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intro stats

Stats Data And Models 5th Global Edition Richard De Veaux, Paul Velleman, David Bock - Solutions

Sophomore slump? A CEO complains that the winners of his“rookie junior executive of the year” award often turn out to have less impressive performance the following year. He wonders whether the award actually encourages them to slack off.Can you offer a better explanation?
Disk drives 2016 again Recall the data on disk drives we saw in Chapter 6, Exercise 4. Suppose we want to predict Price from Capacity.a) Find the slope estimate, b1.b) What does it mean, in this context?c) Find the intercept, b0.d) What does it mean, in this context? Is it meaningful?e) Write down
Bookstore sales revisited Recall the data we saw in Chapter 6, Exercise 3 for a bookstore. The manager wants to predict Sales from Number of Sales People Working.a) Find the slope estimate, b1.b) What does it mean, in this context?c) Find the intercept, b0.d) What does it mean, in this context? Is
Residual interpretations The newborn grandson of one of the authors was 48 cm long and weighed 3 kg. According to the regression model of Exercise 3, what was his residual? What does that say about him?
Least squares interpretations A least squares regression line was calculated to relate the length (cm) of newborn boys to their weight in kg. The line is weight = -5.36 + 0.1675 length.Explain in words what this model means. Should new parents(who tend to worry) be concerned if their newborn’s
True or false II If false, explain briefly.a) Some of the residuals from a least squares linear model will be positive and some will be negative.b) Least squares means that some of the squares of the residuals are minimized.c) We write yn to denote the predicted values and y to denote the observed
True or false If false, explain briefly.a) We choose the linear model that passes through the most data points on the scatterplot.b) The residuals are the observed y-values minus the y-values predicted by the linear model.c) Least squares means that the square of the largest residual is as small as
Planets (more or less) Is there any pattern to the locations of the planets in a distant solar system? The table shows the average distance of each of the planets from the star.a) Make a scatterplot, and describe the association.(Remember: direction, form, and strength!)b) Why would you not want to
Vehicle weights The department of transportation hoped that they could measure the weights of big trucks without actually stopping the vehicles by using a newly developed “weight-inmotion”scale. To see if the new device was accurate, they conducted a calibration test. They weighed several
Thrills III For the roller coaster data in Exercise 49:a) Explain why in looking for a variable that explains rank, you will be hoping for a negative correlation.b) Do any of the provided variables provide a strong predictor for roller coaster rank?
Thrills II For the roller coaster data in Exercise 49:a) Examine the relationship between Initial Drop and Speed.b) Examine the relationship between Initial Drop and Height.c) What conclusions can you safely draw about the initial drop of a roller coaster? Is Initial Drop strongly correlated with
Thrills 2013 In a poll, a roller-coaster ride called Bizarro dropped to 4th after earning the top steel coaster rank for six straight years. Data on the top 11 steel coasters from this poll are at the bottom of the page. What do these data indicate about the Length of the track and the Duration of
Housing price sampled In a dataset of 1057 New York homes offered for sale, a histogram of the ages looks like this:We drew 1000 samples of 105 homes from this dataset and found the IQR and the range of each sample. Below are histograms of the 1000 IQRs and 1000 ranges. For which of these
Coasters 2015 sampled Return to the data on roller coasters seen in Exercise 23. Here is the distribution of the lengths of the rides of 241 coasters.We drew samples of 60 coasters from the full set of 241. We then repeated this 1000 times. For each sample, we found the mean and median. Here are
