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mathematics
statistics the art and science
Statistics The Art And Science Of Learning From Data 4th Edition Alan Agresti, Christine A. Franklin, Bernhard Klingenberg - Solutions
Consider the same setting as that of Exercise 4.37. Of the 100 participants, 45 are male and 55 are female. During the design of the study, one member of the research team suggests that all males be given the active drug and all females be given the placebo. Another member of the team wants to
In an experimental study, science faculty (n = 127) from research universities rated application materials of a student. The 127 application folders were identical except that some were labeled male and some were labeled female. A folder was randomly assigned to each faculty member. The application
During the one-week period of January 11–18, 2012, Facebook conducted an experiment to research whether emotional states can be transferred to others via emotional contagion. Facebook users were randomly selected to be part of two parallel studies in which Facebook manipulated the exposure to
In a survey conducted by voucher cloud.net and reported in the Palm Beach Post, it was found that of 2645 people who had participated in an extramarital affair, the average amount spent per month on the affairwas $444. a. No information was given on how the surveyed individuals were selected. What
Was the motto €œWomen and Children First€ followed on the fateful journey of the Titanic? Refer to the following table on surviving the sinking of the Titanic.a. What€™s the percentage of children and female adult passengers who survived? What€™s the
The journal Energy Policy (2014, 65: 57–67) presents a survey of opinions about fracking. Hydraulic fracturing, or fracking, is the process of drilling through rock and injecting a pressurized mixture of sand, water, and chemicals that fractures the rock and releases oil and gas. There has been
The clarity and cut of a diamond are two of the four C€™s of diamond grading. (The other two are color and carat.) For a sample of diamonds, the following table lists the clarity (rated as internally flawless, IF, very very slightly included, VVS, very slightly included, VS, slightly
Every General Social Survey (GSS) includes the question, €œTaken all together, would you say that you are very happy, pretty happy, or not too happy?€ The table below uses the 2010 survey to cross-tabulate happiness with family income, measured as the response to the question,
In a study published in the July 7, 2014, edition of the American Journal of Medicine, it was suggested that lack of exercise contributed more to weight gain than eating too much. The study examined the current exercise habits and caloric intake of a sample of both males and females. a. Was this an
Tony’s mother is extremely proud that her son will graduate college in a few months. She expresses concern, however, when Tony tells her that following graduation, he plans to move to Las Vegas to become a professional poker player. He mentions that his friend Nick did so and is now earning more
Andy once heard about a car crash victim who died because he was pinned in the wreckage by a seat belt he could not undo. As a result, Andy refuses to wear a seat belt when he rides in a car. How would you explain to Andy the fallacy behind relying on this anecdotal evidence?
A 2014 study (http://www. futurity.org/foreign-languages-make-us-less-moral/) examined the relationship between using a foreign language and acting for the common good. They examined two groups of people, one that used their native language and one that used a foreign language. Each group was
One hundred forty-eight men and women without heart disease or diabetes enrolled in a study. Half of the subjects were randomly assigned to a low-carb diet (<40 g/d), and the others were given a low-fat diet (<30% of daily energy intake from total fat). Subjects on the low-carb diet lost more
An r2 measure of 0.85 implies thata. The correlation between x and y equals 0.85.b. For a one-unit increase in x, we predict y to increase by 85%.c. 85% of the response variable y can be explained by the linear relationship between x and y.d. 85% of the variability we observe in the response
The slope of the regression equation and the correlation are similar in the sense thata. They do not depend on the units of measurement.b. They both must fall between -1 and +1.c. They both have the same sign.d. Neither can be affected by severe regression outliers.
You can summarize the data for two categorical variables x and y bya. drawing a scatter plot of the x- and y-values.b. constructing a contingency table for the x- and y-values.c. calculating the correlation between x and y.d. constructing a box plot for each variable.
