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Introduction To Statistics And Data Analysis 5th Edition Roxy Peck, Chris Olsen, Jay L Devore - Solutions

3. After your class has collected appropriate data, use them to construct a scatterplot. Comment on the interesting features of the plot. Does it look like there is a relationship between age and flexibility?
2. Working as a class, decide on a reasonable way to collect data on the two variables of interest.
1. Age and the measure of flexibility just described will be measured for a group of individuals. Our goal is to determine whether there is a relationship between age and this measure of flexibility.What are two reasons why it would not be a good idea to use just the students in your class as the
9. If the relationship between two variables is nonlinear, it is preferable to model the relationship using a nonlinear model rather than fitting a line to the data. A plot of the residuals from a linear fit is particularly useful in determining whether a nonlinear model would be a more appropriate
8. The value of the correlation coefficient as well as the values for the intercept and slope of the least-squares line can be sensitive to influential observations in the data set, particularly if the sample size is small. Because potentially influential observations are those whose x values are
7. It is not enough to look at just r2 or just se when assessing a linear model. These two measures address different aspects of the fit of the line. In general, we would like to have a small value for se (which indicates that deviations from the line tend to be small) and a large value for r2
6. Remember that the least-squares line may be the “best” line (in that it has a smaller sum of squared deviations than any other line), but that doesn’t necessarily mean that the line will produce good predictions. Be cautious of predictions based on a least-squares line without any
5. Be careful in interpreting the value of the slope and intercept in the least-squares line. In particular, in many instances interpreting the intercept as the value of y that would be predicted when x 5 0 is equivalent to extrapolating way beyond the range of the x values in the data set, and
4. Beware of extrapolation. It is dangerous to assume that a linear model fit to data is valid over a wider range of x values. Using the least-squares line to make predictions outside the range of x values in the data set often leads to poor predictions.
3. The least-squares line for predicting y from x is not the same line as the least-squares line for predicting x from y. The least-squares line is, by definition, the line that has the smallest possible sum of squared deviations of points from the line in the y direction(it minimizes os y
2. A correlation coefficient near 0 does not necessarily imply that there is no relationship between two variables. Before such an interpretation can be given, it is important to examine a scatterplot of the data carefully. Although it may be true that the variables are unrelated, there may in fact
1. Correlation does not imply causation. A common media blunder is to infer a causeand-effect relationship between two variables simply because there is a strong correlation between them. Don’t fall into this trap! A strong correlation implies only that the two variables tend to vary together in
5.50 Determining the age of an animal can sometimes be a difficult task. One method of estimating the age of harp seals is based on the width of the pulp canal in the seal’s canine teeth. To investigate the relationship between age and the width of the pulp canal, researchers recorded age and
5.49 The paper “Population Pressure and Agricultural Intensity” (Annals of the Association of American Geographers [1977]: 384–396) reported a positive relationship between population density and agricultural intensity. The following data consist of measures of population density (x) and
5.48 The article “Organ Transplant Demand Rises Five Times as Fast as Existing Supply” (San Luis Obispo Tribune, February 23, 2001) included a graph that showed the number of people waiting for organ transplants each year from 1990 to 1999. The following data are approximate values and were
5.47 A study, described in the paper “Prediction of Defibrillation Success from a Single Defibrillation Threshold Measurement” (Circulation [1988]:1144 –1149) investigated the relationship between defibrillation success and the energy of the defibrillation shock (expressed as a multiple of
