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inferential statistics
Stats Modeling The World AP Edition Grades 9-12 3rd Edition David E. Bock, Paul F. Velleman, Richard D. De Veaux - Solutions
SAT scores. How strong was the association between student scores on the Math and Verbal sections of the old SAT? Scores on this exam ranged from 200 to 800 and were widely used by college admissions offices. Here are summaries and plots of the scores for a graduating class at Ithaca High School:a)
Fuel economy. A consumer organization has reported test data for 50 car models. We will examine the association between the weight of the car (in thousands of pounds) and the fuel efficiency (in miles per gallon).Shown are the scatterplot, summary statistics, and regression analysis:
Used cars 2007, again. Based on the analysis of used car prices you did for Exercise 14, create a 95% confidence interval for the slope of the regression line and explain what your interval means in context.
Marriage age 2003, again. Based on the analysis of marriage ages since 1975 given in Exercise 13, give a 95%confidence interval for the rate at which the age gap is closing. Clearly explain what your confidence interval means.
Marriage age 2003. The scatterplot suggests a decrease in the difference in ages at first marriage for men and women since 1975. We want to examine the regression to see if this decrease is significant.
Cholesterol, finis. Based on the regression output seen in Exercise 8, create a 95% confidence interval for the slope of the regression line and interpret your interval in the proper context.
Last dog. Based on the regression output seen in Exercise 7, create a 95% confidence interval for the slope of the regression line and interpret your interval in the proper context.
More cholesterol. Look again at Exercise 8 s regression output for age and cholesterol level.a) The output reports s = 46.16. Explain what that means in this context.b) What s the value of the standard error of the slope of the regression line?c) Explain what that means in this context.
Second frank. Look again at Exercise 7 s regression output for the calorie and sodium content of hot dogs.a) The output reports s = 59.66. Explain what that means in this context.b) What s the value of the standard error of the slope of the regression line?c) Explain what that means in this context.
Cholesterol 2007. Does a person s cholesterol level tend to change with age? Data collected from 1406 adults aged 45 to 62 produced the regression analysis shown. Assuming that the data satisfy the conditions for inference, examine the association between age and cholesterol level.Dependent
Hot dogs. Healthy eating probably doesn t include hot dogs, but if you are going to have one, you d probably hope it s low in both calories and sodium. In its July 2007 issue, Consumer Reports listed the number of calories and sodium content (in milligrams) for 13 brands of all-beef hot dogs it
Second home. Exercise 4 shows computer output examining the association between the sizes of houses and their sale prices.a) Check the assumptions and conditions for inference.b) Find a 95% confidence interval for the slope and interpret it.
Movie budgets: the sequel. Exercise 3 shows computer output examining the association between the length of a movie and its cost.a) Check the assumptions and conditions for inference.b) Find a 95% confidence interval for the slope and interpret it.
House prices. How does the price of a house depend on its size? Data from Saratoga, New York, on 1064 randomly selected houses that had been sold include data on price ($1000 s) and size (1000 s ft2), producing the following graphs and computer output:
Movie budgets. How does the cost of a movie depend on its length? Data on the cost (millions of dollars) and the running time (minutes) for major release films of 2005 are summarized in these plots and computer output:
Drug use. The European School Study Project on Alcohol and Other Drugs, published in 1995, investigated the use of marijuana and other drugs. Data from 11 countries are summarized in the following scatterplot and regression analysis. They show the association between the percentage of a country s
Hurricane predictions. In Chapter 7 we looked at data from the National Oceanic and Atmospheric Administration about their success in predicting hurricane tracks. Here is a scatterplot of the error (in nautical miles) for predicting hurricane locations 72 hours in the future vs. the year in which
Ranking universities, redux. In Exercise 47 you read about the world s top universities, as ranked by the Institute of Higher Education. The table shows the geographical distribution of these universities by groups of 100.(Not all groups have exactly 100 because of ties in the rankings.) Do these
Ranking universities. In 2004 the Institute of Higher Education at Shanghai s Jiao Tong University evaluated the world s universities. Among their criteria were the size of the institution, the number of Nobel Prizes and Fields Medals won by faculty and alumni, and the faculty s research output.
Education by age. Use the survey results in the table to investigate differences in education level attained among different age groups in the United States.
Race and education, part 2. Consider only the people who have graduated from high school from Exercise 43.Do these data suggest there are significant differences in opportunities for black and Hispanic Americans who have completed high school to pursue college or advanced degrees?