Which one of the following statements is correct?a. The correlation is always the same as the slope of the regression line.b. The mean of the residuals from the least-squares regression line is 0 only when r = 0.c. The correlation is the percentage of points that lie in the quadrants where x and y
One can interpret r = 0.30 asa. A weak, positive associationb. 30% of the time ŷ = yc. ŷ changes 0.30 units for every one-unit increase in xd. A stronger association than two variables with r = -0.70
Which of the following is not a property of r?a. r is always between -1 and 1.b. r depends on which of the two variables is designated as the response variable.c. r measures the strength of the linear relationship between x and y.d. r does not depend on the units of y or x.e. r has the same sign as
In a study of graduate students who took the Graduate Record Exam (GRE), the Educational Testing Service reported a correlation of 0.37 between undergraduate grade point average (GPA) and the graduate first year GPA.14 This means thata. As undergraduate GPA increases by one unit, graduate
Access the Newnan GA Temp’s file on the book’s website, which contains data on average annual temperatures for Newnan, Georgia, during the 20th century. Fit a regression line to these temperatures and interpret the trend. Compare the trend to the trend found in Example 12 for Central Park, New
Example 11 discussed how the winning height in the Olympic high jump changed over time. Using the High Jump data file on the book€™s website, we get (see also Figure 3.16) Women_Meters = -10.94 + 0.0065 (Year_Women) for predicting the women€™s winning height (in meters) using
Repeat the previous exercise using x = percent with at least a high school education. This shows that an outlier is not especially influential if its x-value is not relatively large or small.Repeat the previous exerciseFor the U.S. Statewide Crime data file on the book’s website, let y = violent
For the U.S. Statewide Crime data file on the book’s website, let y = violent crime rate and x = percent with a college education.a. Construct a scatter plot. Identify any points that you think may be influential in a regression analysis.b. Fit the regression line, using all 51 observations.
The data in the Animals file on the book’s website holds observations on the average longevity (in years) and gestational period (in days) for a variety of animals. Exercise 3.52 showed the scatter plot together with the regression equation with intercept 6.29 and slope 0.045 and an r2 value of
Consumer Reports magazine (June 2013) reported purchasing samples of ground turkey from different brands to test for the presence of bacteria. The table below shows the number of samples that tested positive for Enterococcus bacteria for packages that claimed no use of antibiotics in the processing
Does the life expectancy of animals depend on the length of their gestational period? The data in the Animals file on the book€™s website show observations on the average longevity (in years) and average gestational period (in days) for 21 animals. (Source: Wildlife Conservation
Most cars are fuel efficient when running at a steady speed of around 40 to 50 mph. A scatter plot relating fuel consumption (measured in mpg) and steady driving speed (measured in mph) for a mid-sized car is shown below. The data are available in the Fuel file on the book’s Web site. (Source:
Refer to the previous exercise.a. For this example, it seems that the average sodium content is as good a predictor as the one resulting from the regression equation. Do you expect r2 to be large or small? Why?b. For this data, r = -0.017. Interpret r2.c. Show the algebraic relationship between the
The Internet Use data file on the book’s website contains data on the number of individuals in a country with broadband access and the population size for each of 32 nations. When using population size as the explanatory variable, x, and broadband subscribers as the response variable, y, the
Zagat restaurant guides publish ratings of restaurants for many large cities around the world (see www.zagat.com). The review for each restaurant gives a verbal summary as well as a 0- to 30-point rating of the quality of food, décor, service, and the cost of a dinner with one drink and tip. For
For the 32 nations in Example 7, we found a correlation of 0.614 between Internet use and Facebook use (both as percentages of population). The regression equation is predicted Facebook use = 7.90 + 0.439 Internet usea. Based on the correlation value, the slope had to be positive. Why?b. Indonesia
Refer to the previous exercise. The correlation with the cost of a dinner is 0.68 for food quality rating, 0.69 for service rating, and 0.56 for décor rating. According to the definition of r2 as a measure for the reduction in the prediction error, which of these three ratings can be used to make
Sketch a scatter plot for which r > 0, but r = 0 after one of the points is deleted.