5.46 Food intake of grazing animals is limited by the rate grass can be chewed and swallowed, as well as the rate at which food can be digested. The authors of the paper “What Constrains Daily Intake in Thomson’s Gazelles?” (Ecology [1999]: 2338–2347) observed the grazing activity of
5.45 The paper “Aspects of Food Finding by Wintering Bald Eagles” (The Auk [1983]: 477– 484) examined the relationship between the time that eagles spend aloft searching for food (indicated by the percentage of eagles soaring) and relative food availability. The accompanying data were taken
5.44 The following data on x 5 frying time (in seconds)and y 5 moisture content (%) appeared in the paper“Thermal and Physical Properties of Tortilla Chips as a Function of Frying Time” (Journal of Food Processing and Preservation [1995]: 175 –189):x 5 10 15 20 25 30 45 60 y 16.3 9.7 8.1 4.2
5.43 With a bit of algebra, we can show that SSResid 5 s1 2 r2d os y 2 yd2 from which it follows that se 5În 2 1 n 2 2Ï1 2 r2 sy Unless n is quite small, (n 2 1)/(n 2 2) < 1, so se < Ï1 2 r2 sya. For what value of r is se as large as sy? What is the least-squares line in this case?b. For what
5.41 A study was carried out to investigate the relationship between the hardness of molded plastic (y, in Brinell units) and the amount of time elapsed since the plastic was molded (x, in hours). Summary quantities include n 5 15, SSResid 5 1235.470, and SSTo 5 25,321.368. Calculate and interpret
5.40 ● The article referenced in the previous exercise also gave data on the percentage of operating costs covered by park revenues for the 2007–2008 fiscal year.Number of Employees, x Percent of Operating Cost Covered by Park Revenues, y 95 37 95 19 102 32 69 80 67 17 77 34 81 36 116 32 51 38
5.39 ● The article “California State Parks Closure List Due Soon” (The Sacramento Bee, August 30, 2009) gave the following data on y 5 number of employees in fiscal year 2007–2008 and x 5 total size of parks (in acres)for the 20 state park districts in California:Number of Employees, y
5.38 ● The paper “Accelerated Telomere Shortening in Response to Life Stress” (Proceedings of the National Academy of Sciences [2004]: 17312–17315) described a study that examined whether stress accelerates aging at a cellular level. The accompanying data on a measure of perceived stress
5.36 ● Cost-to-charge ratio (the percentage of the amount billed that represents the actual cost) for inpatient and outpatient services at 11 Oregon hospitals is shown in the following table (Oregon Department of Health Services, 2002). A scatterplot of the data is also shown.Cost-to-Charge Ratio
5.35 ● The paper “Effects of Age and Gender on Physical Performance” (Age [2007]: 77–85) describes a study of the relationship between age and 1-hour swimming performance. Data on age and swim distance for over 10,000 men participating in a national long-distance 1-hour swimming competition
5.34 ● The relationship between x 5 total number of salmon in a creek and y 5 percentage of salmon killed by bears that were transported away from the stream prior to the bear eating the salmon was examined in the paper “Transportation of Pacific Salmon Carcasses from Streams to Riparian
5.33 Some types of algae have the potential to cause damage to river ecosystems. The accompanying data on algae colony density (y) and rock surface area (x)for nine rivers is a subset of data that appeared in a scatterplot in a paper in the journal Aquatic Ecology(2010: 33–40).x 50 55 50 79 44 37
5.32 ● Northern flying squirrels eat lichen and fungi, which makes for a relatively low quality diet. The authors of the paper “Nutritional Value and Diet Preference of Arboreal Lichens and Hypogeous Fungi for Small Mammals in the Rocky Mountains” (Canadian Journal of Zoology [2008]:
5.31 ● The paper referenced in the previous exercise also gave the 6-minute walk distances for 248 girls age 3 to 18 years. The median 6-minute walk times for girls for the five age groups were 492.4 578.3 655.8 657.6 660.9a. With x 5 representative age and y 5 median distance walked in 6
5.30 ● The data in the accompanying table is from the paper “Six-Minute Walk Test in Children and Adolescents” (The Journal of Pediatrics [2007]: 395–399).Two hundred and eighty boys completed a test that measures the distance that the subject can walk on a flat, hard surface in 6 minutes.
5.28 ● The accompanying data resulted from an experiment in which weld diameter x and shear strength y (in pounds) were determined for five different spot welds on steel. A scatterplot shows a strong linear pattern. With osx 2 xd2 5 1000 and osx 2 xds y 2 yd 5 8577, the least-squares line is
5.27 Explain why the slope b of the least-squares line always has the same sign (positive or negative) as the sample correlation coefficient r.