Pregnancies. Most pregnancies result in live births, but some end in miscarriages or stillbirths. A June 2001 National Vital Statistics Report examined those outcomes in the United States during 1997, broken down by the age of the mother. The table shows counts consistent with that report. Is there
Race and education. Data from the U.S. Census Bureau show levels of education attained by age 30 for a sample of U.S. residents.*2 Do these data highlight significant differences in education levels attained by these groups?
Survival on the Titanic, one more time. In Exercise 40 you could have checked for a difference in the chances of survival for men and women using two-proportion z procedures.a) Find the z value for this approach.b) Show that the square of your calculated value of z is the value of you calculated in
Steering revisited. You could have checked the data in Exercise 39 for evidence of racial steering using twoproportion z procedures.a) Find the z value for this approach, and show that when you square your z-value, you get the value of you calculated in Exercise 39.b) Show that the resulting
Titanic, redux. Newspaper headlines at the time, and traditional wisdom in the succeeding decades, have held that women and children escaped the Titanic in greater proportions than men. Here s a table with the relevant data. Do you think that survival was independent of whether the person was male
Racial steering. A subtle form of racial discrimination in housing is racial steering. Racial steering occurs when real estate agents show prospective buyers only homes in neighborhoods already dominated by that family s race. This violates the Fair Housing Act of 1968. According to an article in
Eating in front of the TV, II. In Exercise 37 we saw a survey of people who were asked if they agreed with the statement I like to nibble while reading or watching TV.Does a person s culture tend to influence the response?On the next page we have random samples from each of the five countries that
Eating in front of the TV. Roper Reports asked a random sample of people in 30 countries whether they agreed with the statement I like to nibble while reading or watching TV. Allowable responses were Agree completely , Agree somewhat , Neither disagree nor agree , Disagree somewhat , Disagree
Full moon, next phase. In Exercise 34 you found that the expected cell counts failed to satisfy the conditions for inference.a) Find a sensible way to combine some cells that will make the expected counts acceptable.b) Test a hypothesis about the full moon and state your conclusion.
Grades again. In some situations where the expected cell counts are too small, as in the case of the grades given
Full moon. Some people believe that a full moon elicits unusual behavior in people. The table shows the number of arrests made in a small town during weeks of six full moons and six other randomly selected weeks in the same year. We wonder if there is evidence of a difference in the types of
Grades. Two different professors teach an introductory Statistics course. The table shows the distribution of final grades they reported. We wonder whether one of these professors is an easier gradera) Will you test goodness-of-fit, homogeneity, or independence?b) Write appropriate null
Working parents. In July 1991 and again in April 2001, the Gallup Poll asked random samples of 1015 adults about their opinions on working parents. The table on the next page summarizes responses to the question Considering the needs of both parents and children, which of the following do you see
Montana revisited. The poll described in Exercise 29 also investigated the respondents party affiliations based on what area of the state they lived in. Test an appropriate hypothesis about this table and state your conclusions.
Fish diet. Medical researchers followed 6272 Swedish men for 30 years to see if there was any association between the amount of fish in their diet and prostate cancer.( Fatty Fish Consumption and Risk of Prostate Cancer, Lancet, June 2001)a) Is this a survey, a retrospective study, a prospective
Montana. A poll conducted by the University of Montana classified respondents by whether they were male or female and political party, as shown in the table. We wonder if there is evidence of an association between being male or female and party affiliation.a) Is this a test of homogeneity or
Cars. A random survey of autos parked in the student lot and the staff lot at a large university classified the brands by country of origin, as seen in the table. Are there differences in the national origins of cars driven by students and staff?
Cranberry juice. It s common folk wisdom that drinking cranberry juice can help prevent urinary tract infections in women. In 2001 the British Medical Journal reported the results of a Finnish study in which three groups of 50 women were monitored for these infections over 6 months. One group drank
Bingeing and politics. Students in a large Statistics class at a university in the Northeast were asked to describe their political position and whether they had engaged in binge drinking (5 drinks at a sitting for a man;4 for a woman)
Birth order and college choice. Students in an Introductory Statistics class at a large university were classified by birth order and by the college they attend.
NYPD and sex discrimination. The table below shows the rank attained by male and female officers in the New York City Police Department (NYPD). Do these data indicate that men and women are equitably represented at all levels of the department
Titanic. Here is a table we first saw in Chapter 3 showing who survived the sinking of the Titanic based on whether they were crew members, or passengers booked in first-, second-, or third-class staterooms:
Does your doctor know? (part 5). In Exercises 14, 16, 18, and 20, we considered data on articles in the NEJM.The original study listed 23 different Statistics methods.(The list read: t-tests, contingency tables, linear regression, . . . .) Why would it not be appropriate to use chisquare methods on
Childbirth, part 5. In Exercises 13, 15, 17, and 19, we ve looked at a study examining epidurals as one factor that might inhibit successful breastfeeding of newborn babies. Suppose a broader study included several additional issues, including whether the mother drank alcohol, whether this was a
Does your doctor know? (part 4). In Exercises 14, 16, and 18, we ve tested a hypothesis about whether the use of statistics in NEJM medical articles has changed over time. The table shows the test s residuals.