Second inning 2016 Perhaps fans are just more interested in teams that win. The displays below are based on American League teams for the 2016 season. (Data in Attendance 2016)a) Do winning teams generally enjoy greater attendance at their home games? Describe the association.b) Is attendance more
Attendance 2016 American League baseball games are played under the designated hitter rule, meaning that pitchers, often weak hitters, do not come to bat. Baseball owners believe that the designated hitter rule means more runs scored, which in turn means higher attendance. Is there evidence that
Burgers again In the previous exercise, you analyzed the association between the amounts of fat and sodium in fast food hamburgers. What about fat and calories? Here are data for the same burgers:a) Analyze the association between fat content and calories using correlation and scatterplots.*b) Find
Burgers Fast food is often considered unhealthy because much of it is high in both fat and sodium. But are the two related? Here are the fat and sodium contents of several brands of burgers.a) Analyze the association between fat content and sodium using correlation and scatterplots.*b) Find
Drug abuse A survey was conducted in the United States and 10 countries of Western Europe to determine the percentage of teenagers who had used marijuana and other drugs. The results are summarized in the following table.a) Create a scatterplot.b) What is the correlation between the percent of
Fuel economy 2016 Here are engine size (displacement, in liters) and gas mileage (estimated combined city and highway) for a random sample of 10 model cars (taken from Fuel economy 2016 and identified in the data with Sample = “Yes”)a) Make a scatterplot for these data.b) Describe the
Interest rates and mortgages 2015 Since 1980, average mortgage interest rates have fluctuated from a low of nearly 3%to a high of over 14%. Is there a relationship between the amount of money people borrow and the interest rate that’s offered? Here is a scatterplot of Mortgage Loan Amount in a
Income and housing Here is a scatterplot of the Housing Cost Index vs. the Median Family Income for 10 regions in a country. The correlation is 0.66.a) Describe the relationship between the Housing Cost Index and the Median Family Income by region.b) If we standardized both variables, what would
Sample survey A polling organization is checking its database to see if the data sources it used sampled the same ZIP codes.The variable Datasource = 1 if the data source is MetroMedia, 2 if the data source is DataQwest, and 3 if it’s RollingPoll. The organization finds that the correlation
Baldness and heart disease Medical researchers followed 1435 middle-aged men for a period of 5 years, measuring the amount of Baldness present (none = 1, little = 2, some = 3, much = 4, extreme = 5) and presence of Heart Disease(No = 0, Yes = 1). They found a correlation of 0.089 between the two
Correlation conclusions II The correlation between Fuel Efficiency (as measured by miles per gallon) and Price of 150 cars at a large dealership is r = -0.34. Explain whether or not each of these possible conclusions is justified:a) The more you pay, the lower the fuel efficiency of your car will
Correlation conclusions I The correlation between Age and Income as measured on 120 people is r = 0.65. Explain whether or not each of these possible conclusions is justified:a) When Age increases, Income increases as well.b) The form of the relationship between Age and Income is straight.c) There
Smartphones and life expectancy A survey of the world’s nations in 2014 shows a strong positive correlation between percentage of the country using smartphones and life expectancy in years at birth.a) Does this mean that smartphones are good for your health?b) What might explain the strong
Height and reading A researcher studies children in elementary school and finds a strong positive linear association between height and reading scores.a) Does this mean that taller children are generally better readers?b) What might explain the strong correlation?
