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mathematics
statistics

Statistics Informed Decisions Using Data 5th Edition Michael Sullivan III - Solutions

The following data represent the percentage of 18- to 24-year-olds enrolled in college. Construct a time-series plot and comment on any trends.
Stocks may be categorized by industry. Go to www.pearsonhighered.com/sullivanstats and download the file 2_3_19. The data represent the three-year rate of return of stocks categorized as consumer defensive and industrial (as of November 25, 2014). (a) Construct a relative frequency distribution for
The following two graphics represent the number of reported shark attacks and fatalities worldwide since 1900. Write a report about the trends in the graphs. In your report discuss the apparent contradiction between the increase in shark attacks, but the decrease in fatality rate.
1. True or False: When plotting an ogive, the plotted points have x-coordinates that are equal to the upper limits of each class. 2. True or False: When plotting a frequency polygon, we plot the percentages for each class above the midpoint and connect the points with line segments.
The following frequency polygon represents the cumulative grade point average of a random sample of students at an engineering school.(a) What is the class width? How many classes are represented in the graph? (b) What is the midpoint of the first class? What are the lower and upper limits of the
The following frequency polygon represents the number of hours each week a random sample of adult Americans exercises.(a) What is the class width? How many classes are represented in the graph? (b) What is the midpoint of the first class? What are the lower and upper limits of the first class? (c)
The following relative frequency ogive represents the graduation rate of all four-year universities in the United States.(a) What is the class width? (b) Approximately 10% of all four-year universities have a graduation rate below what level? (c) What percent of all four-year universities have a
The following relative frequency ogive represents the lengths of a random sample of tornadoes in the United States.(a) What is the class width? (b) Approximately 92% of all tornadoes are less than what length? (c) What percent of all tornadoes have a length less than 5.9 miles? (d) More than 50% of
The following time-series plot shows the annual unemployment and inflation rates for the years 1992 through 2014.(a) Estimate the unemployment rate in 2011. (b) In what year was the unemployment rate highest? (c) In what year was the inflation rate highest? (d) In what year were the unemployment
The following is a USA Today-type graph. Explain how it is misleading.
The following data represent health care expenditures per capita (per person) and as a percentage of the U.S. gross domestic product (GDP) from 2003 to 2012. Gross domestic product is the total value of all goods and services created during the course of the year.(a) Construct a time-series plot
The average per gallon price for regular unleaded gasoline in the United States rose from $1.46 in 2001 to $2.77 in 2015. (a) Construct a graphic that is not misleading to depict this situation. (b) Construct a misleading graphic that makes it appear the average price roughly quadrupled between
Between 1980 and 2012, the number of adults in the United States who were overweight more than doubled from 15% to 35%. (a) Construct a graphic that is not misleading to depict this situation. (b) Construct a misleading graphic that makes it appear that the percent of overweight adults has more
The following pie chart displays the position played by the most valuable player (MVP) in the National League of Major League Baseball from 1931 thru 2013. Explain how the graphic is misleading. What should be done to improve the graphic?
The graph shows the median income for females from 2007 to 2013 in constant 2013 dollars.(a) How is the graph misleading? What does the graph seem to convey? (b) Redraw the graph so that it is not misleading. What does the new graph seem to convey?
An article in a student newspaper claims that younger drivers are safer than older drivers and provides the following graph to support the claim. Explain how this graph is misleading.
The U.S. Strategic Oil Reserve is a government-owned stockpile of crude oil. It was established after the oil embargo in the mid-1970s and is meant to serve as a national defense fuel reserve, as well as to offset reductions in commercial oil supplies that would threaten the U.S. economy. The
Harris Interactive conducted a poll of U.S. adults and asked, "When there is a voiceover in a commercial, which type of voice is more likely to sell me a car?" Results of the survey are in the bar graph.(a) How many participants were in the survey? (b) What is the relative frequency of the
The following data represent the percentage of total adjusted gross income (AGI) earned and percentage of tax paid by various income classes. The top 1% represents the percentage of total AGI earned and tax paid by those whose income is higher than 99% of all earners. The bottom 50% represents the
In 2013, the average earnings of a high school graduate were $30,286. At $50,738, the average earnings of a recipient of a bachelor's degree were about 66% higher. (a) Construct a misleading graph that a college recruiter might create to convince high school students that they should attend
The following frequency distribution represents the cause of death in homicides for the year 2013. Type of Weapon Frequency Firearms....................................................8438 Knives or cutting instruments...........................1486 Personal weapons (hands, fists,
The following frequency distribution represents the number of live births (in thousands) in the United States in 2012 by age of mother. Age of Mother (years) Births
A random sample of 60 couples married for seven years were asked to give the number of children they have. The results of the survey are as follows:(a) Construct a frequency distribution of the data. (b) Construct a relative frequency distribution of the data. (c) Construct a cumulative frequency
The table shows the home ownership rate in each of the 50 states and Washington, DC, in 2013.The state with the highest home ownership rate is West Virginia and the lowest is Washington, DC. With a lower class limit of the first class of 45 and a class width of 5: (a) Construct a frequency
The following data represent the diameter (in inches) of a random sample of 34 Keebler Chips Deluxeâ„¢ Chocolate Chip Cookies.(a) Construct a frequency distribution.(b) Construct a relative frequency distribution.(c) Construct a cumulative frequency distribution.(d) Construct a cumulative
For Super Bowl XLVII, there were 82,566 tickets sold for a total value of $218,469,636. What was the mean price per ticket?