Childbirth, part 4. In Exercises 13, 15, and 17, we ve tested a hypothesis about the impact of epidurals on successful breastfeeding. The table shows the test s residuals.
Does your doctor know? (part 3). In Exercises 14 and 16, we ve begun to examine whether the use of statistics in NEJM medical articles has changed over time.a) Calculate the component of chi-square for the 1989/No cell.b) For this test, . What s the P-value?c) State your conclusion.
Childbirth, part 3. In Exercises 13 and 15, we ve begun to examine the possible impact of epidurals on successful breastfeeding.a) Calculate the component of chi-square for the epidural/no breastfeeding cell.b) For this test, . What s the P-value?c) State your conclusion.
Does your doctor know? (part 2). The table in Exercise 14 shows whether NEJM medical articles during various time periods included statistics or not. We re planning to do a chi-square test.a) How many degrees of freedom are there?b) The smallest expected count will be in the 1989/No cell. What is
Childbirth, part 2. In Exercise 13, the table shows results of a study investigating whether aftereffects of epidurals administered during childbirth might interfere with successful breastfeeding. We re planning to do a chisquare test.a) How many degrees of freedom are there?b) The smallest
Does your doctor know? A survey7 of articles from the New England Journal of Medicine (NEJM) classified them according to the principal statistics methods used.The articles recorded were all non-editorial articles appearing during the indicated years. Let s just look at whether these articles used
Childbirth, part 1. There is some concern that if a woman has an epidural to reduce pain during childbirth, the drug can get into the baby s bloodstream, making the baby sleepier and less willing to breastfeed. In December 2006, the International Breastfeeding Journal published results of a study
Lottery numbers. The fairness of the South African lottery was recently challenged by one of the country s political parties. The lottery publishes historical statistics at its Website (http://www.nationallottery.co.za/lotto/statistics.aspx). Here is a table of the number of times each of the 49
Hurricane frequencies. The National Hurricane Center provides data that list the numbers of large (category 3, 4, or 5) hurricanes that have struck the United States, by decade since 1851 (http://www.nhc.noaa.gov/Deadliest_Costliest.shtml). Here are the data:
Pi. Many people know the mathematical constant is approximately 3.14. But that s not exact. To be more precise, here are 20 decimal places:3.14159265358979323846. Still not exact, though. In fact, the actual value is irrational, a decimal that goes on forever without any repeating pattern. But
Fruit flies. Offspring of certain fruit flies may have yellow or ebony bodies and normal wings or short wings.Genetic theory predicts that these traits will appear in the ratio 9:3:3:1 (9 yellow, normal: 3 yellow, short: 3 ebony, normal: 1 ebony, short). A researcher checks 100 such flies and finds
Violence against women 2005. In its study When Men Murder Women, the Violence Policy Center (www.vpc.org)reported that 1857 women were murdered by men in 2005. Of these victims, a weapon could be identified for 1752 of them. Of those for whom a weapon could be identified, 966 were killed by guns,
NYPD and race. Census data for New York City indicate that 29.2% of the under-18 population is white, 28.2% black, 31.5% Latino, 9.1% Asian, and 2% other ethnicities. The New York Civil Liberties Union points out that, of 26,181 police officers, 64.8% are white, 14.5% black, 19.1% Hispanic, and
Mileage. A salesman who is on the road visiting clients thinks that, on average, he drives the same distance each day of the week. He keeps track of his mileage for several weeks and discovers that he averages 122 miles on Mondays, 203 miles on Tuesdays, 176 miles on Wednesdays, 181 miles on
Nuts. A company says its premium mixture of nuts contains 10% Brazil nuts, 20% cashews, 20% almonds, and 10% hazelnuts, and the rest are peanuts. You buy a large can and separate the various kinds of nuts. Upon weighing them, you find there are 112 grams of Brazil nuts, 183 grams of cashews, 207
M&M s. As noted in an earlier chapter, the Masterfoods Company says that until very recently yellow candies made up 20% of its milk chocolate M&M s, red another 20%, and orange, blue, and green 10% each.The rest are brown. On his way home from work the day he was writing these exercises, one of the
Dice. After getting trounced by your little brother in a children s game, you suspect the die he gave you to roll may be unfair. To check, you roll it 60 times, recording the number of times each face appears. Do these results cast doubt on the die s fairness?a) If the die is fair, how many times
Which test again? For each of the following situations, state whether you d use a chi-square goodness-of-fit test, a chi-square test of homogeneity, a chi-square test of independence, or some other statistical test:a) Is the quality of a car affected by what day it was built? A car manufacturer
Which test? For each of the following situations, state whether you d use a chi-square goodness-of-fit test, a chisquare test of homogeneity, a chi-square test of independence, or some other statistical test:a) A brokerage firm wants to see whether the type of account a customer has (Silver, Gold,
Hamsters. How large are hamster litters? Among 47 golden hamster litters recorded, there were an average of 7.72 baby hamsters, with a standard deviation of 2.5 hamsters per litter.a) Create and interpret a 90% confidence interval.b) Would a 98% confidence interval have a larger or smaller margin
Batteries. We work for the Watchdog for the Consumer consumer advocacy group. We ve been asked to look at a battery company that claims its batteries last an average of 100 hours under normal use. There have been several complaints that the batteries don t last that long, so we decide to test them.
