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intro stats

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

Annual incomes The mean annual income of a group of assistant chefs is €20,500, while the median income is €24,595.The standard deviation is €1,800.a) If a Normal model is used for these incomes, what would be the annual income of the top 1%?b) How confident are you in the answer of part
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 N(100, 15)describing IQ scores, what percent of people’s IQs would you expect to bea) over 80?b) under 90?c) between 112 and 132?
Park visitors’ heights At an amusement park, visitors have to be taller than 1.5 meters to ride on the Rock n’ Roll coaster.From past records, the management of the amusement park knows that the height of park visitors is normally distributed with mean 1.6 meters and standard deviation of 0.4
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
Newborn baby weights A hospital keeps record of the weights of newborn babies and finds that these are normally distributed with a mean weight of 3.5 kg and a standard deviation of 0.5 kg.a) Draw the normal model for newborn baby weights. Clearly label it, showing what the 68–95–99.7 rule
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
Food packages A food company that ships food packages worldwide claims that its food packages have a median weight of 3 kilograms and an IQR of 1.9 kilograms.a) The company plans to include a new advertisement sheet weighing 100 grams in each package. What will be the new median and IQR?b) If the
Placement exams Clara took her college’s placement exams in Physics and Statistics. In Physics, she scored 85 and in Statistics 88. The overall results on the Physics exam had a mean of 74 and a standard deviation of 6, while the mean Statistics score was 80, with a standard deviation of 7. On
Temperatures A town’s January high temperatures average 36F 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.
Mensa People with z-scores above 2.5 on an IQ test are sometimes classified as geniuses. If IQ scores have a mean of 100 and a standard deviation of 15 points, what IQ score do you need to be considered a genius?
Stats test The mean score on the Stats exam was 75 points with a standard deviation of 5 points, and Gregor’s z-score was-2. How many points did he score?
Pizza price differences The mean price of pizza in Baltimore was $2.85, $0.23 higher than the mean price of $2.62 in Dallas.To see if that difference was real, or due to chance, we took the 156 prices from Baltimore and Dallas and mixed those 312 prices together. Then we randomly chose 2 groups of
Pizza prices by city (Data in Pizza prices) The company that sells frozen pizza to stores in four markets in the United States(Denver, Baltimore, Dallas, and Chicago) wants to examine the prices that the stores charge for pizza slices. Here are boxplots comparing data from a sample of stores in
Stereograms shuffled From Exercise 50 it appeared that the mean log fusion time for the VV group was greater than that of the NV group. Could the difference be due to chance? The histogram below shows the difference in the means of the log fusion times by randomly selecting two groups (ignoring the
Cost of living sampled From Exercise 16 it appeared that the mean cost of a cappuccino was slightly higher than the mean cost of a dozen eggs. Given the variation among the prices, could that difference be due just to chance? To examine that further, we took 1000 random samples of 100 cities and
Stereograms, revisited Because of the skewness of the distributions of fusion times described in Exercise 49, we might consider a re-expression. Here are the boxplots of the log of fusion times. Is it better to analyze the original fusion times or the log fusion times? Explain. 00 0.0 Log Fusion
Stereograms Stereograms appear to be composed entirely of random dots. However, they contain separate images that a viewer can “fuse” into a three-dimensional (3D) image by staring at the dots while defocusing the eyes. An experiment was performed to determine whether knowledge of the embedded
Rainmakers The table lists the amounts of rainfall (in acrefeet)from the 26 clouds seeded with silver iodide discussed in Exercise 40. (Data in Cloud seeding)a) Why is acre-feet a good way to measure the amount of precipitation produced by cloud seeding?b) Plot these data, and describe the
Assets again Here are the same data you saw in Exercise 45 after re-expressions as the square root of assets (in $M) and the logarithm of assets (in $M):a) Which re-expression do you prefer? Why?b) In the square root re-expression, what does the value 50 actually indicate about the company’s
Music library Students were asked how many songs they had in their digital music libraries. Here’s a display of the responses:a) What aspect of this distribution makes it difficult to summarize, or to discuss, center and spread?b) What would you suggest doing with these data if we want to
Assets Here is a histogram of the assets (in millions of dollars)of 79 companies chosen from the Forbes list of the nation’s top corporations: (Data in Companies)a) What aspect of this distribution makes it difficult to summarize, or to discuss, center and spread?b) What would you suggest doing
Baseball 2016 American League baseball teams play their games with the designated hitter rule, meaning that pitchers do not bat.The league believes that replacing the pitcher, typically a weak hitter, with another player in the batting order produces more runs and generates more interest among