More correlation errors Students in the economics class discussed in Exercise 31 also wrote these conclusions. Explain the mistakes they made.a) “There was a very strong correlation of 1.22 between Life Expectancy and GDP.”b) “The correlation between Literacy Rate and GDP was 0.83.This shows
Correlation errors Your economics instructor assigns your class to investigate factors associated with the gross domestic product (GDP) of nations. Each student examines a different factor (such as Life Expectancy, Literacy Rate, etc.) for a few countries and reports to the class. Apparently, some
More predictions Hurricane Katrina’s hurricane force winds extended 120 miles from its center. Katrina was a big storm, and that affects how we think about the prediction errors.Suppose we add 120 miles to each error to get an idea of how far from the predicted track we might still find damaging
Prediction units The errors in predicting hurricane tracks(examined in this chapter) were given in nautical miles. A statutory mile is 0.86898 nautical mile. Most people living on the Gulf Coast of the United States would prefer to know the prediction errors in statutory miles rather than nautical
Association V A researcher investigating the association between two variables collected some data and was surprised when he calculated the correlation. He had expected to find a fairly strong association, yet the correlation was near 0.Discouraged, he didn’t bother making a scatterplot. Explain
Cold nights Is there an association between time of year and the nighttime temperature in North Dakota? A researcher assigned the numbers 1–365 to the days January 1–December 31 and recorded the temperature at 2:00 A.M. for each. What might you expect the correlation between Day Number and
Traffic headaches A study of traffic delays in 68 cities found the following relationship between Total Delay (in total hours lost) and Mean Highway Speed:Is it appropriate to summarize the strength of association with a correlation? Explain. Total Delay (hr) 750,000 600,000 450,000 300,000 150,000
Streams and hard water In a study of streams in the Adirondack Mountains, the following relationship was found between the water’s pH and its hardness (measured in grains):Is it appropriate to summarize the strength of association with a correlation? Explain. (Data in Streams) 8.0 7.6 7.2 7.2
Antidepressants A study compared the effectiveness of several antidepressants by examining the experiments in which they had passed the FDA requirements. Each of those experiments compared the active drug with a placebo, an inert pill given to some of the subjects. In each experiment, some patients
Coasters 2015 Most roller coasters get their speed by dropping down a steep initial incline, so it makes sense that the height of that drop might be related to the speed of the coaster. Here’s a scatterplot of top Speed and largest Drop for 75 roller coasters around the world.a) Does the
Car thefts The National Insurance Crime Bureau reports that Honda Accords, Honda Civics, and Toyota Camrys are the cars most frequently reported stolen, while Ford Tauruses, Pontiac Vibes, and Buick LeSabres are stolen least often. Is it reasonable to say that there’s a correlation between the
Politics A candidate for office claims that “there is a correlation between television watching and crime.” Criticize this statement on statistical grounds.
Matching II Here are several scatterplots. The calculated correlations are -0.977, -0.021, 0.736, and 0.951. Which is which? (a) (c) + (b)
Matching Here are several scatterplots. The calculated correlations are 0.006, -0.977, -0.487, and 0.777. Which is which? (a) + (b) + + (c) (d) +
Coffee sales Owners of a new coffee shop tracked sales for the first 20 days and displayed the data in a scatterplot (by day).a) Make a histogram of the daily sales since the shop has been in business.b) State one fact that is obvious from the scatterplot, but not from the histogram.c) State one
Firing pottery A ceramics factory can fire eight large batches of pottery a day. Sometimes a few of the pieces break in the process. In order to understand the problem better, the factory records the number of broken pieces in each batch for three days and then creates the scatterplot shown.a) Make
Kentucky Derby 2017 The fastest horse in Kentucky Derby history was Secretariat in 1973. The scatterplot shows speed(in miles per hour) of the winning horses each year.What do you see? In most sporting events, performances have improved and continue to improve, so surely we anticipate a positive
Performance IQ scores vs. brain size. A study examined brain size (measured as pixels counted in a digitized magnetic resonance image [MRI] of a cross section of the brain) and IQ (4 performance scales of the Wechsler IQ test) for college students. The scatterplot shows the Performance IQ scores
Scatterplots II Which of these scatterplots showa) little or no association?b) a negative association?c) a linear association?d) a moderately strong association?e) a very strong association? 3 (4)
Scatterplots Which of these scatterplots showa) little or no association?b) a negative association?c) a linear association?d) a moderately strong association?e) a very strong association? (1) (3) + H (2) (4) H
Association IV Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and
Association III Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and
Dexterity scores Scores on a test of dexterity are recorded by timing a subject who is inverting pegs by picking them up with one hand, manipulating them to turn them over, and then placing them back in a frame. A typical 3-year-old needs about 6.0 seconds to invert a peg, but a 6-year-old takes
Salaries and logs For an analysis of the salaries of your company, you plot the salaries of all employees against the number of years they have worked for the company. You find that plotting the base-10 logarithm of salary makes the plot much straighter.A part-time shipping clerk who has worked at
Blizzards A study finds that during blizzards, online sales are highly associated with the number of snow plows on the road;the more plows, the more online purchases. The director of an association of online merchants suggests that the organization should encourage municipalities to send out more
Bookstore sales again A larger firm is considering acquiring the bookstore of Exercise 3. An analyst for the firm, noting the relationship seen in Exercise 3, suggests that when they acquire the store they should hire more people because that will drive higher sales. Is his conclusion justified?