The following table shows data on gender (coded as 1 = female, 2 = male) and preferred type of chocolate (coded as 1 = white, 2 = milk, 3 = dark) for a sample of 10 students.The students€™ teacher enters the data into software and reports a correlation of 0.640 between gender and type of
Consider the data:x 3 4 5 6 7y 8 13 12 14 16a. Sketch a scatter plot.b. If one pair of (x, y) values is removed, the correlation for the remaining four pairs equals 1. Which pair is it?c. If one y value is changed, the correlation for the five pairs equals 1. Identify the y value and how it
Match the following scatter plots with the correlation values.1. r = -0.92. r = -0.53. r = 04. r = 0.6 (b) х (c) (d)
For the 32 nations in the Internet Use data file on the book€™s website, consider the following correlations:a. Which pair of variables exhibits the strongest linear relationship?b. Which pair of variables exhibits the weakest linear relationship?c. In Example 7, we found the correlation
The previous problem discusses GDP, which is a commonly used measure of the overall economic activity of a nation. For this group of nations, the GDP data have a mean of 1909 and a standard deviation of 3136 (in billions of U.S. dollars).a. The five-number summary of GDP is minimum = 204, Q1 = 378,
For the 100 cars on the lot of a used-car dealership, would you expect a positive association, negative association, or no association between each of the following pairs of variables? Explain why.a. The age of the car and the number of miles on the odometerb. The age of the car and the resale
In recent election years, political scientists have analyzed whether a gender gap exists in political beliefs and party identification. The table shows data collected from the 2010 General Social Survey on gender and party identification (ID).a. Identify the response and explanatory variables.b.
For the following pairs of variables, which more naturally is the response variable and which is the explanatory variable?a. Carat (= weight) and price of a diamondb. Dosage (low/medium/high) and severity of adverse event (mild/moderate/strong/serious) of a drugc. Top speed and construction type
According to a story in the Guardian newspaper (football.guardian.co.uk), in the United Kingdom the mean wage for a Premiership player in 2006 was £676,000. True or false: If the income distribution is skewed to the right, then the median salary was even larger than £676,000.
A teacher summarizes grades on an exam by Min = 26, Q1 = 67, Q2 = 80, Q3 = 87, Max = 100, Mean = 76, Mode = 100, Standard deviation = 76, IQR = 20.She incorrectly recorded one of these. Which one do you think it was? Why?
The mean GPA for all students at a community college in the fall semester was 2.77. A student with a GPA of 2.0 wants to know her relative standing in relation to the mean GPA. A numerical summary that would be useful for this purpose is thea. Standard deviationb. Medianc. Interquartile ranged.
Which statement about the standard deviation s is false?a. s can never be negative.b. s can never be zero.c. For bell-shaped distributions, about 95% of the data fall within X̅ ± 2s.d. s is a nonresistant (sensitive to outliers) measure of variability, as is the range.
The side-by-side box plots below show the unemployment rate among 15- to 24-year-olds in 28 European nations for each gender. The two outliers shown for each box plot refer to the same countries, Greece and Spain. Write a short paragraph comparing the distribution for the males to the one for the
In a study of graduate students who took the Graduate Record Exam (GRE), the Educational Testing Service reported that for the quantitative exam, U.S. citizens had a mean of 529 and standard deviation of 127, whereas the non-U.S. citizens had a mean of 649 and standard deviation of 129. Which of
The distribution of high school graduation rates in the United States in 2009 had a minimum value of 79.9 (Texas), first quartile of 84.0, median of 87.4, third quartile of 89.8, and maximum value of 91.8 (Wyoming) (Statistical Abstract of the United States, data available on book’s website.)a.