5.25 Explain why it can be dangerous to use the leastsquares line to obtain predictions for x values that are substantially larger or smaller than those contained in the sample.
5.24 ● The following data on sale price, size, and landto-building ratio for 10 large industrial properties appeared in the paper “Using Multiple Regression Analysis in Real Estate Appraisal” (Appraisal Journal [2002]: 424–430):Property Sale Price (millions of dollars)Size (thousands of sq.
5.21 Studies have shown that people who suffer sudden cardiac arrest have a better chance of survival if a defibrillator shock is administered very soon after cardiac arrest. How is survival rate related to the time between when cardiac arrest occurs and when the defibrillator shock is delivered?
5.20 Use the least-squares line from Exercise 5.19 to predict the J.D. Powers Quality Score for Hawaiian Airlines and Northwest Airlines.
5.19 The article “No-Can-Do Attitudes Irk Fliers” (USA Today, September 15, 2010) included the accompanying data on airline quality score and a ranking based on the number of passenger complaints per 100,000 passengers boarded. In the complaint ranking, a rank of 1 is best, corresponding to
5.18 The relationship between hospital patient-to-nurse ratio and various characteristics of job satisfaction and patient care has been the focus of a number of research studies. Suppose x 5 patient-to-nurse ratio is the independent variable. For each of the following potential dependent variables,
5.17 A sample of 548 ethnically diverse students from Massachusetts were followed over a 19-month period from 1995 and 1997 in a study of the relationship between TV viewing and eating habits (Pediatrics[2003]: 1321–1326). For each additional hour of television viewed per day, the number of fruit
5.16 ● The authors of the paper “Evaluating Existing Movement Hypotheses in Linear Systems Using Larval Stream Salamanders” (Canadian Journal of Zoology [2009]:292–298) investigated whether water temperature was related to how far a salamander would swim and whether it would swim upstream
5.15 The authors of the paper “Statistical Methods for Assessing Agreement Between Two Methods of Clinical Measurement” (International Journal of Nursing Studies[2010]: 931–936) compared two different instruments for measuring a person’s ability to breathe out air.(This measurement is
5.14 Two scatterplots are shown below. Explain why it makes sense to use the least-squares regression line to summarize the relationship between x and y for one of these data sets but not the other. (Hint: See Example 5.5.)Scatterplot 1:30 40 50 60 70 80 90 100 110 30 40 50 60 70 80 90 100 yx 110
5.12 An auction house released a list of 25 recently sold paintings. Eight artists were represented in these sales. The sale price of each painting also appears on the list. Would the correlation coefficient be an appropriate way to summarize the relationship between artist (x) and sale price (y)?
5.11 It may seem odd, but one of the ways biologists can tell how old a lobster is involves measuring the concentration of a pigment called neurolipofuscin in the eyestalk of a lobster. (We are not making this up!) The authors of the paper “Neurolipofuscin is a Measure of Age in Panulirus argus,
5.10 ● ▼ The accompanying data were read from graphs that appeared in the article “Bush Timber Proposal Runs Counter to the Record” (San Luis Obispo Tribune, September 22, 2002). The variables shown are the number of acres burned in forest fires in the western United States and timber
5.9 ● Data from the U.S. Federal Reserve Board (Household Debt Service Burden, 2002) on the percentage of disposable personal income required to meet consumer loan payments and mortgage payments for selected years are shown in the following table:Consumer Debt Household Debt Consumer Debt
5.7 The authors of the paper “Flat-footedness is Not a Disadvantage for Athletic Performance in Children Aged 11 to 15 Years” (Pediatrics [2009]: e386–e392) studied the relationship between y 5 arch height and scores on a number of different motor ability tests for 218 children.They reported
5.6 ● The accompanying data are x 5 cost (cents per serving) and y 5 fiber content (grams per serving)for 18 high-fiber cereals rated by Consumer Reports(www.consumerreports.org/health).Cost per Serving Fiber per Serving 33 7 46 10 49 10 62 7 41 8 19 7 77 12 71 12 30 8 Cost per Serving Fiber per
5.1 For each of the scatterplots shown, answer the following questions:a. Does there appear to be a relationship between x and y?b. If so, does the relationship appear to be linear?c. If so, would you describe the linear relationship as positive or negative?a. Construct a scatterplot of y 5
●● use the least-squares regression line to make predictions.
