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intro stats

Stats Data And Models 4th Global Edition Richard D. De Veaux, Paul Velleman, David E. Bock - Solutions

Kentucky Derby 2014 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 Weschler IQ test) for college students. The scatterplot shows the Performance IQ scores vs.
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? (1) (2) + + + +
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) (4) +
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 4-year-old needs about 2.5 seconds to invert a peg, but a 9-year-old takes 2
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
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 dramatically
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 2014 Disk drives have been getting larger.Their capacity is now often given in terabytes (TB) where 1 TB = 1000 gigabytes, or about a trillion bytes. A search of prices for external disk drives on Amazon.com in early 2014 found the following data:a) Prepare a scatterplot of Price
Bookstore sales Consider the following data from a small bookstore.a) Prepare a scatterplot of Sales against Number of sales people working.b) What can you say about the direction of the association?c) What can you say about the form of the relationship?d) What can you say about the strength of the
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
If you travel overseas, you know that what’s really important is not the amount in your wallet but the amount it can buy. UBS (one of the largest banks in the world)prepared a report comparing prices, wages, and other economic conditions in cities around the world for their international clients.
Profits Here is a stem-and-leaf display showing profits as a percent of sales for 29 of the Forbes 500 largest U.S.a) Find the 5-number summary.b) Draw a boxplot for these data.c) Find the mean and standard deviation.d) Describe the distribution of profits for these corporations. -0 99 -0 1234 0
Some assembly required A company that markets build-it-yourself furniture sells a computer desk that is advertised with the claim “less than an hour to assemble.”However, through postpurchase surveys the company has learned that only 25% of its customers succeeded in building the desk in under
Bike safety 2012 The Bicycle Helmet Safety Institute website includes a report on the number of bicycle fatalities per year in the United States. The table below shows the counts for the years 1994–2012.a) What are the W’s for these data?b) Display the data in a stem-and-leaf display.c) Display
Engines, again Horsepower is another measure commonly used to describe auto engines. Here are the summary statistics and histogram displaying horsepowers of the same group of 38 cars discussed in Exercise 31.a) Describe the shape, center, and spread of this distribution.b) What is the interquartile
Engines One measure of the size of an automobile engine is its “displacement,” the total volume (in liters or cubic inches) of its cylinders. Summary statistics for several models of new cars are shown. These displacements were measured in cubic inches.a) How many cars were measured?b) Why
Birth order revisited Consider again the data on birth order and college majors in Exercise 28.a) What is the marginal distribution of majors?b) What is the conditional distribution of majors for the oldest children?c) What is the conditional distribution of majors for the children born second?d)
Herbal medicine Researchers for the Herbal Medicine Council collected information on people’s experiences with a new herbal remedy for colds. They went to a store that sold natural health products. There they asked 100 customers whether they had taken the cold remedy and, if so, to rate its
Birth order Is your birth order related to your choice of major? A Statistics professor at a large university polled his students to find out what their majors were and what position they held in the family birth order. The results are summarized in the table.a) What percent of these students are
Mail Here are the number of pieces of mail received at a school office for 36 da) Plot these data.b) Find appropriate summary statistics.c) Write a brief description of the school’s mail deliveries.d) What percent of the days actually lie within one standard deviation of the mean? Comment. 123 70
Music and memory Is it a good idea to listen to music when studying for a big test? In a study conducted by some Statistics students, 62 people were randomly assigned to listen to rap music, Mozart, or no music while attempting to memorize objects pictured on a page. They were then asked to list
Be quick! Avoiding an accident when driving can depend on reaction time. That time, measured from the moment the driver first sees the danger until he or she steps on the brake pedal, is thought to follow a Normal model with a mean of 1.5 seconds and a standard deviation of 0.18 second.a) Use the
Sluggers Babe Ruth was the first great “slugger” in baseball.His record of 60 home runs in one season held for 34 years until Roger Maris hit 61 in 1961. Mark McGwire(with the aid of steroids) set a new standard of 70 in 1998. Listed below are the home run totals for each season McGwire played.