For each of the following variables, sketch a box plot that would be plausible.a. Exam score 1min = 0, max = 100, mean = 87, standard deviation = 102b. IQ (mean = 100 and standard deviation = 16)c. Weekly religious contribution (median = $10 and mean = $172
In 2009, the five-number summary statistics for the distribution of statewide percentage of people without health insurance had a minimum of 4.4% (Massachusetts), Q1 = 12.35%, median = 14.8%, Q3 = 17.3%, and maximum of 26.1% (Texas) (Statistical Abstract of the United States, data available on
According to Statistical Abstract of the United States, 2012, average salary (in dollars) of primary and secondary school classroom teachers in 2009 in the United States varied among states with a five number summary of: minimum = 35,070, Q1 = 45,840, median = 48,630, Q3 = 55,820, maximum = 69,119.
The data values below represent the closing prices of the 20 most actively traded stocks on the NASDAQ Stock Exchange (rounded to the nearest dollar) on May 2, 2014.a. Sketch a dot plot or construct a stem-and-leaf plot.b. Find the median, the first quartile, and the third quartile.c. Sketch a box
Refer to the previous exercise about hurricane damage and the histogram shown there.a. For this data, 93% of damages (i.e., all but the two most expensive) fall within one standard deviation of the mean. Why is this so different from the 68% the empirical rule suggests?b. How would removing the
The histogram shows the distribution of the damage (in billion dollars) of the 30 most costly hurricanes hitting the U.S. mainland between 1900 and 2010. (Numbers are inflation adjusted and in 2010 dollars). The data are available in the Hurricane file on the book€™s website.a. Describe
In a guidebook about interesting hikes to take in national parks, each hike is classified as easy, medium, or hard and by the length of the hike (in miles). Which classification is quantitative and which is categorical?
The U.S. Bureau of the Census reported a median sales price of new houses sold in March 2014 of $290,000. Would you expect the mean sales price to have been higher or lower? Explain.
The Animals data set on the book’s website has data on the average longevity (measured in years) for 21 animals.a. Construct a stem-and-leaf plot of longevityb. Construct a histogram of longevity.c. Summarize what you see in the histogram or stemand- leaf plot. (Most animals live to be how old?
For the question €œHow many children have you ever had?€ in the 2010 General Social Survey, the results werea. Which is the most appropriate graph to display the data€”dot plot, stem-and-leaf plot, or histogram? Why?b. Based on sketching or using software to construct
A recent survey asked 1200 university students in China to pick the personality trait that most defines a person as “cool.” The possible responses allowed, and the percentage making each, were individualistic and innovative (47%), stylish (13.5%), dynamic and capable (9.5%), easygoing and
The table shows the number of 18- to 24-year-old noncitizens living in the United States between 2010 and 2012.Noncitizens aged 18 to 24 in the United StatesRegion of Birth ................................Number (in Thousands)Africa
Explain what is wrong with the following pie chart, which depicts the federal government breakdown by category for 2010. Federal Spending for 2010 Education (1%) Other (18%) Interest on Social Security (20%) national debt (5%) Defense Medicaid Medicare (19%) (8%) (13%) Unemployment and welfare (16%)
Explain what is wrong with the time plot shown of the annual license fee paid by British subjects for watching BBC programs. At 1.8% above inilation fee will be £185 by 2013 150 140 Tockay's licence £131.50 130 120 110 At enrrent inflation 100 fee is f158 by 2013 90 1996 97 98 99 00 01 02 03 04
Example 17 discussed EU carbon dioxide emissions, which had a mean of 7.9 and standard deviation of 3.6.a. Finland’s observation was 11.5. Find its z-score and interpret.b. Sweden’s observation was 5.6. Find its z-score, and interpret.c. The UK’s observation was 7.9. Find the z-score and
The 2013 unemployment rates of countries in the European Union shown in Exercise 2.63 ranged from 4.9 to 27.3, with Q1 = 7.15, median = 10.15, Q3 = 13.05, a mean of 11.1, and a standard deviation of 5.6.a. In a box plot, what would be the values at the outer edges of the box, and what would be the
The Energy Information Administration records per capita consumption of energy by country. The box plot below shows 2011 per capita energy consumption (in millions of BTUs) for 36 OECD countries, with a mean of 195 and a standard deviation of 120. Iceland had the largest per capita consumption at
In recent years, many European nations have suffered from relatively high youth unemployment. For the 28 EU nations, the table below shows the unemployment rate among 15- to 24-year-olds in 2013, also available as a file on the book€™s website. If you are computing the statistics below by
Use the Mean versus Median web app on the book’s website to investigate how the standard deviation changes as the data change. When you start the app, you have a blank graph. Under “Options”, you can request to show the standard deviation of the points you create by clicking in the graph.a.