●● find the equation of the least-squares regression line and interpret the slope and intercept in context.
●● compute and interpret the value of the correlation coefficient.
●● informally describe the form, direction, and strength of a linear relationship based on a scatterplot.
●● the role of a residual plot in assessing whether a line is an appropriate way to describe the relationship between two numerical variables.Students will be able to:
●● why it is important to consider both the standard deviation about the regression line and the value of r2 when assessing the usefulness of the least-squares regression line.
●● why it is risky to use the least-squares line to make predictions outside the range of the data.
●● the meaning of least-squares in the context of fitting a regression line.
●● how a line is used to describe the relationship between two numerical variables.
●● the difference between a statistical relationship and a causal relationship (the difference between correlation and causation).
●● that the relationship between two numerical variables can be described in terms of form, strength, and direction.
4.72 Age at diagnosis for each of 20 patients under treatment for meningitis was given in the paper“Penicillin in the Treatment of Meningitis” (Journal of the American Medical Association [1984]: 1870–1874). The ages (in years) were as follows:18 18 25 19 23 20 69 18 21 18 20 18 18 20 18 19
4.71 The Los Angeles Times (July 17, 1995) reported that in a sample of 364 lawsuits in which punitive damages were awarded, the sample median damage award was$50,000, and the sample mean was $775,000. What does this suggest about the distribution of values in the sample?
4.70 ● The accompanying data on milk volume (in grams per day) were taken from the paper “Smoking During Pregnancy and Lactation and Its Effects on Breast Milk Volume” (American Journal of Clinical Nutrition [1991]:1011–1016):Smoking 621 793 593 545 753 655 mothers 895 767 714 598 693
4.69 ● The article “Comparing the Costs of Major Hotel Franchises” (Real Estate Review [1992]: 46–51) gave the following data on franchise cost as a percentage of total room revenue for chains of three different types:Budget 2.7 2.8 3.8 3.8 4.0 4.1 5.5 5.9 6.7 7.0 7.2 7.2 7.5 7.5 7.7 7.9
4.68 ● The article “Can We Really Walk Straight?” (American Journal of Physical Anthropology [1992]: 19–27) reported on an experiment in which each of 20 healthy men was asked to walk as straight as possible to a target 60 m away at normal speed. Consider the following data on cadence
4.67 ● The amount of aluminum contamination (in parts per million) in plastic was determined for a sample of 26 plastic specimens, resulting in the following data(“The Log Normal Distribution for Modeling Quality Data When the Mean Is Near Zero,” Journal of Quality Technology[1990]:
4.66 The paper cited in Exercise 4.65 also reported values of single-leg power for a low workload. The sample mean for n 5 13 observations was x 5 119.8(actually 119.7692), and the 14th observation, somewhat of an outlier, was 159. What is the value of x for the entire sample?