The following data represent the miles per gallon for a 2013 Ford Fusion for six randomly selected vehicles. Compute the mean, median, and mode miles per gallon. 34.0, 33.2, 37.0, 29.4, 23.6, 25.9
The following data represent the amount of time (in minutes) a random sample of eight students took to complete the online portion of an exam in Sullivan's Statistics course. Compute the mean, median, and mode time. 60.5, 128.0, 84.6, 122.3, 78.9, 94.7, 85.9, 89.9
Match the histograms shown to the summary statistics:Mean MedianI.....................42...........................42II.....................31...........................36III...................31...........................26IV...................31...........................32(a)(b) (c) (d)
In the 2013 Current Population Survey conducted by the U.S. Census Bureau, two average household incomes were reported: $51,939 and $72,641. One of these averages is the mean and the other is the median. Which is the mean? Support your answer.
The acidity or alkalinity of a solution is measured using pH. A pH less than 7 is acidic; a pH greater than 7 is alkaline. The following data represent the pH in samples of bottled water and tap water.(a) Determine the mean, median, and mode pH for each type of water. Comment on the differences
A histogram of the connection time, in seconds, to an Internet service provider for 30 randomly selected connections is shown. The mean connection time is 39.007 seconds and the median connection time is 39.065 seconds. Identify the shape of the distribution. Which measure of central tendency
A histogram of the annual subscription cost (in dollars) for 26 biology journals is shown. The mean subscription cost is $1846 and the median subscription cost is $1142. Identify the shape of the distribution. Which measure of central tendency better describes the "center" of the distribution?
Go to www.pearsonhighered.com/sullivanstats to obtain the data 3_1_35. The data represent the blood alcohol concentration (BAC), in percent, of a random sample of drivers involved in fatal car accidents. A BAC of 0 indicates that no alcohol was present. Draw a histogram of the data, describe the
The data represent the results of a survey conducted by the author. The column "Texts" represents the number of texts the individual sent for the month prior to the survey. Draw a relative frequency histogram and determine the mean and median number of texts for each gender. Make some general
The Fair Isaacs Corporation has devised a model that is used to determine creditworthiness of individuals, called a FICO score. FICO scores range in value from 300 to 850, with a higher score indicating a more creditworthy individual. The distribution of FICO scores is skewed left with a median
According to a Credit Suisse Survey, the mean net worth of all individuals in the United States in 2014 was $301,000, while the median net worth was $45,000. (a) Which measure do you believe better describes the typical individual's net worth? Support your opinion. (b) What shape would you expect
You are negotiating a contract for the Players Association of the NBA. Which measure of central tendency will you use to support your claim that the average player's salary needs to be increased? Why? As the chief negotiator for the owners, which measure would you use to refute the claim made by
For each of the following situations, determine which measure of central tendency is most appropriate and justify your reasoning. (a) Average price of a home sold in Pittsburgh, Pennsylvania, in 2011 (b) Most popular major for students enrolled in a statistics course (c) Average test score when the
1. The sum of the deviations about the mean always equals ________. 2. The standard deviation is used in conjunction with the ________ to numerically describe distributions that are bell shaped. The ________ measures the center of the distribution, while the standard deviation measures the ________
The following data represent the miles per gallon for a 2013 Ford Fusion for six randomly selected vehicles. Compute the range, sample variance, and sample standard deviation miles per gallon.34.0, 33.2, 37.0, 29.4, 23.6, 25.9
The following data represent the amount of time (in minutes) a random sample of eight students took to complete the online portion of an exam in Sullivan's Statistics course. Compute the range, sample variance, and sample standard deviation time. 60.5, 128.0, 84.6, 122.3, 78.9, 94.7, 85.9, 89.9
Which histogram depicts a higher standard deviation? Justify your answer.(a)(b)
The following data represent exam scores in a statistics class taught using traditional lecture and a class taught using a "flipped" classroom. The "flipped" classroom is one where the content is delivered via video and watched at home, while class time is used for homework and activities.(a) Which
The acidity or alkalinity of a solution is measured using pH. A pH less than 7 is acidic, while a pH greater than 7 is alkaline. The following data represent the pH in samples of bottled water and tap water.(a) Which type of water has more dispersion in pH using the range as the measure of
The data on the following page represent the pulse rates (beats per minute) of nine students enrolled in a section of Sullivan's course in Introductory Statistics. Treat the nine students as a population.Student PulsePerpectual Bempah............................76Megan
Stocks may be categorized by sectors. Go to www.pearsonhighered.com/sullivanstats and download 3_2_27 using the file format of your choice. The data represent the one-year rate of return (in percent) for a sample of consumer cyclical stocks and industrial stocks for the period December 2013 through
In December 2014, the average price of regular unleaded gasoline excluding taxes in the United States was $3.06 per gallon, according to the Energy Information Administration. Assume that the standard deviation price per gallon is $0.06 per gallon to answer the following. (a) What minimum
Compute the sample standard deviation of the following test scores: 78, 78, 78, 78. What can be said about a data set in which all the values are identical?
