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mathematics
statistics the art and science

Questions and Answers of Statistics The Art and Science

Nonparametric statistical methods are useda. Whenever the response variable is known to have a normal distribution.b. Whenever the assumptions for a parametric method are not perfectly satisfied.c.
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
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
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
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
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.
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
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
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
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
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
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
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
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
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 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
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
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
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 =
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
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
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
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 =
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
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
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
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
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
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
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
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
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
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 +
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
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€™
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
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
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
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.
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
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
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
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
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
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
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,
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
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
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.
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 =
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
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
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
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
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
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
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
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
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
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
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
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
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
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,
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,
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”,
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 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
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 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
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,
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
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
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.
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
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
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
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
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
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
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,
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
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,
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.
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
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
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
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
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
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
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
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.
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
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
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?

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