And it means? Every statement about a confidence interval contains two parts: the level of confidence and the interval. Suppose that an insurance agent estimating the mean loss claimed by clients after home burglaries created the 95% confidence interval ($1644, $2391).a) What s the margin of error
Color or text? In an experiment, 32 volunteer subjects are briefly shown seven cards, each displaying the name of a color printed in a different color (example: red, blue, and so on). The subject is asked to perform one of two tasks: memorize the order of the words or memorize the order of the
Fritos. As a project for an introductory Statistics course, students checked 6 bags of Fritos marked with a net weight of 35.4 grams. They carefully weighed the contents of each bag, recording the following weights (in grams):35.5, 35.3, 35.1, 36.4, 35.4, 35.5. Is there evidence that the mean
Rainmakers? In an experiment to determine whether seeding clouds with silver iodide increases rainfall, 52 clouds were randomly assigned to be seeded or not. The amount of rain they generated was then measured (in acre-feet). Create a 95% confidence interval for the average amount of additional
Speeding. A newspaper report in August 2002 raised the issue of racial bias in the issuance of speeding tickets.The following facts were noted:16% of drivers registered in New Jersey are black.Of the 324 speeding tickets issued in one month on a 65-mph section of the New Jersey Turnpike, 25% went
Insulin and diet. A study published in the Journal of the American Medical Association examined people to see if they showed any signs of IRS (insulin resistance syndrome) involving major risk factors for Type 2 diabetes and heart disease. Among 102 subjects who consumed dairy products more than 35
Irises. Can measurements of the petal length of flowers be of value when you need to determine the species of a certain flower? Here are the summary statistics from measurements of the petals of two species of irises. (R. A.Fisher, The Use of Multiple Measurements in Axonomic Problems. Annals of
Bread. Clarksburg Bakery is trying to predict how many loaves of bread to bake. In the last 100 days, the bakery has sold between 95 and 140 loaves per day. Here are a histogram and the summary statistics for the number of loaves sold for the last 100 days.
Online testing. The Educational Testing Service is now administering several of its standardized tests online the CLEP and GMAT exams, for example. Since taking a test on a computer is different from taking a test with pencil and paper, one wonders if the scores will be the same.To investigate this
Bipolar kids. The June 2002 American Journal of Psychiatry reported that researchers used medication and psychotherapy to treat children aged 7 to 16 who exhibit bipolar symptoms. After 2 years, symptoms had cleared up in only 26 of the 89 children involved in the study.a) Write a 95% confidence
Teach for America, Part II. The study described in Exercise 22 also looked at scores in mathematics and language. Here are software outputs for the appropriate tests. Explain what they show
Legionnaires disease. In 1974, the Bellevue-Stratford Hotel in Philadelphia was the scene of an outbreak of what later became known as legionnaires disease. The cause of the disease was finally discovered to be bacteria that thrived in the air-conditioning units of the hotel.Owners of the Rip Van
Teach for America. Several programs attempt to address the shortage of qualified teachers by placing uncertified instructors in schools with acute needs often in inner cities. A 1999 2000 study compared students taught by certified teachers to others taught by uncertified teachers in the same
Wall Street. In September of 2000, the Harris Poll organization asked 1002 randomly sampled American adults whether they agreed or disagreed with the following statement:
Meals. A college student is on a meal program. His budget allows him to spend an average of $10 per day for the semester. He keeps track of his daily food expenses for 2 weeks; the data are given in the table. Is there strong evidence that he will overspend his food allowance?Explain.