4.65 ● The paper “The Pedaling Technique of Elite Endurance Cyclists” (International Journal of Sport Biomechanics[1991]: 29–53) reported the following data on single-leg power at a high workload:244 191 160 187 180 176 174 205 211 183 211 180 194 200a. Calculate and interpret the sample
4.64 ● The risk of developing iron deﬁciency is especially high during pregnancy. Detecting such a deﬁciency is complicated by the fact that some methods for determining iron status can be affected by the state of pregnancy itself. Consider the following data on transferrin receptor
4.63 ● The percentage of juice lost after thawing for 19 different strawberry varieties appeared in the article “Evaluation of Strawberry Cultivars with Different Degrees of Resistance to Red Scale” (Fruit Varieties Journal [1991]: 12–17):46 51 44 50 33 46 60 41 55 46 53 53 42 44 50 54 46
4.60 ● Although bats are not known for their eyesight, they are able to locate prey (mainly insects) by emitting high-pitched sounds and listening for echoes. A paper appearing in Animal Behaviour (“The Echolocation of Flying Insects by Bats” [1960]: 141–154)gave the following distances (in
4.58 ● A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (in seconds) to complete the escape(“Oxygen Consumption and Ventilation During Escape from an Offshore Platform,” Ergonomics [1997]: 281–292):389 356 359 363 375
4.56 ● The technical report “Ozone Season Emissions by State” (U.S. Environmental Protection Agency, 2002) gave the following nitrous oxide emissions (in thousands of tons) for the 48 states in the continental U.S. states:76 22 40 7 30 5 6 136 72 33 0 89 136 39 92 40 13 27 1 63 33 60 27 16 63
4.55 Research by the Food and Drug Administration(FDA) shows that acrylamide (a possible cancercausing substance) forms in high-carbohydrate foods cooked at high temperatures and that acrylamide levels can vary widely even within the same brand of food (Associated Press, December 6, 2002). FDA
reported the standard deviation?Based on respondent estimates, users spent an average of 629 minutes (about 10.5 hours) per week using their cell phone on or off line for any reason.
4.54 The paper “Portable Social Groups: Willingness to Communicate, Interpersonal Communication Gratifications, and Cell Phone Use among Young Adults” (International Journal of Mobile Communications [2007]: 139–156) describes a study of young adult cell phone use patterns.a. Comment on the
4.53 The authors of the paper “Delayed Time to Defibrillation after In-Hospital Cardiac Arrest” (New England Journal of Medicine [2008]: 9–16) described a study of how survival is related to the length of time it takes from the time of a heart attack to the administration of defibrillation
4.52 The accompanying table gives the mean and standard deviation of reaction times (in seconds) for each of two different stimuli:Stimulus 1Stimulus 2Mean 6.0 3.6 Standard deviation 1.2 0.8 If your reaction time is 4.2 seconds for the ﬁrst stimulus and 1.8 seconds for the second stimulus, to
4.51 ● The following data values are 2009 per capita expenditures on public libraries for each of the 50 U.S. states and the District of Columbia (from www.statemaster.com):16.84 16.17 11.74 11.11 8.65 7.69 7.48 7.03 6.20 6.20 5.95 5.72 5.61 5.47 5.43 5.33 4.84 4.63 4.59 4.58 3.92 3.81 3.75 3.74
4.50 The average reading speed of students completing a speed-reading course is 450 words per minute(wpm). If the standard deviation is 70 wpm, ﬁnd the z score associated with each of the following reading speeds.a. 320 wpmc. 420 wpmb. 475 wpmd. 610 wpm
4.48 Suppose that your statistics professor returned yourﬁrst midterm exam with only a z score written on it.She also told you that a histogram of the scores was approximately normal. How would you interpret each of the following z scores?a. 2.2d. 1.0b. 0.4e. 0c. 1.8
4.47 An advertisement for the “30-inch Wonder” that appeared in the September 1983 issue of the journal Packaging claimed that the 30-inch Wonder weighs cases and bags up to 110 pounds and provides accuracy to within 0.25 ounce. Suppose that a 50-ounce weight was repeatedly weighed on this
4.46 The paper “Modeling and Measurements of Bus Service Reliability” (Transportation Research [1978]:253–256) studied various aspects of bus service and presented data on travel times (in minutes) from several different routes. The accompanying frequency distribution is for bus travel times
4.45 The report “Who Borrows Most? Bachelor’s Degree Recipients with High Levels of Student Debt” (www.collgeboard.com/trends) reported the following percentiles for amount of student debt for those graduating with a bachelor’s degree in 2010:10th percentile 5 $0 25th percentile 5 $0 50th