Correlation facts II If we assume that the conditions for correlation are met, which of the following are true? If false, explain briefly.a) A correlation of 0.02 indicates a strong, positive association.b) Standardizing the variables will make the correlation 0.c) Adding an outlier can
Correlation facts If we assume that the conditions for correlation are met, which of the following are true? If false, explain briefly.a) A correlation of -0.98 indicates a strong, negative association.b) Multiplying every value of x by 2 will double the correlation.c) The units of the correlation
Disk drives 2016 Disk drives have been getting larger.Their capacity is now often given in terabytes (TB), where 1 TB is roughly equal to 1000 gigabytes, or about a trillion bytes. A search of prices for external disk drives found the following data:Capacity (in TB) Price (in $)0.5 64.11 1 85.11 2
Association II Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and
Association Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and
Tomatoes Agricultural scientists are working on developing an improved variety of Roma tomatoes. Marketing research indicates that customers are likely to bypass Romas that weigh less than 70 grams. The current variety of Roma plants produces fruit that averages 74 grams, but 11% of the tomatoes
BMI values The ideal BMI for a female is between 18.5 and 24.9.A year ago, a group of female friends had an average BMI of 25.4, and 54% of them exceeded the ideal maximum BMI of 24.9.a) If a Normal model is appropriate, what was the standard deviation of the BMI values of the females a year ago?b)
Body temperatures Most people think that the “normal”adult body temperature is 98.6F. That figure, based on a 19th-century study, has recently been challenged. In a 1992 article in the Journal of the American Medical Association, researchers reported that a more accurate figure may be
Diastolic blood pressure Suppose the diastolic blood pressure of a group of patients can be described by a Normal model with a mean of 85 mmHg and a standard deviation of 10 mmHg.a) What fraction of patients are expected to have diastolic blood pressure less than 80 mmHg?b) In what diastolic blood
Tires A tire manufacturer believes that the treadlife of its snow tires can be described by a Normal model with a mean of 32,000 miles and standard deviation of 2500 miles.a) If you buy one of these tires, would it be reasonable for you to hope it will last 40,000 miles? Explain.b) Approximately
Cholesterol Assume the cholesterol levels of adult American women can be described by a Normal model with a mean of 188 mg/dL and a standard deviation of 24.a) Draw and label the Normal model.b) What percent of adult women do you expect to have cholesterol levels over 200 mg/dL?c) What percent of
IQ, finis Consider the IQ model N(100, 15) one last time.a) What IQ represents the 15th percentile?b) What IQ represents the 98th percentile?c) What’s the IQR of the IQs?
Cattle, finis Consider the Angus weights model N(1152, 84)one last time.a) What weight represents the 40th percentile?b) What weight represents the 99th percentile?c) What’s the IQR of the weights of these Angus steers?
More IQs In the Normal model N(100, 15) from Exercise 10, what cutoff value boundsa) the highest 5% of all IQs?b) the lowest 30% of the IQs?c) the middle 80% of the IQs?
Park visitors’ heights, part III Based on the model N(1.6,0.4)describing park visitors’ heights from Exercise 29, what are the cutoff values fora) the highest 10% of the heights?b) the lowest 10% of the heights?c) the middle 30% of the heights?