The 2012 General Social Survey asked, “On the average day, about how many hours do you personally watch television?” Of 1298 responses, the mode was 2, the median was 2, the mean was 3.09, and the standard deviation was 2.87. Based on these statistics, what would you surmise about the shape of
The table below shows data (from a 2004 Bureau of the Census report) on the number of times 20- to 24-year-old men have been married.a. Verify that the mean number of times men have been married is 0.16 and that the standard deviation is 0.37.b. Find the actual percentages of observations within 1,
According to the National Association of Home Builders, the median selling price of new homes in the United States in February 2014 was $261,400. Which of the following is the most plausible value for the standard deviation: - $15,000, $1000, $60,000, or $1,000,000? Why? Explain what’s
For Russia, the United Nations reported a life expectancy of 70. Suppose we add this observation to the data set for Western Europe in the previous exercise. Would you expect the standard deviation to be larger, or smaller, than the value for the Western European countries alone? Why?
The Human Development Report 2013, published by the United Nations, showed life expectancies by country. For Western Europe, some values reported were Austria 81, Belgium 80, Denmark 80, Finland 81, France 83, Germany 81, Greece 81, Ireland 81, Italy 83, Netherlands 81, Norway 81, Portugal 80,
The table in the next column shows the number of times 20€“24-year-old U.S. residents have been married, based on a Bureau of the Census report from 2004. The frequencies are actually thousands of people. For instance, 8,418,000 men never married, but this does not affect
The players on the New York Yankees baseball team in 2014 had a mean salary of $7,387,498 and a median salary of $5,500,000.6 What do you think causes these two values to be so different (data in NYY salary file on book’s website.)?
Pick up a recent issue of a national newspaper, such as The New York Times or USA Today, or consult a news website, such as msnbc.com or cnn.com. Identify an article that used statistical methods. Did it use descriptive statistics, inferential statistics, or both? Explain.
True or false? In a particular study, you could use descriptive statistics, or you could use inferential statistics, but you would rarely need to use both.
Inferential statistics are useda. To describe whether a sample has more females or males.b. To reduce a data file to easily understood summaries.c. To make predictions about populations by using sample data.d. When we can’t use statistical software to analyze data.e. To predict the sample data we
The Gallup organization has asked opinions about support of labor unions since its first poll in 1936, when 72% of the American population approved of them. In its 2014 poll, it found that support of labor unions had fallen to 53% of Americans, based ona sample of 1,540 adults.a. Calculate an
For the marketing study about sales in Example 5, identify the (a) sample and population (b) descriptive and inferential aspects.