Sample A study in South Africa focusing on the impact of health insurance identified 1590 children at birth and then sought to conduct follow-up health studies 5 years later. Only 416 of the original group participated in the 5-year follow-up study. This made researchers concerned that the
Winter Olympics 2010 speed skating The top 36 women’s 500-m speed skating times are listed in the table in the next column.a) The mean finishing time was 40.72 seconds, with a standard deviation of 9.82 seconds. If the Normal model is appropriate, what percent of the times should be within 5
Liberty’s nose Is the Statue of Liberty’s nose too long? Her nose measures 46, but she is a large statue, after all. Her arm is 42 feet long. That means her arm is 42>45 = 9.3 times as long as her nose. Is that a reasonable ratio? Shown in the table are arm and nose lengths of 18 girls in a
Teen drivers 2013 The National Highway Traffic Safety Administration reported that there were 3206 fatal accidents involving drivers between the ages of 15 and 19 years old the previous year, of which 65.5%involved male drivers. Of the male drivers, 18.4%involved drinking, while of the female
Old Faithful? Does the duration of an eruption have an effect on the length of time that elapses before the next eruption?a) The histogram below shows the duration (in minutes)of those 222 eruptions. Describe this distribution.b) Explain why it is not appropriate to find summary statistics for this
Old Faithful It is a common belief that Yellowstone’s most famous geyser erupts once an hour at very predictable intervals. The histogram below shows the time gaps(in minutes) between 222 successive eruptions. Describe this distribution. #of Inter-eruption Intervals 40 30 20 20 10 40.0 65.0
Seasons Average daily temperatures in January and July for 60 large U.S. cities are graphed in the histograms below.a) What aspect of these histograms makes it difficult to compare the distributions?b) What differences do you see between the distributions of January and July average temperatures?c)
Hard water II The data set from England and Wales also notes for each town whether it was south or north of Derby. Here are some summary statistics and a comparative boxplot for the two regions.a) What is the overall mean mortality rate for the two regions?b) Do you see evidence of a difference in
Hard water In an investigation of environmental causes of disease, data were collected on the annual mortality rate (deaths per 100,000) for males in 61 large towns in England and Wales. In addition, the water hardness was recorded as the calcium concentration (parts per million, ppm) in the
Accidents Progressive Insurance asked customers who had been involved in auto accidents how far they were from home when the accident happened. The data are summarized in the table.a) Create an appropriate graph of these data.b) Do these data indicate that driving near home is particularly
Let’s play cards You pick a card from a deck (see description in Chapter 9) and record its denomination(7, say) and its suit (maybe spades).a) Is the variable suit categorical or quantitative?b) Name a game you might be playing for which you would consider the variable denomination to be
e-Books A study by the Pew Internet & American Life Project found that 78% of U.S residents over 16 years old read a book in the past 12 months. They also found that 21% had read an e-book using a reader or computer during that period. A newspaper reporting on these findings concluded that 99% of
Cramming One Thursday, researchers gave students enrolled in a section of basic Spanish a set of 50 new vocabulary words to memorize. On Friday, the students took a vocabulary test. When they returned to class the following Monday, they were retested—without advance warning. Both sets of test
Streams As part of the course work, a class at an upstate NY college collects data on streams each year. Students record a number of biological, chemical, and physical variables, including the stream name, the substrate of the stream (limestone (L), shale (S), or mixed (M)), the pH, the temperature
Fraud detection A credit card bank is investigating the incidence of fraudulent card use. The bank suspects that the type of product bought may provide clues to the fraud. To examine this situation, the bank looks at the Standard Industrial Code (SIC) of the business related to the transaction.
Acid rain Based on long-term investigation, researchers have suggested that the acidity (pH) of rainfall in the Shenandoah Mountains can be described by the Normal model N(4.9, 0.6).a) Draw and carefully label the model.b) What percent of storms produce rainfall with pH over 6?c) What percent of
State University Public relations staff at State U.phoned 850 local residents. After identifying themselves, the callers asked the survey participants their ages, whether they had attended college, and whether they had a favorable opinion of the university. The official report to the university’s
Bread Clarksburg Bakery is trying to predict how many loaves to bake. In the past 100 days, they have sold between 95 and 140 loaves per day. Here is a histogram of the number of loaves they sold for the past 100 days.a) Describe the distribution.b) Which should be larger, the mean number of sales
Beanstalks Beanstalk Clubs are social clubs for very tall people. To join, a man must be over 62 tall, and a woman over 510. The National Health Survey suggests that heights of adults may be Normally distributed, with mean heights of 69.1 for men and 64.0 for women. The respective standard
Dialysis In a study of dialysis, researchers found that “of the three patients who were currently on dialysis, 67%had developed blindness and 33% had their toes amputated.”What kind of display might be appropriate for these data? Explain.