CEO compensation logged and sampled Suppose we take logarithms of the CEO compensations in Exercise 47. The histogram of log Compensation looks like this:with a mean of 1.07 and a standard deviation of 0.26.a) According to the Normal model, what percent of CEOs would you expect to earn more than 2
CEO compensation 2014 sampled The Glassdoor Economic Research Blog published the compensation (in millions of dollars) for the CEOs of large companies. The distribution looks like this:The mean CEO compensation is $14.1M and the standard deviation is $11.32M.a) According to the Normal model, what
Customer database A large philanthropic organization keeps records on the people who have contributed. In addition to keeping records of past giving, the organization buys demographic data on neighborhoods from the U.S. Census Bureau.Eighteen of these variables concern ethnicity. Here are a
Receivers 2015 NFL data from the 2015 football season reported the number of yards gained by each of the league’s 488 receivers:The mean is 274.73 yards, with a standard deviation of 327.32 yards.a) According to the Normal model, what percent of receivers would you expect to gain more yards than
Check the model The mean of the 100 car speeds in Exercise 30 was 23.84 mph, with a standard deviation of 3.56 mph.a) Using a Normal model, what values should border the middle 95% of all car speeds?b) Here are some summary statistics.From your answer in parta, how well does the model do in
Winter Olympics 2018 Fifty-three men completed the men’s alpine downhill at the 2018 winter Olympics in PyeongChang.The gold medal winner finished in 100.25 seconds. Here are the times (in seconds) for all competitors.a) The mean time was 103.883 seconds, with a standard deviation of 2.645
Car speeds 100, the picture For the car speed data in Exercise 30, here are the histogram, boxplot, and Normal probability plot of the 100 readings. Do you think it is appropriate to apply a Normal model here? Explain. # of Cars 20 20 15 10- + 15.0 22.5 30.0 Speed (mph) Speed(mph) 32 28 24- 20 22
Trees, part II Later on, the forester in Exercise 39 shows you a histogram of the tree diameters he used in analyzing the woods that was for sale. Do you think he was justified in using a Normal model? Explain, citing some specific concerns. # of Trees N 4 0.0 4.5 9.0 Diameter (In.) 13.5 18.0
Rivets A company that manufactures rivets believes the shear strength (in pounds) is modeled by N(800, 50).a) Draw and label the Normal model.b) Would it be safe to use these rivets in a situation requiring a shear strength of 750 pounds? Explain.c) About what percent of these rivets would you
Trees A forester measured 27 of the trees in a large woods that is up for sale. He found a mean diameter of 10.4 inches and a standard deviation of 4.7 inches. Suppose that these trees provide an accurate description of the whole forest and that a Normal model applies.a) Draw the Normal model for
Short park visitors In Exercise 29, we suggested the model N(1.6,0.4) for heights of park visitors. What height would be unusual to record for a park visitor? Explain.38. High IQ Exercise 10 proposes modeling IQ scores with N(100, 15). What IQ would you consider to be unusually high?Explain.
Club attendance The management of a club recorded the attendance of people entering the club every Saturday for a whole year. The management reported that the mean attendance was 483 individuals. While the management did not report the standard deviation, which of these values do you think is most
Middle-aged individuals A researcher has told a colleague about a study he is conducting among middle-aged individuals.He has told her the mean and the standard deviation of the ages of the respondents. The colleague remembers that the mean age is 48; however, she cannot recall whether the standard
Caught speeding Suppose police set up radar surveillance on the Stanford street described in Exercise 30. They handed out a large number of tickets to speeders going a mean of 28 mph, with a standard deviation of 2.4 mph, a maximum of 33 mph, and an IQR of 3.2 mph. Local law prescribes fines of
Metal plates, part II Suppose the company in Exercise 31 sold a set of metal plates whose minimum thickness was 4.1 mm, median 4.42 mm, standard deviation 0.098 mm, and IQR 1.34 mm. They sold for €9.95 per mm thickness, while total production cost was €17.56. Find the minimum, median, standard