4.44 Suppose that your younger sister is applying for entrance to college and has taken the SAT. She scored at the 83rd percentile on the verbal section of the test and at the 94th percentile on the math section of the test. Because you have been studying statistics, she asks you for an
4.43 A student took two national aptitude tests. The national average and standard deviation were 475 and 100, respectively, for the ﬁrst test and 30 and 8, respectively, for the second test. The student scored 625 on the ﬁrst test and 45 on the second test. Use z scores to determine on which
4.41 Mobile homes are tightly constructed for energy conservation. This can lead to a buildup of indoor pollutants. The paper “A Survey of Nitrogen Dioxide Levels Inside Mobile Homes” (Journal of the Air Pollution Control Association [1988]: 647–651) discussed various aspects of NO2
4.40 The U.S. Census Bureau (2000 census) reported the following relative frequency distribution for travel time to work for a large sample of adults who did not work at home:Travel Time(minutes) Relative Frequency 0 to ,5 .04 5 to ,10 .13 10 to ,15 .16 15 to ,20 .17 20 to ,25 .14 25 to ,30 .05 30
4.39 ▼ In a study investigating the effect of car speed on accident severity, 5000 reports of fatal automobile accidents were examined, and the vehicle speed at impact was recorded for each one. For these 5000 accidents, the average speed was 42 mph and the standard deviation was 15 mph. A
4.38 The average playing time of compact discs in a large collection is 35 minutes, and the standard deviation is 5 minutes.a. What value is 1 standard deviation above the mean? 1 standard deviation below the mean?What values are 2 standard deviations away from the mean? (Hint: See Example 4.14.)b.
4.37 Shown here are the number of auto accidents per year for every 1000 people in each of 40 occupations(Knight Ridder Tribune, June 19, 2004):Occupation Accidents per 1000 Occupation Accidents per 1000 Student 152 Banking, finance 89 Physician 109 Customer service 88 Lawyer 106 Manager 88
4.36 Fiber content (in grams per serving) and sugar content (in grams per serving) for 18 high fiber cereals(www.consumerreports.com) are shown below.Fiber Content 7 10 10 7 8 7 12 12 8 13 10 8 12 7 14 7 8 8 Sugar Content 11 6 14 13 0 18 9 10 19 6 10 17 10 10 0 9 5 11a. Find the median, quartiles,
4.35 The article “Going Wireless” (AARP Bulletin, June 2009)reported the estimated percentage of U.S. households with only wireless phone service (no landline) for the 50 states and the District of Columbia. In the accompanying data table, each state was also classified into one of three
4.34 Data on the gasoline tax per gallon (in cents) as of April 2010 for the 50 U.S. states and the District of Columbia are shown below (AARP Bulletin, June 2010).State Gasoline Tax per Gallon Alabama 20.9 Alaska 8.0 Arizona 19.0 Arkansas 21.8 California 48.6 Colorado 22.0 Connecticut 42.6
4.33 The report “Who Moves? Who Stays Put? Where’s Home?” (Pew Social and Demographic Trends, December 17, 2008) gave the accompanying data for the 50 U.S. states on the percentage of the population that was born in the state and is still living there. The data values have been arranged in
4.32 Based on a large national sample of working adults, the U.S. Census Bureau reports the following information on travel time to work for those who do not work at home:lower quartile 5 7 minutes median 5 18 minutes upper quartile 5 31 minutes Also given was the mean travel time, which was
4.31 The standard deviation alone does not measure relative variation. For example, a standard deviation of $1 would be considered large if it is describing the variability from store to store in the price of an ice cube tray. On the other hand, a standard deviation of$1 would be considered small
4.30 In 1997, a woman sued a computer keyboard manufacturer, charging that her repetitive stress injuries were caused by the keyboard (Genessey v.Digital Equipment Corporation). The jury awarded about $3.5 million for pain and suffering, but the court then set aside that award as being unreasonable
4.29 The Ministry of Health and Long-Term Care in Ontario, Canada, publishes information on the time that patients must wait for various medical procedures on its web site (www.health.gov.on.ca). For two cardiac procedures completed in fall of 2005, the following information was provided:Procedure

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