups. Group 1 was treated with acupuncture; group 2 was treated with sham acupuncture (patients believed that they were being treated with acupuncture but were not); and group 3 was not treated at all. The number of headache days per month was recorded for each patient before the treatments began. The number of headache days per month after treatment was also measured. a. Conduct a test to determine whether there are differences in the number of headache days before treatment between the three groups of patients. b. Test to determine whether differences exist after treatment. If so, what are the differences? c. Why was the test in part (a) conducted?

XrA16-13 The battle between customers and car dealerships is often intense. Customers want the lowest price, and dealers want to extract as much money as possible. One source of conflict is the trade-in car. Most dealers will offer a relatively low trade-in in anticipation of negotiating the final package. In an effort to determine how dealers operate, a consumer organization undertook an experiment. Seventy-two individuals were recruited. Each solicited an offer on his or her 5-year-old Toyota Camry. The exact same car was used throughout the experiment. The only variables were the age and gender of the “owner.” The ages were categorized as (1) young, (2) middle, and (3) senior. The cash offers are stored in columns 1 and 2. Column 1 stores the data for female owners, and column 2 contains the offers made to male owners. The first 12 rows in both columns represent the offers made to young people, the next 12 rows represent the middle group, and the last 12 rows represent the elderly owners. a. Can we infer that differences exist between the six groups? b. If differences exist, determine whether the differences are due to gender, age, or some interaction.

XrA16-14 In the presidential elections of 2000 and2004, the vote in the state of Florida was crucial. It is important for the political parties to track party affiliation. Surveys in Broward and Miami-Dade counties were conducted in 1990, 1996, 2000, and 2004. The numbers of Democrats, Republicans, and other voters were recorded for both counties and for all four years. Test each of the following. a. Party affiliation changed over the four surveys in Broward. b. Party affiliation changed over the four surveys in Miami-Dade. c. There were differences between Broward and Miami-Dade in 2004.

XrA16-15 Auto manufacturers are required to test their vehicles for a variety of pollutants in the exhaust. The amount of pollutant varies even among identical vehicles so that several vehicles must be tested. The engineer in charge of testing has collected data (in grams per kilometer driven) on the amounts of two pollutants-carbon monoxide and nitrous oxide-for 50 identical vehicles. The engineer believes the company can save money by testing for only one of the pollutants because the two pollutants are closely linked; that is, if a car is emitting a large amount of carbon monoxide, it will also emit a large amount of nitrous oxide. Do the data support the engineer’s belief?

XrA16-16 In 2003, there were 129,142,000 workers in the United States The general manager for a public transportation company wanted to learn more about how workers commute to work and how long it takes them. A random sample of workers was interviewed. Each reported how he or she typically get to work and how long it takes. Estimate with 95% confidence the total amount of time spent commuting.

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. In 2012, there were 221,963,000 Americans aged 21 years or more. GSS2012* Does the amount of education affect respondents' beliefs about the role of government in the following question? “Should government do more or less to solve country’s problems?” The responses are HELPNOT: 1 = Government should do more; 2, 3, 4, 5 = Government does too much. Is there enough evidence to conclude that there are differences in the responses among the five categories of educational attainment (DEGREE: 0 = Left high school, 1 = High school, 2 = Junior college, 3 = Bachelor’s degree, 4 = Graduate)?

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. In 2012, there were 221,963,000 Americans aged 21 years or more. GSS2012* The survey asked respondents the following question: “Generally speaking, do you think of yourself as a Republican Democrat, Independent, or what?” Estimate the number of Americans who consider themselves Republicans (PARTYID: 5 = Not strong Republican, 6 = Strong Republican).

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. In 2012, there were 221,963,000 Americans aged 21 years or more. GSS2012* Are Republicans more financially successful than either Democrats or Independents? Are there differences in total family income (INCOME) between the three political categories (PARTYID3: 1 = Democrat, 2 = Independent, 3 = Republican)? Conduct a test to answer the question.

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. In 2012, there were 221,963,000 Americans aged 21 years or more. GSS2012* The survey asked respondents the following question, “Should government reduce income differences between rich and poor?” How does the educational attainment affect responses to the question? Use an appropriate technique to determine whether education (EDUC) and support for government action to reduce income differences between rich and poor (EQWLTH: 1 = Government act; 2, 3, 4, 5, 6, 7 = No government action) are linearly related.

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. In 2012, there were 221,963,000 Americans aged 21 years or more. GSS2012* The survey asked respondents the following question, “Should government improve standard of living of poor people?” The responses are HELPPOOR: 1 = Government act; 2, 3, 4, 5 = People should help themselves. Is there enough evidence to infer that there are differences between Democrats, Independents, and Republicans (PARTYID3) in their answers to the question?

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. In 2012, there were 221,963,000 Americans aged 21 years or more. GSS2012* Estimate the number of Americanswho were born outside the United States (BORN: 1 = United States, 2 = Not in the United States).

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. In 2012, there were 221,963,000 Americans aged 21 years or more. GSS2012* The survey asked the following question.A doctor tells a couple that there is one chance in four that their child will have an inherited disease. Does this mean that each of the couple’s children will have the same risk of suffering the illness? (ODDS2: 1 = Yes, 2 = No, 8 = Don’t know, 9 = No answer) Estimate the number of Americans who know the correct answer.

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. In 2012, there were 221,963,000 Americans aged 21 years or more. GSS2012* As societies age the demands on thehealth-care system grow. It becomes more important for individuals to ensure that they are taking steps to become and maintain good health. The survey asked respondents to judge their own health. Is there enough evidence to conclude that majority of the population believes that their health is excellent or good (HEALTH: 1 = Excellent, 2 = Good)?