The following data represent the asking price, in dollars, for a random sample of 2010 coupes and a random sample of 2010 Chevy Camaros.(a) Find the mean and standard deviation price for each sample.(b) Explain why the mean is higher for Camaros yet the standard deviation is less.
Recall that blocking refers to the idea that we can reduce the variability in a variable by segmenting the data by some other variable. The given data represent the recumbent length (in centimeters) of a sample of 10 males and 10 females who are 40 months of age.(a) Determine the standard deviation
Would it be appropriate to say that a distribution with a standard deviation of 10 centimeters is more dispersed than a distribution with a standard deviation of 5 inches? Support your position.
Which of the following would have a higher standard deviation? (a) IQ of students on your campus (b) IQ of residents in your home town? Why?
Recently, a random sample of 25-34 year olds was asked, "How much do you currently have in savings, not including retirement savings?" The following data represent the responses to the survey. Approximate the mean and standard deviation amount of savings.Savings
The data on the next page represent the male and female population, by age, of the United States in 2012.(a) Approximate the population mean and standard deviation of age for males.(b) Approximate the population mean and standard deviation of age for females.(c) Which gender has the higher mean
The following data represent the age of the mother at childbirth for 1980 and 2013.(a) Approximate the population mean and standard deviation of age for mothers in 1980.(b) Approximate the population mean and standard deviation of age for mothers in 2013.(c) Which year has the higher mean age?(d)
The following frequency distribution represents the age of people living in poverty in 2013 based on a random sample of residents of the United States. In this frequency distribution, the class widths are not the same for each class. Approximate the mean and standard deviation age of a person
The following data represent the number of live multiple-delivery births (three or more babies) in 2012 for women 15 to 54 years old.Age Number of Multiple
The following frequency distribution represents the birth weight of all babies born in the United States in 2012.Weight (grams) Number of
1. The ________ represents the number of standard deviations an observation is from the mean. 2. The ________ ________ of a data set is a value such that k percent of the observations are less than or equal to the value. 3. ________ divide data sets into fourths. 4. The ________ ________ is the
The highest batting average ever recorded in Major League Baseball was by Ted Williams in 1941 when he hit 0.406. That year, the mean and standard deviation for batting average were 0.2806 and 0.0328. In 2014, Jose Altuve was the American League batting champion, with a batting average of 0.341. In
Ryan Murphy, nephew of the author, swims for the University of California at Berkeley. Ryan's best time in the 100-meter backstroke is 45.3 seconds. The mean of all NCAA swimmers in this event is 48.62 seconds with a standard deviation of 0.98 second. Ryan's best time in the 200-meter backstroke is
Violent crimes include rape, robbery, assault, and homicide. The following is a summary of the violent-crime rate (violent crimes per 100,000 population) for all 50 states in the United States plus Washington, D.C., in 2012. Q1 = 252.4 Q2 = 333.8 Q3 = 454.5 (a) Provide an interpretation of these
One variable that is measured by online homework systems is the amount of time a student spends on homework for each section of the text. The following is a summary of the number of minutes a student spends for each section of the text for the fall 2014 semester in a College Algebra class at Joliet
The following data represent the monthly rate of return of Google common stock from its inception in January 2007 through November 2014.(a) Determine and interpret the quartiles.(b) Check the data set for outliers.