MPG A consumer organization wants to compare gas mileage figures for several models of cars made in the United States with autos manufactured in other countries. The data for a random sample of cars classified as “midsize” are found in the file MPG 2016.a) Create graphical displays for the
Cholesterol and smoking A study that examined the health risks of smoking measured the cholesterol levels of people who had smoked for at least 25 years and people of similar ages who had smoked for no more than 5 years and then stopped.Create appropriate graphical displays for both groups, and
Industrial experiment Engineers at a computer production plant tested two methods for accuracy in drilling holes into a PC board. They tested how fast they could set the drilling machine by running 10 boards at each of two different speeds. To assess the results, they measured the distance (in
Cloud seeding In an experiment to determine whether seeding clouds with silver iodide increases rainfall, 52 clouds were randomly assigned to be seeded or not. The amount of rain they generated was then measured (in acre-feet). Here are the summary statistics:a) Which of the summary statistics are
Test marks A class of fourth-grade Mathematics students took a November test. The five-number summaries for the 16 girls and 12 boys in the class are shown in the table below:a) Which group had the highest mark?b) Which group had the greater range?c) Which group had the greater interquartile
Framingham cholesterol The Framingham Heart Study recorded the cholesterol levels of more than 1400 participants.(Data in Framingham) Here is an ogive of the distribution of these cholesterol measures. (An ogive shows the percentage of cases at or below a certain value.) Construct a boxplot for
Derby speeds 2017 (Data in Kentucky Derby 2017) How fast do horses run? Kentucky Derby winners run well over 30 miles per hour, as shown in this graph. The graph shows the percentage of Derby winners that have run slower than each given speed.Note that few have won running less than 33 miles per
Anxiety scores Prior to an exam, 30 students in a class took an anxiety test, and the following are the summary statistics for the anxiety scores obtained by gender:a) Create side-by-side boxplots comparing the anxiety scores of male and female students from the information given.b) Write a brief
Caffeine A student study of the effects of caffeine asked volunteers to take a memory test 2 hours after drinking soda. Some drank caffeine-free cola, some drank regular cola (with caffeine), and others drank a mixture of the two (getting a half-dose of caffeine). Here are the 5-number summaries
Heart beats Here are summary statistics for the number of heart beats (per minute) of a group of adults:Suppose you didn’t have access to the data. Answer the following questions from the summary statistics alone:a) Would you describe this distribution as symmetric or skewed? Explain.b) Are there
Graduation? A survey of major universities asked what percentage of incoming freshmen usually graduate “on time” in 4 years.Use the summary statistics given to answer the questions that follow.a) Would you describe this distribution as symmetric or skewed? Explain.b) Are there any outliers?
Eye and hair color A survey of 1021 school-age children was conducted by randomly selecting children from several large urban elementary schools. Two of the questions concerned eye and hair color. In the survey, the following codes were used:The statistics students analyzing the data were asked to
Test scores Three statistics classes all took the same test.Histograms and boxplots of the scores for each class are shown below. Match each class with the corresponding boxplot. 9 # of Students 4 2 8 # of Students 6 2 30 30 60 Class 1 90 30 # of Students + 3 2 30 30 60 Class 2 100- Scores 80 80
Ozone Ozone levels (in parts per billion, ppb) were recorded at sites in New Jersey monthly between 1926 and 1971. Here are boxplots of the data for each month (over the 46 years), lined up in order (January = 1):a) In what month was the highest ozone level ever recorded?b) Which month has the
Employment rates The following graph displays the EU-28 trends in employment rates for individuals aged 20–64 by gender.a) Comment on the type of data displayed in the figure.b) Describe all patterns you see in the figure.c) What was the highest gender gap in employment rate and in which year did
Fuel economy and cylinders Describe what these boxplots tell you about the relationship between the number of cylinders a car’s engine has and the car’s fuel economy (mpg). 35 35 30 30 25 25 20 20 Fuel Efficiency 15 4 5 6 8 Cylinders
Market amounts The following two boxplots show the amount (in Euro) spent at a local market by 23 individuals, 11 of whom are males and 12 of whom are females. Write a brief report discussing what these data show. 100 80 80 60 09 Money T 40- 20 20 21 24 0 Females Males Gender
Financial service providers The following display shows the distribution of financial service providers (FSP) per inhabitant in 2015 for the countries Austria (AT), Switzerland (CH), Germany (DE), Spain (ES), the Netherlands (NL), and the United Kingdom (UK).a) Which of the six FSP distributions
Women’s basketball Here are boxplots of the points scored during the first 10 games of the season for both Scyrine and Alexandra:a) Summarize the similarities and differences in their performance so far.b) The coach can take only one player to the state championship.Which one should she take?