Singers by parts The boxplots shown display the heights(in inches) of 130 members of the choir we saw in Exercise 3.40. Now we have information about what part they sing.a) It appears that the median height for sopranos is missing, but actually the median and the upper quartile are equal. How could
Prenatal care Results of a 1996 American Medical Association report about the infant mortality rate for twins carried for the full term of a normal pregnancy are shown on the next page, broken down by the level of prenatal care the mother had received.a) Is the overall rate the average of the other
Bananas Here are the prices (in cents per pound) of bananas reported from 15 markets surveyed by the U.S.Department of Agriculture.51 52 45 48 53 52 50 49 52 48 43 46 45 42 50a) Display these data with an appropriate graph.b) Report appropriate summary statistics.c) Write a few sentences about this
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
Eggs Hens usually begin laying eggs when they are about 6 months old. Young hens tend to lay smaller eggs, often weighing less than the desired minimum weight of 43 grams.a) The average weight of the eggs produced by the young hens is 48.3 grams, and only 26% of their eggs exceed the desired
Body temperatures Most people think that the“normal” adult body temperature is 98.6°F. 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 98.2°F.
Kindergarten Companies that design furniture for elementary school classrooms produce a variety of sizes for kids of different ages. Suppose the heights of kindergarten children can be described by a Normal model with a mean of 39.2 inches and standard deviation of 1.9 inches.a) What fraction of
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 196 mg/dL and a standard deviation of 27.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, 16) 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, 16) from Exercise 2, what cutoff value boundsa) the highest 5% of all IQs?b) the lowest 30% of the IQs?c) the middle 80% of the IQs?
More cattle Based on the model N(1152, 84) describing Angus steer weights from Exercise 25, what are the cutoff values fora) the highest 10% of the weights?b) the lowest 20% of the weights?c) the middle 40% of the weights?
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 2013 NFL data from the 2013 football season reported the number of yards gained by each of the league’s 181 wide receivers:The mean is 426.98 yards, with a standard deviation of 408.34 yards.a) According to the Normal model, what percent of receivers would you expect to gain more yards
Check the model The mean of the 100 car speeds in Exercise 26 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 statisticsFrom your answer in parta, how well does the model do in
Winter Olympics 2010 downhill Fifty-nine men completed the men’s alpine downhill race in Vancouver.The gold medal winner finished in 114.3 seconds.Here are the times (in seconds) for all competitors(espn.go.com/olympics/winter/2010/results/_/sport/1/event/2):a) The mean time was 117.34 seconds,
Car speeds, the picture For the car speed data in Exercise 26, here is 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 6 + 15.0 22.5 30.0 Speed (mph) Speed (mph) 32 28 2222 24 20
Trees, part II Later on, the forester in Exercise 35 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. 4 3 # of Trees 2 - + 0.0 00 4.5 9.0 Diameter (in.) 13.5
Rivets A company that manufactures rivets believes the shear strength (in pounds) is modeled by N(700, 40).a) Draw and label the Normal model.b) Would it be safe to use these rivets in a situation requiring a shear strength of 650 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
High IQ Exercise 8, proposes modeling IQ scores with N(100, 16). What IQ would you consider to be unusually high? Explain.
Small steer In Exercise 25, we suggested the model N(1152, 84) for weights in pounds of yearling Angus steers. What weight would you consider to be unusually low for such an animal? Explain.
Rock concerts A popular band on tour played a series of concerts in large venues. They always drew a large crowd, averaging 21,359 fans. While the band did not announce(and probably never calculated) the standard deviation, which of these values do you think is most likely to be correct:20, 200,
Professors A friend tells you about a recent study dealing with the number of years of teaching experience among current college professors. He remembers the mean but can’t recall whether the standard deviation was 6 months, 6 years, or 16 years. Tell him which one it must have been, and why.