Car speeds 100 again For the car speed data in Exercise 30, recall that the mean speed recorded was 23.84 mph, with a standard deviation of 3.56 mph. To see how many cars are speeding, John subtracts 20 mph from all speeds.a) What is the mean speed now? What is the new standard deviation?b) His
Metal plates The thickness of a set of metal plates can be described by a Normal model with a mean of 4.3 mm and a standard deviation of 0.12 mm.a) Suppose that the company manufacturing these metal plates decides to increase the thickness of each metal plate by 0.2 mm. What would be the new mean
Car speeds 100 John Beale of Stanford, California, recorded the speeds of cars driving past his house, where the speed limit read 20 mph. The mean of 100 readings was 23.84 mph, with a standard deviation of 3.56 mph. (He actually recorded every car for a two-month period. These are 100
Park visitors’ heights, part II Using N(1.6,0.4), the Normal model for heights of park visitors in Exercise 13, answer the following questions:a) How many standard deviations from the mean would a park visitor with height 1.55 meters be?b) Which would be more unusual, a park visitor’s height
MP3s Two companies market new batteries targeted at owners of personal music players. DuraTunes claims a mean battery life of 11 hours, while RockReady advertises 12 hours.a) Explain why you would also like to know the standard deviations of the battery lifespans before deciding which brand to
Exam performance Two classmates, Pearl and Faye, wanted to compare their performance on the Mathematics and Accounting exams. Pearl scored 81 on the Mathematics exam and 84 on the Accounting exam, while Faye scored 77 and 90 on the Mathematics and Accounting exams, respectively. The scores of the
Combining scores again The first Stat exam had a mean of 80 and a standard deviation of 4 points; the second had a mean of 70 and a standard deviation of 15 points. Reginald scored an 80 on the first test and an 85 on the second. Sara scored an 88 on the first but only a 65 on the second. Although
Combining test scores The first Stats exam had a mean of 65 and a standard deviation of 10 points; the second had a mean of 80 and a standard deviation of 5 points. Derrick scored an 80 on both tests. Julie scored a 70 on the first test and a 90 on the second.They both totaled 160 points on the two
Windy In the last chapter, we looked at three outliers arising from a plot of Average Wind Speed by Month in the Hopkins Forest. Each was associated with an unusually strong storm, but which was the most remarkable for its month?Here are the summary statistics for each of those three months:The
Music library again Corey has 4929 songs in his computer’s music library. The songs have a mean duration of 242.4 seconds with a standard deviation of 114.51 seconds. On the Nickel, by Tom Waits, is 380 seconds long. What is its z-score?
Cold U? A high school senior uses the Internet to get information on February temperatures in the town where he’ll be going to college. He finds a website with some statistics, but they are given in degrees Celsius. The conversion formula isF = 9>5C + 32. Determine the Fahrenheit equivalents
SAT or ACT? Each year thousands of high school students take either the SAT or the ACT, standardized tests used in the college admissions process. Combined SAT Math and Verbal scores go as high as 1600, while the maximum ACT composite score is 36. Since the two exams use very different scales,
Parcel deliveries The parcels delivered by an online clothing company during the year 2019 had weights varying between 21 and 106 ounces, with a mean weight of 48 ounces, and standard deviation of 18 ounces. The quartiles and median weights were 33, 65, and 87 ounces, respectively.a) Find the range
Payroll Here are the summary statistics for the weekly payroll of a small company: lowest salary = +300, mean salary = +700, median = +500, range = +1200, IQR = +600, first quartile = +350, standard deviation = +400.a) Do you think the distribution of salaries is symmetric, skewed to the left, or
Wisconsin ACT 2015 The histogram shows the distribution of mean ACT composite scores for all Wisconsin public schools in 2015. 80.1% of the data points fall between one standard deviation below the mean and one standard deviation above the mean.a) Give two reasons that a Normal model is not
Music library Corey has 4929 songs in his computer’s music library. The lengths of the songs have a mean of 242.4 seconds and standard deviation of 114.51 seconds. A Normal probability plot of the song lengths looks like this:a) Do you think the distribution is Normal? Explain.b) If it isn’t

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