Your university is interested in determining the proportion of students who would be interested in completing summer courses online, compared to on campus. A survey is taken of 100 students who intend to take summer courses.a. Identify the sample and the population.b. For the study, explain the
Your instructor will show you how to create data files by using the software for your course. Use it to create the data file you constructed by hand in Exercise 1.20 or 1.21.Data FromConstruct a data file describing the purchasing behavior of the five people, described be-low, who visit a shopping
We’ll see that the amount by which statistics vary from sample to sample always depends on the sample size. This important fact can be illustrated by thinking about what would happen in repeated flips of a fair coin.a. Which case would you find more surprising—flipping the coin five times
Suppose a liberal arts student is interested in exploring graduate school in his or her field. The student identifies a program in which he or she is interested and finds the name of a few students from that program to interview. In this context, identify what is meant by the (a) Subject,(b)
The Current Population Survey (CPS) is a survey conducted by the U.S. Bureau of the Census for the Bureau of Labor Statistics. It provides a comprehensive body of data on the labor force, unemployment, wealth, poverty, and so on. The data can be found online at www.census.gov/cps/. Data from the
According to the U.S. Bureau of the Census, Current Population Reports 2013, the mean and median income for households with health insurance was $86,431 and $66,000, respectively. For households without health insurance, the mean and median income was $53,373 and $39,000, respectively. Does this
According to a recent Current Population Survey of U.S. married-couple households, 13% are traditional (with children and with only the husband in the labor force), 31% are dual-income with children, 25% are dual-income with no children, and 31% are other (such as older married couples whose
Identify each of the following variables as either categorical or quantitative.a. Choice of diet (vegan, vegetarian, neither)b. Time spent shopping online per weekc. Ownership of a tablet (yes, no)d. Number of siblings
Few of the shark attacks listed in Table 2.1 are fatal. Overall, 63 fatal shark attacks were recorded in the ISAF from 2004 to 2013, with 2 reported in Florida, 2 in Hawaii, 4 in California, 15 in Australia, 13 in South Africa, 6 in Réunion Island, 4 in Brazil, and 6 in the Bahamas. The rest
In 2012 in the United States, most electricity was generated from coal (37%), natural gas (30%), or nuclear power plants (19%). Hydro-power accounted for 7% of the total electricity produced; other renewable sources such as wind or solar power accounted for 5%. Other non-renewable sources (such as
The data shown in Exercise 2.9 give frequencies of fatal shark attacks for different regions. Using software or sketching, construct a bar graph, ordering the regions (i) Alphabetically(ii) As in a Pareto chart. Which do you prefer? WhyIn problem 2.9Few of the shark attacks listed in Table 2.1
For a trip to Miami, Florida, over spring break in 2014, the data below (obtained from travelocity.com) show the price per night (in U.S. dollars) for various hotel rooms.a. Construct a stem-and-leaf plot. Truncate the data to the first two digits for purposes of constructing the plot. For example,
The figure below shows the stem-and-leaf plot for the cereal sugar values from Example 5, using split stems.Stem and Leaf Plot for Cereal Sugar Values with Leaf Unit = 1000a. What was the smallest and largest amount of sugar found in the 20 cereals?b. What sugar values are represented on the 6th
Repeat the preceding exercise fora. The scores of students (out of 100 points) on a very easy exam in which most score perfectly or nearly so, but a few score very poorlyb. The weekly church contribution for all members of a congregation, in which the three wealthiest members contribute generously
The Animals data set at the book’s website contains data on the length of the gestational period (in days) of 21 animals.a. Using software, plot a histogram of the gestational period.b. Do you see any observation that is unusual? Which animal is it?c. Is the distribution right-skewed or
For each of the following variables, would you use the median or mean for describing the center of the distribution? Why?a. Salary of employees of a universityb. Time spent on a difficult examc. Scores on a standardized test
For each of the following variables, would you use the median or mean for describing the center of the distribution? Why?a. Charges on a credit cardb. Weight of male students in your class this semesterc. Life expectancy of females in developed nations.
The Energy Information Agency reported the CO2 emissions (measured in gigatons, Gt) from fossil fuel combustion for the top 10 emitting countries in 2011. These are China (8 Gt), the United States (5.3 Gt), India (1.8 Gt), Russia (1.7 Gt), Japan (1.2 Gt), Germany (0.8 Gt), Korea (0.6 Gt),
The dot plot shows the cereal sodium values from Example 4. What aspect of the distribution causes the mean to be less than the median?
An article in the Journal of American College Health reports that, in a survey of 1845 college students from a large, southeastern public university, 27% were at risk for at least one sleep disorder, with a margin of error of 2%. Explain how this margin of error provides an inferential statistical
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