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inferential statistics
Intro Stats 6th Edition Richard D. De Veaux, Paul F. Velleman, David Bock - Solutions
Titanic investigation The Titanic 2020 dataset includes more variables than just those discussed in Chapter 2.Others include the crew’s job and where each person boarded the ship. Stories, biographies, and pictures can be found on the site: www.encyclopedia-titanica. Using the dataset,
Hopkins Forest investigation The Hopkins Forest dataset includes all 24 weather variables reported by the researchers. Many of the variables (e.g., temperature, relative humidity, solar radiation, wind) are reported as daily averages, minima and maxima. Using any of these variables, compare the
Salty fries? (Data in Burger King items) Is the mean amount of salt higher in menu items that contain meat?a) Compare the sodium content of the meat and non-meat items with displays and summary statistics.b) By shuffling the variable Meat 1000 times, investigate whether the mean sodium content
Shelves shuffled (Data in Cereals) Consumer groups are concerned that cereals with a high sugar content (usually designed for children) are placed just where kids are most likely to see them—in the middle shelf of the supermarket.The variable Middle indicates whether the cereal is located on
Global500 2014 Here is a stem-and-leaf display showing profits (in $M) for 30 of the 500 largest global corporations(as measured by revenue). The stems are split; each stem represents a span of 5000 ($M), from a profit of 43,000($M) to a loss of 7000 ($M). Use the stem-and-leaf to answer the
Some assembly required A company that markets buildit-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 2015 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 1994–2015.
California wildfires, counted The following boxplots show the number of wildfires in California that occurred each month between 2013 and 2019. That is, for each month we recorded the counts for those seven years. The first plot is on a raw scale (top) and the second one is after applying a
Pay According to the Bureau of Labor Statistics, the mean hourly wage for Chief Executives in 2009 was $80.43 and the median hourly wage was $77.27. By contrast, for General and Operations Managers, the mean hourly wage was $53.15 and the median was $44.55. Are these wage distributions likely to be
California wildfires size Cal Fire (www.fire.ca.gov) keeps a record of wildfires in California from 2013 to the present.The two boxplots below depict the area burned per fire(in thousands of acres and in log-acres) between 2013 and 2019.a) Which year had the most devastating fire (in area burned)?
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 R1.31a) Describe the shape, center, and spread of this distribution.b) What is the
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 R1.28.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
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 days.a) 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.
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 “they” (“they step on the brake pedal”) steps on the brake pedal, is thought to follow a Normal model with a mean of 1.5 seconds and a standard
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 follow-up
Winter Olympics 2010 speed skating The times from the first race of the women’s 2 * 500-m speed skating event are listed in the following table. (www.olympic.org/vancouver-2010/speed-skating/2x500m-women)a) The mean finishing time was 40.72 seconds, with a standard deviation of 9.82 seconds. If
Liberty’s nose Is the Statue of Liberty’s nose too long?Her nose measures 4′6″, but she is a large statue, after all.Her arm is 42 feet long. That means her arm is 42>4.5 = 9.3 times as long as her nose. Is that a reasonable ratio? Shown in the table are arm and nose lengths of 18 female
PhD program acceptance rates by year In exerciseR1.12 we examined data from the TheGradCafe.com. Here, we’ll examine PhD program self-reported annual acceptance rates for each year from 2006 to 2020 for individuals who did their undergraduate studies in the United States.c) Let’s classify the
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
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. 40 40 30 # of Inter-eruption Intervals 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?
Hard water II The dataset 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 tablea) 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 standard deck 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 categorical.Explain.c) Name a
GPA and graduate school admissions TheGradCafe.com is a website for aspiring students applying to American graduate school programs where they can share their experiences in the application process. In particular, applicants can anonymously contribute their own data (their GPA, GRE scores, program
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 North American Industry Classification System (NAICS) of the business related
Shenandoah 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
State University Public relations staff members 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
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 part of Tall Clubs International (TCI), which is (according to their website) “the social organization for WOMEN 5′10″ and MEN 6′2″ and TALLer!.” The National Health Survey suggests that heights of adults may be Normally distributed, with mean heights of
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 display the heights(in inches) of 130 members of a choir by the part they sing. Height (in.) 76- 72 2 68 64 60 Alto Bass Soprano Tenor Part
Penalty shootouts at the World Cup. Tied games after the group stage in the World Cup tournament are settled with a penalty shootout, with the two teams alternating turns taking penalty kicks. The table on the next page summarizes the outcome of each penalty kick by kick order (for up to 5 kicks)
Bananas Here are the prices (in cents per pound) of bananas reported from 15 markets surveyed by the U.S.Department of Agriculture?a) Display these data with an appropriate graph.b) Report appropriate summary statistics.c) Write a few sentences about this distribution. 51 52 45 48 53 52 50 49 52 48
Caring for household members, 2018 The American Time Use Survey (ATUS) is an annual survey conducted by the Bureau of Labor Statistics (http://www.bls.gov) to better understand how Americans spend their time over the course of a 24-hour period. In Chapter 4, Exercise 53, we examined data on time
Leisure time, 2018 The American Time Use Survey (ATUS)is an annual survey conducted by the Bureau of Labor Statistics(http://www.bls.gov) to better understand how Americans spend their time over the course of a 24-hour period. Let’s consider data on time spent socializing, relaxing, and leisure.