Body temperatures Data from a sample of 65 female patients and 65 male patients on their body temperature (in Fahrenheit)on the last morning during their stay in a short-term hospital are displayed in the following two histograms:a) What would you change about these histograms to make them easier
Shown below are the histogram and summary statistics for the daily number of patients visiting a clinic during a given month.a) Which statistics would you use to identify the center and spread of this distribution? Why?b) Are there any outliers? Explain.c) Create a boxplot for these data.d) Write a
Population growth 2010, by region (Data in Population growth 2010) Below is a “back-to-back” stem-and-leaf display that shows two datasets at once—one going to the left, one to the right. The display compares the percent change in population for two regions of the United States (based on
Tendon transfers People with spinal cord injuries may lose function in some, but not all, of their muscles. The ability to push oneself up is particularly important for shifting position when seated and for transferring into and out of wheelchairs.Surgeons compared two operations to restore the
Sugar in cereals Sugar is a major ingredient in many breakfast cereals. The histogram displays the sugar content as a percentage of weight for 49 brands of cereal. The boxplots compare sugar content for adult and children’s cereals.a) What is the range of the sugar contents of these cereals?b)
Slalom times 2018 The Men’s Giant Slalom skiing event consists of two runs whose times are added together for a final score. Two displays of the giant slalom times in the 2018 Winter Olympics at PyeongChang are shown below.a) What features of the distribution can you see in both the histogram and
Rock concert deaths Crowd Management Strategies (www.crowdsafe.com) monitors accidents at rock concerts. In their database, they list the names and other variables of victims whose deaths were attributed to “crowd crush” at rock concerts.Here are the histogram and boxplot of the victims’ ages
Cost of living 2016, more cities Here are the same three prices as in Exercise 15 but for 576 cities around the world.(Prices are all in US$ as of August 2016; data in COLall 2016.)a) In general, which commodity is the most expensive?b) Is a carton of eggs ever more expensive than a
Cost of living 2016, selected cities To help travelers know what to expect, researchers collected the prices of commodities in 16 cities throughout the world. Here are boxplots comparing the average prices of a bottle of water, a dozen eggs, and a cappuccino in the 16 cities (prices are all in US$
House prices The following boxplot displays the prices (in British pounds) of 35 houses, 19 of which have a garage and 16 of which do not. Compare the two groups and interpret what you find. Prices 200000 180000 160000 140000 120000 100000 80000 T T House has a garage House does not have a garage
Car values A group of 25 friends compared their car values(in Euro) at the end of 2019 and derived the following statistics.a) Which W’s of the data can you identify?b) What kind of display is appropriate to make the data more easily readable?c) Are there any outliers present in the data?
Exoplanets re-expressed Here are the exoplanet distances of Exercise 11, re-expressed to the log scale:a) Is this a better scale to understand these distances?b) The low outlier is “sol”– that is, it is the distance of the sun from the earth. Do you think it belongs with these data? Planets
Exoplanets Discoveries of planets beyond our solar system have grown rapidly. Here is a histogram showing the distance (in lightyears)from earth to stars that have known planets (as of 2016):Explain why it might be beneficial to re-express these distances. Planets 40 30 20 10 0 1000 3000 Distance
Load factors 2017 over time, a second look Here is a timeplot of the same domestic load factors as in Exercise 9, but this time with a different smoother (called a median smoother)applied.a) What can you see in the time plot with the smoother that you might have missed in the original time plot of
Load factors 2017 over time Here is a timeplot of each monthly load factor for domestic flights for 2000 to 2013 along with a lowess smooth.a) Describe the patterns you see in this plot.b) Do you expect the overall pattern to continue for another decade? Why or why not? Domestic Load Factor 82.5
Load factors 2017 by year again The boxplots of exercise 6 show a single possible outlier. But that month in 2015 would not be an outlier in any of the other months in the display. Do you think it should still be considered an outlier? Explain your reasoning.