Caught speeding Suppose police set up radar surveillance on the Stanford street described in Exercise 26.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
Cattle, part III Suppose the auctioneer in Exercise 27 sold a herd of cattle whose minimum weight was 980 pounds, median was 1140 pounds, standard deviation 84 pounds, and IQR 102 pounds. They sold for 40 cents a pound, and the auctioneer took a $20 commission on each animal.Then, for example, a
Car speeds again For the car speed data in Exercise 26, 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 friend
More cattle Recall that the beef cattle described in Exercise 25 had a mean weight of 1152 pounds, with a standard deviation of 84 pounds.a) Cattle buyers hope that yearling Angus steers will weigh at least 1000 pounds. To see how much over(or under) that goal the cattle are, we could subtract 1000
Car speeds 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 representative
Cattle Using N(1152, 84), the Normal model for weights of Angus steers in Exercise 9,a) How many standard deviations from the mean would a steer weighing 1000 pounds be?b) Which would be more unusual, a steer weighing 1000 pounds or one weighing 1250 pounds?
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
Final exams Anna, a language major, took final exams in both French and Spanish and scored 87 on each. Her roommate Megan, also taking both courses, scored 79 on the French exam and 94 on the Spanish exam. Overall, student scores on the French exam had a mean of 84 and a standard deviation of 6,
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 15 points; the second had a mean of 85 and a standard deviation of 10 points.Derrick scored an 85 on both tests. Julie scored a 70 on the first test and a 100 on the second. They both totaled 170 points on the
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?
Checkup One of the authors has an adopted grandson whose birth family members are very short. After examining him at his 2-year checkup, the boy’s pediatrician said that the z-score for his height relative to American 2-year-olds was -0.56. Write a sentence explaining what that means.
Stats test, part II Suppose your Statistics professor reports test grades as z-scores, and you got a score of 2.20 on an exam. Write a sentence explaining what that means.
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 is °F = 9>5°C + 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,
Hams A specialty foods company sells “gourmet hams” by mail order. The hams vary in size from 4.15 to 7.45 pounds, with a mean weight of 6 pounds and standard deviation of 0.65 pounds. The quartiles and median weights are 5.6, 6.2, and 6.55 pounds.a) Find the range and the IQR of the weights.b)
Payroll Here are the summary statistics for the weekly payroll of a small company: lowest salary = +350, mean salary = +700, median = +700, range = +1200, IQR = +700, first quartile = +450, standard deviation = +250.a) Do you think the distribution of salaries is symmetric, skewed to the left, or
Wisconsin ACT math The histogram shows the distribution of mean ACT mathematics scores for all Wisconsin public schools in 2011. The vertical lines show the mean and one standard deviation above and below the mean. 78.8% of the data points are between the two outer lines.a) Give two reasons that a
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
IQs revisited Based on the Normal model N(100, 16)describing IQ scores, what percent of people’s IQs would you expect to bea) over 80?b) under 90?c) between 112 and 132?
Normal cattle The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152 pounds. Suppose that weights of all such animals can be described by a Normal model with a standard deviation of 84 pounds. What percent of steers weigha) over 1250 pounds?b) under 1200
IQ Some IQ tests are standardized to a Normal model, with a mean of 100 and a standard deviation of 16.a) Draw the model for these IQ scores. Clearly label it, showing what the 68–95–99.7 Rule predicts.b) In what interval would you expect the central 95%of IQ scores to be found?c) About what
Guzzlers? Environmental Protection Agency (EPA) fuel economy estimates for automobile models tested recently predicted a mean of 24.8 mpg and a standard deviation of 6.2 mpg for highway driving. Assume that a Normal model can be applied.a) Draw the model for auto fuel economy. Clearly label it,
Hotline A company’s customer service hotline handles many calls relating to orders, refunds, and other issues.The company’s records indicate that the median length of calls to the hotline is 4.4 minutes with an IQR of 2.3 minutes.a) If the company were to describe the duration of these calls in
Shipments A company selling clothing on the Internet reports that the packages it ships have a median weight of 68 ounces and an IQR of 40 ounces.a) The company plans to include a sales flyer weighing 4 ounces in each package. What will the new median and IQR be?b) If the company recorded the

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