World Happiness 2020, again The World Happiness Report also summarizes GDP per capita within each country, to consider the question of whether more wealthy countries tend to have happier populations. Consider the following plots for the GDP per capita within each country. Do you think it is
World Happiness 2020 The World Happiness Report is an annual report published by the United Nations that studies the happiness levels of individuals in each country along with other measures of well-being. For each of 153 countries, the report provides a happiness score (called Ladder Score),
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 54 grams.a) The average weight of the eggs produced by the young hens is 50.9 grams, and only 28% 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 an article in the Journal of the American Medical Association, researchers reported that a more accurate figure may be
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 38.2 inches and standard deviation of 1.8 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 188 mg/dL and a standard deviation of 24.
IQ, finis Consider the IQ model N1100, 152 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 N11152, 842 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 N1100, 152 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?
More cattle Based on the model N11152, 842 describing Angus steer weights from Exercise 29, 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?
The histogram of log Compensation looks like this:a) According to the Normal model, what percent of CEOs would you expect to earn more than 2 standard deviations above the mean compensation?b) Is that percentage appropriate for these data?with a standard deviation of 0.05.c) Do you think the
CEO compensation logged and sampled Suppose we take logarithms of the CEO compensations in Exercise
CEO compensation sampled The Glassdoor Economic Research Blog published the compensation (in millions of dollars) for the CEOs of large companies. The distribution looks like this: (Data in CEO Compensation 2019)The mean CEO compensation is $14.1M and the standard deviation is $11.32M.a) According
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 2019 NFL data from the 2019 football season reported the number of yards gained by each of the league’s 508 receivers:The mean is 253.76 yards, with a standard deviation of 312.36 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.
Winter Olympics 2018 downhill Fifty-three men completed the men’s alpine downhill part of the super combined. The gold medal winner finished in 100.25 seconds. Here are the times(in seconds) for all competitors.a) The mean time was 103.88 seconds, with a standard deviation of 2.64 seconds. If the
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.
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.
Rivets A company that manufactures rivets believes the shear strength (in pounds) is modeled by N1800, 502.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
High IQ Exercise 10 proposes modeling IQ scores with N1100, 152. What IQ would you consider to be unusually high?Explain.
Small steer In Exercise 29, we suggested the model N11152, 842 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 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
Cattle, part III Suppose the auctioneer in Exercise 31 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
More cattle Recall that the beef cattle described in Exercise 29 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
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
Cattle Using N11152, 842, the Normal model for weights of Angus steers in Exercise 13,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?
Headphones Two companies market new batteries targeted at owners of bluetooth headphones. 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 83 on each. Her roommate Megan, also taking both courses, scored 77 on the French exam and 95 on the Spanish exam. Overall, student scores on the French exam had a mean of 81 and a standard deviation of 5,
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
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?The outliers had values of 6.73 mph, 3.93 mph, and 2.53 mph, for
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 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 = $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 2019 The histogram shows the distribution of mean ACT composite scores for all Wisconsin public schools in 2019. 75.3% 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
Incomes The mean household income in the US in 2019 was about $89,930 and the standard deviation was about $85,000.(The median income was $59.039.) If we used the Normal model for these incomes,a) What would be the household income of the top 1%?b) How confident are you in the answer in part a?c)
ACT scores The Mathematics section of the ACT test had a mean of 20.9 and an SD of 5.3 for the years 2013–2015. If these are well modeled by a Normal distribution, about what percent of students scoreda) over 31?b) under 18?c) between 18 and 31?
IQs revisited Based on the Normal model N1100, 152 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
Stats test Suppose your statistics professor reports test grades as z-scores, and you got a score of 2.20 on an exam.a) Write a sentence explaining what that means.b) Your friend got a z-score of -1. If the grades satisfy the Nearly Normal Condition, about what percent of the class scored lower
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 -1.88. Write a sentence explaining what that means.
IQ Some IQ tests are standardized to a Normal model, with a mean of 100 and a standard deviation of 15.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,
Women’s shoe sizes The shoe size data for women has a mean of 38.46 and a standard deviation of 1.84. To convert to U.S. sizes, use USsize = EuroSize * 0.7865 - 22.5.a) What is the mean women’s shoe size for these respondents in U.S. units?b) What is the standard deviation in U.S. units?
Men’s shoe sizes In Chapter 2 (Exercise 16) we saw data on shoe sizes of students, reported in European sizes. For the men, the mean size was 44.65 with a standard deviation of 2.03. To convert euro shoe sizes to U.S. sizes for men, use the equation USsize = EuroSize * 0.7865 - 24.a) What is the
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
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
Placement exams An incoming freshman took her college’s placement exams in French and mathematics. In French, she scored 82 and in math 86. The overall results on the French exam had a mean of 72 and a standard deviation of 8, while the mean math score was 68, with a standard deviation of 12.On
Temperatures A town’s January high temperatures average 36°F with a standard deviation of 10°, while in July the mean high temperature is 74° and the standard deviation is 8°. In which month is it more unusual to have a day with a high temperature of 55°? Explain.
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