Extraordinary months (Data in Load factors 2017) Look at the boxplots by month in Exercise 5. The low outlier in April is for April of 2003. At that time, there was concern over the deadly SARS virus, which may have depressed international travel. Do you think the data for April 2003 should be set
Load factors 2017 by year Here is a display of the domestic load factors by year through 2017:Discuss the patterns you see in this display. 82.5 75.0 67.5 HI H HH HIH 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Year
Load factors 2017 by month Here is a display of the international load factors by month for the period from 2002 to 2017:Discuss the patterns you see in this display. 80 15 International Load Factor 70 Month HI 1 2 3 4 5 6 7 8 9 10 11 12 Month
Prisons 2014 In a way, boxplots are the opposite of histograms.A histogram divides the number line into equal intervals and displays the number of data values in each interval. A boxplot divides the data into equal parts and displays the portion of the number line each part covers. These two plots
Fuel economy The boxplot shows the fuel economy ratings for 67 model year 2012 subcompact cars. Some summary statistics are also provided. The extreme outlier is the Mitsubishi i-MiEV, an electric car whose electricity usage is equivalent to 112 miles per gallon.If that electric car is removed from
Load factors, 2017 by season We can also compare domestic load factors for September through March versus those for April through August:Compare and contrast what these histograms show. # of Months 20 20 15 10 5 # of Months 30 30+ 20 20 # 10 63 67 71 75 79 83 87 Domestic Load Factor Fall/Winter 71
Load factors 2017 The Research and Innovative Technology Administration of the Bureau of Transportation Statistics (www.TranStats.bts.gov/Data_Elements.aspx?Data=2) reports load factors(passenger-miles as a percentage of available seatmiles)for commercial airlines for every month from October 2002
Be a Simpson Can you design a Simpson’s paradox? Two companies are vying for a city’s “Best Local Employer” award to be given to the company most committed to hiring local residents.Although both employers hired 300 new people in the past year, Company A brags that it deserves the award
Obesity and exercise The Centers for Disease Control and Prevention (CDC) has estimated that 19.8% of Americans over 15 years old are obese. The CDC conducts a survey on obesity and various behaviors. Here is a table on self-reported exercise classified by body mass index (BMI):Body Mass Index
Blood pressure A company held a blood pressure screening clinic for its employees. The results are summarized in the table below by Age and Blood pressure:Age Under 30 30–49 Over 50 Blood Pressure Low 27 37 31 Normal 48 91 93 High 23 51 73a) Find the marginal distribution of blood pressure
Twin births In 2000, the Journal of the American Medical Association(JAMA) published a study that examined pregnancies that resulted in the birth of twins. Births were classified as preterm with intervention (induced labor or cesarean), preterm without procedures, or term/post-term. Researchers
Test answers A student had to undergo a test which consisted of 50 Yes/No questions. The following contingency table compares the student’s answers with the actual correct answers:Actual Answers Yes No Yes 18 9 No 6 17a) For what percentage of questions was the actual answer a No?b) For what
Parking lots A survey of autos parked in student and staff lots at a large university classified the brands by country of origin, as seen in the table.Driver Student Staff Origin American 107 105 European 33 12 Asian 55 47a) What percent of all the cars surveyed were foreign?b) What percent of the
Student commencements revisited Examine the table about commencements of students studying in Australia on a student visa, shown in Exercise 35. Compare the distributions of commencements across the different sectors for the years 2018 and 2019.