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. In 2012, there were 221,963,000 Americans aged 21 years or more. GSS2012* The world economy took a hit during the 2007–2009 financial crisis. Have American families recovered? Estimate with 95% confidence to mean family income (INCOME).

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. In 2012, there were 221,963,000 Americans aged 21 years or more. GSS2012* Do individuals who want the government to help people improve their standard of living also believe that government should do more to solve the country’s problems? Conduct a test to determine whether there is a positive linear relationship between these variables (HELPPOOR: Should government improve standard of living of poor people? 1 = Government act; 2, 3, 4, 5 = People should help themselves; HELPNOT: Should government do more or less to solve country’s problems? 1 = Government should do more; 2, 3, 4, 5 = Government does too much).

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. In 2012, there were 221,963,000 Americans aged 21 years or more. GSS2012* Do people who work for themselves(WRKSLF: 1 = Self-employed, 2 = Someone else) make more income (RINCOME) than people who work for someone else? Conduct a test to answer the question.

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. In 2012, there were 221,963,000 Americans aged 21 years or more. GSS2012* Do native-born Americans work harder than Americans born outside the United States (BORN: 1 = United States, 2 = Not in the United States)? Is there enough statistical evidence to conclude that those born in the United States work longer hours (HRS1) than non-natives?

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. In 2012, there were 221,963,000 Americans aged 21 years or more. GSS2012* One measure of the health of the economy is how many workers believe that it is easy to find a job with another employer with approximately the same income and fringe benefits as they have now. Estimate the number of people who believe that it is very easy (JOBFIND: 1 = Very easy).

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. In 2012, there were 221,963,000 Americans aged 21 years or more. GSS2012* Is there enough evidence to conclude that Republicans get the correct answer to the following question correct more often than do Democrats (PARTYID3: 1 = Democrat, 3 = Republican): “The center of the earth is very hot.” (1 = True, 2 = False, 8 = Don’t know, 9 = No answer)? The correct answer: True.

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. In 2012, there were 221,963,000 Americans aged 21 years or more. GSS2012* Do people tend to marry similarly educated individuals? To answer the question, perform a statistical analysis to determine whether there is enough evidence to infer that one’s educational attainment (EDUC) and spouse’s educational attainment (SPEDUC) are positively linearly related.

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. According to the U.S. Census, there were 220,958,853 adults in the United States in 2010. SCF2010:\All* Is there enough evidence to conclude that there are differences between the three working categories (OCCAT2: 1 = Managerial/professional, 2= Technical/sales/services, 3 = Other) in terms of whether the household declared bankruptcy in the previous 5 years (BNKRUPLAST5: 1 = Yes)?

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. According to the U.S. Census, there were 220,958,853 adults in the United States in 2010. SCF2010:\MC* Do middle-class households headed by women (HHSEX: 1 = Male, 2 = Female) spend more money on food at home than their male counterparts (FOODHOME)? Conduct a test to answer the question.

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. According to the U.S. Census, there were 220,958,853 adults in the United States in 2010. SCF2010:\All* Are female and male heads of households equally likely to carry a balance on their credit cards? Conduct a test to determine whether there is a difference between the sexes (HHSEX: 1 = Male, 2 = Female) with respect to carrying a balance on credit cards (NOCCBAL: 0 = Carry a balance, 1 = Do not carry a balance).

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. According to the U.S. Census, there were 220,958,853 adults in the United States in 2010. SCF2010:\All* Females are now attending colleges and universities in greater numbers than men. In the past men were more likely than women to have graduate degrees. Conduct a test to determine whether there is enough evidence to infer that males (HHSEX: 1 = Male, 2 = Female) continue to be more likely than females to have a graduate degree (EDUC 17 = Graduate degree).

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. According to the U.S. Census, there were 220,958,853 adults in the United States in 2010. SCF2010:\All* In 2010, the American economy was still faltering because of the housing meltdown during 2007–2009. One sign of the difficulty is people struggling to pay their living expenses. Estimate the number of people who said that their overall household expenses were unusually high (EXPENSHILO: 1).

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. According to the U.S. Census, there were 220,958,853 adults in the United States in 2010. SCF2010:\All* Is there sufficient evidence to conclude that there are differences in income (INCOME) between the four categories of educational attainment (EDCL: 1 = No high school diploma, 2 = High school diploma, 3 = Some college, 4 = College degree)?

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. According to the U.S. Census, there were 220,958,853 adults in the United States in 2010. SCF2010:\UC The upper class in the 2010 survey had household net worth between $1,345,975 and $7,402,095. Money kept in checking accounts earns no interest but are kept to pay bills. Estimate the mean amount held in checking accounts by households in the upper class (CHECKING).

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. According to the U.S. Census, there were 220,958,853 adults in the United States in 2010. SCF2010:\UC* Do upper-class households get a great deal of the income from interest and dividends? To answer the question, estimate the mean interest and dividend income for upper-class households (INTDIVINC).

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. According to the U.S. Census, there were 220,958,853 adults in the United States in 2010. SCF2010:\All* One way to examine the issue of family structure is to determine the number of households with no spouse or partner. Estimate the proportion of households whose head is neither married nor living with partner (MARRIED: 2).

Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. According to the U.S. Census, there were 220,958,853 adults in the United States in 2010. SCF2010:\MC* Do middle-class heads of households who have a high school diploma only have more assets (ASSET) than those who did not finish high school (EDCL: 1 = No high school diploma, 2 = High school diploma)? Use an appropriate statistical technique to answer the question.