Newspapers. Who reads the newspaper more, men or women? Eurostat, an agency of the European Union (EU), conducts surveys on several aspects of daily life in EU countries. Recently, the agency asked samples of 1000 respondents in each of 14 European countries whether they
Cesareans. Some people fear that differences in insurance coverage can affect healthcare decisions. A survey of several randomly selected hospitals found that 16.6% of 223 recent births in Vermont involved cesarean deliveries, compared to 18.8% of 186 births in New Hampshire. Is this evidence that
Hearing. Fitting someone for a hearing aid requires assessing the patient s hearing ability. In one method of assessment, the patient listens to a tape of 50 English words. The tape is played at low volume, and the patient is asked to repeat the words. The patient s hearing ability score is the
Recruiting. In September 2002, CNN reported on a method of grad student recruiting by the Haas School of Business at U.C.-Berkeley. The school notifies applicants by formal letter that they have been admitted, and also e-mails the accepted students a link to a Web site that greets them with
Computer use. A Gallup telephone poll of 1240 teens conducted in 2001 found that boys were more likely than girls to play computer games, by a margin of 77% to 65%.Equal numbers of boys and girls were surveyed.a) What kind of sampling design was used?b) Give a 95% confidence interval for the
Smoking. In the depression and heart attack research described in Exercise 13, 32% of the diseased group were smokers, compared with only 23.7% of those free of heart disease.a) Create a 95% confidence interval for the difference in the proportions of smokers in the two groups.b) Is this evidence
Age. In a study of how depression may affect one s ability to survive a heart attack, the researchers reported the ages of the two groups they examined. The mean age of 2397 patients without cardiac disease was 69.8 years, while for the 450 patients with cardiac disease, the mean and standard
Risk. A study of auto safety determined the number of driver deaths per million vehicle sales for the model years 1995 1999, classified by type of vehicle. The data below are for 6 midsize models and 6 SUVs. Wondering if there is evidence that drivers of SUVs are safer, we hope to create a 95%
Feeding fish. In the midwestern United States, a large aquaculture industry raises largemouth bass. Researchers wanted to know whether the fish would grow better if fed a natural diet of fathead minnows or an artificial diet of food pellets. They stocked six ponds with bass fingerlings weighing
Petitions. To get a voter initiative on a state ballot, petitions that contain at least 250,000 valid voter signatures must be filed with the Elections Commission. The board then has 60 days to certify the petitions. A group wanting to create a statewide system of universal health insurance has
Babies. The National Perinatal Statistics Unit of the Sydney Children s Hospital reports that the mean birth weight of all babies born in Australia in 1999 was 3360 grams about 7.41 pounds. A Missouri hospital reports that the average weight of 112 babies born there last year was 7.68 pounds, with
Teen drinking. A study of the health behavior of school-aged children asked a sample of 15-year-olds in several different countries if they had been drunk at least twice.The results are shown in the table, by gender. Give a 95%confidence interval for the difference in the rates for males and
Gehrig. Ever since Lou Gehrig developed amyotrophic lateral sclerosis (ALS), this deadly condition has been commonly known as Lou Gehrig s disease. Some believe that ALS is more likely to strike athletes or the very fit.Columbia University neurologist Lewis P. Rowland recorded personal histories of
Streams. Researchers in the Adirondack Mountains collect data on a random sample of streams each year.One of the variables recorded is the substrate of the streams the type of soil and rock over which they flow.
Pottery. Archaeologists can use the chemical composition of clay found in pottery artifacts to determine whether different sites were populated by the same ancient people. They collected five samples of Romano British pottery from each of two sites in Great Britain the Ashley Rails site and the New
Drugs. In a full-page ad that ran in many U.S. newspapers in August 2002, a Canadian discount pharmacy listed costs of drugs that could be ordered from a Web site in Canada. The table compares prices (in US$) for commonly prescribed drugs.
Women. The U.S. Census Bureau reports that 26% of all U.S. businesses are owned by women. A Colorado consulting firm surveys a random sample of 410 businesses in the Denver area and finds that 115 of them have women owners. Should the firm conclude that its area is unusual? Test an appropriate
Mazes and smells. Can pleasant smells improve learning? Researchers timed 21 subjects as they tried to complete paper-and-pencil mazes. Each subject attempted a maze both with and without the presence of a floral aroma. Subjects were randomized with respect to whether they did the scented trial
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