More politics Look once more at the table summarizing the political views of Intro Stats students in Exercise 30.a) Produce a graphical display comparing the conditional distributions of males and females among the three categories of politics.b) Comment briefly on what you see from the display in
Student commencements The following contingency table contains Department of Education and Training international student enrolment data. These data are derived from the Provider Registration and International Students Management System(PRISMS) database and counts commencements of students studying
Politics revisited Look again at the table of political views for the Intro Stats students in Exercise 30.a) Find the conditional distributions (percentages) of political views for the females.b) Find the conditional distributions (percentages) of political views for the males.c) Make a graphical
More about seniors Look again at the table of post-graduation plans for the senior class in Exercise 29.a) Find the conditional distributions (percentages) of plans for the white students.b) Find the conditional distributions (percentages) of plans for the minority students.c) Create a graph
Glasgow’s population The following data, gathered by the National Records of Scotland, gives the population size of Glasgow, Scotland in the year 2017 by age group and sex.(Data from https://www.understandingglasgow.com/indicators/population/trends/trend_by_sex_and_age_group).T Year 2006 2015
Movies 06-15 How have movies changed during the decade from 2006 to 2015? Here is a contingency table showing the proportion of movies with each of the MPAA categories in each year:a) Are these column percents or row percents? How can you tell?b) Does it look like things have changed much between
Politics Students in an Intro Stats course were asked to describe their politics as “Liberal,” “Moderate,” or “Conservative.”Here are the results:Politics L M C Total Sex Female 35 36 6 77 Male 50 44 21 115 Total 85 80 27 192a) What percent of the class is male?b) What percent of the
Seniors Prior to graduation, a high school class was surveyed about its plans. The following table displays the results for white and minority students (the “Minority” group included African American, Asian, Hispanic, and Native American students):Seniors White Minority Plans 4-Year College 198
Higher education student enrolments The following contingency table contains data gathered by the Higher Education Statistics Agency (HESA) for the academic year 2016/17 on higher education science student enrolments in the United Kingdom by subject area and sex. (Data from
Satisfaction with financial situation The following contingency table contains data gathered by Eurostat from EU-28 in 2013. It illustrates the relationship between income level(measured through the income tercile that the person belongs to on the basis of the distribution at the country level) and
Assessment performance A report by the Department of Education, United Kingdom, shows the data in the following contingency table, which explores whether gender has an impact in performance in the Year 6 National Assessments.The data, which corresponds to the year 2016, shows the percentages of
Diet and politics IV Here is a mosaic plot of the data on Diet and Politics from Exercise 5 combined with data on Gender.a) Are there more men or women in the survey? Explain briefly.b) Does there appear to be an association between Politics and Gender? Explain briefly.c) Does there appear to be an
Being successful revisited Here is a mosaic plot of the data on being successful from Exercise 10:a) Are the differences in sample sizes in the four groups very large? Explain briefly.b) Which factor seems more important in determining how someone responded: Age or Gender? Explain briefly.c)
Communication among teenagers In Pew Research Centre’s Teens Relationships Survey of 2014/2015, 1,009 teenagers aged 13 to 17 who have a close friend were asked to identify the three most common ways through which they get in touch with their closest friend. The table below shows the responses
Education and employment patterns The following contingency table displays the education and employment patterns of young people (aged between 15 and 29 years) in the European Union for the year 2016. The data is categorized by five-year age groups and the possible selections for the education and
Smartphone ownership The PEW Research Centre gathered the following data on the percentages of adults in all six sub-Saharan countries who reported that they own a smartphone in 2013 and 2017. (Data from
Smoking women Look again at the table of smoking prevalence in Exercise 19.a) Compare the smoking rate among 18–24-year-old women to that of men during the time covered by this table.b) Relatively few women over the age of 65 smoke. What other variables might affect this percentage?
Smoking The Centers for Disease Control and Prevention provide data on smoking rates by year and for men and women separately. Here is a table with some of that information:a) What was the smoking rate among 18–24-year-old men in 1974?b) How has the smoking rate among 18–24-year-old men changed
Cartoons You’ll find a number of cartoons throughout this text. Are they simply entertaining, or will they help with learning? Lawrence M. Lesser, Dennis K. Pearl, and John J.Weber III (“Assessing fun items’ effectiveness in increasing learning of college introductory statistics students:
Death from the sky A recent article in Geophysical Research Letters (Asteroid impact effects and their immediate hazards for human populations, 10.1002/2017GL073191) simulated the consequences of an earth impact by an asteroid of 400 m in diameter.They estimate that for a land impact, 60% of deaths
Moviegoers and ethnicity The Motion Picture Association of America studies the ethnicity of moviegoers to understand changes in the demographics of moviegoers over time. Here are the numbers of moviegoers (in millions) classified as Hispanic, African American, Caucasian, and Other for the year
Instagram usage The contingency table below provides data(in percentages) on the distribution of Instagram users worldwide as of July 2019 by age group and gender. (Data from https://www.statista.com/statistics/248769/age-distribution-ofworldwide-instagram-users/). Based on these data, do you think
Graphs in the news Find a bar graph or pie chart of categorical data from a newspaper, a magazine, or the Internet.a) Is the graph clearly labeled?b) Does the graph violate the area principle?c) Does the accompanying article tell the W’s of the variable?d) Do you think the article correctly
Body image and gender The following contingency table of categorical data displays an exploration, by the University of Florida, of how body image is related to gender (Data from https://bolt.mph.ufl.edu/6050-6052/unit-1/case-c-c/).a) What is the total sample size?b) What is the percentage of

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