A survey of 50 randomly selected full-time Joliet Junior College students was conducted during the Fall 2015 semester. In the survey, the students were asked to disclose their weekly income from employment. If the student did not work, $0 was entered.(a) Check the data set for outliers.(b) Draw a
A survey of 40 randomly selected full-time Joliet Junior College students was conducted in the Fall 2015 semester. In the survey, the students were asked to disclose their weekly spending on entertainment. The results of the survey are as follows:(a) Check the data set for outliers. (b) Draw a
Morningstar is a mutual fund rating agency. It ranks a fund's performance by using one to five stars. A one-star mutual fund is in the bottom 10% of its investment class; a five-star mutual fund is at the 90th percentile of its investment class. Interpret the meaning of a five-star mutual fund.
Explain the circumstances for which the interquartile range is the preferred measure of dispersion. What is an advantage that the standard deviation has over the interquartile range?
Explain what each quartile represents.
In 2014, Clayton Kershaw of the Los Angeles Dodgers had the lowest earned-run average (ERA is the mean number of runs yielded per nine innings pitched) of any starting pitcher in the National League, with an ERA of 1.77. Also in 2014, Felix Hernandez of the Seattle Mariners had the lowest ERA of
What does the five-number summary consist of?
The data contains the depth (in kilometers) and magnitude, measured using the Richter Scale, of all earthquakes worldwide that occurred between 12/2/2014 and 12/9/2014. Depth is the distance below the surface of Earth at which the earthquake originates. A one unit increase in magnitude represents
Does hunger improve strategic decision making? That is, if you are hungry are you more likely to make a favorable decision when the outcome of your decision is uncertain (as in business decisions)? To test this theory, researchers randomly divided 30 normal weight individuals into two groups. All
In a boxplot, if the median is to the left of the center of the box and the right whisker is substantially longer than the left whisker, the distribution is skewed _________.
The following data represent the ages of chief justices of the U.S. Supreme Court when they were appointed. Justice Age John Jay...............................................44 John Rutledge.......................................56 Oliver Ellsworth.....................................51 John
1. Generate a data set consisting of the length of each word used in the letter signed by A MOURNER. Be sure to disregard any text that uses proper names, numbers, abbreviations, or titles.2. Calculate the summary statistics for the letter's word lengths. Compare your findings with those of the
1. The _______ variable is the variable whose value can be explained by the value of the explanatory variable. 2. A _______ _______ is a graph that shows the relation between two quantitative variables.
For the 41 nations that participated in TIMMS, the correlation between the percentage of students who skipped class at least once in the past month and the mean score on the exam was -0.52. Does this suggest there is a linear relation between attendance and achievement score? Write a sentence that
A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects eleven 3-yearold children from her practice, measures their heights and head circumference, and obtains the data shown in the table below.(a) If the pediatrician wants
An engineer wanted to determine how the weight of a car affects gas mileage. The following data represent the weights of various domestic cars and their gas mileages in the city for the 2015 model year.(a) Determine which variable is the likely explanatory variable and which is the likely response
The data in the next column represent the maximum wind speed (in knots) and atmospheric pressure (in millibars) for a random sample of hurricanes that originated in the Atlantic Ocean.(a) Draw a scatter diagram treating atmospheric pressure as the explanatory variable. (b) Compute the linear
The following data represent the total compensation for 12 randomly selected chief executive officers (CEO) and the company's stock performance in 2013.(a) One would think that a higher stock return would lead to a higher compensation. Based on this, what would likely be the explanatory
A bear market in the stock market is defined as a condition in which the market declines by 20% or more over the course of at least two months. The following data represent the number of months and percentage change in the S&P500 (a group of 500 stocks).(a) Treating the length of the bear
The ultimate goal in any sport (besides having fun) is to win. One measure of how well a team does is winning percentage. In baseball, a lot of effort goes into figuring out the variables that help to predict a team's winning percentage. Go to www.pearsonhighered.com/sullivanstats to obtain the
What does it mean to say two variables are positively associated? Negatively associated?
On the basis of the scatter diagram below, explain what is wrong with the following statement: "Because the linear correlation coefficient between age and median income is 0.012, there is no relation between age and median income."
The variable "2013 Cost" represents the four-year cost including tuition, supplies, room and board of attending the school. The variable "Annual ROI" represents the return on investment for graduates of the school. It essentially represents how much you would earn on the investment of attending the
What does it mean to say that the linear correlation coefficient between two variables equals 1? What would the scatter diagram look like?
In Problem 15 from Section 4.1, a scatter diagram and correlation coefficient suggested there is a linear relation between the percentage of individuals who have at least a bachelor's degree and median income in the states. In fact, the least-squares regression equation is yÌ‚ = 703.5x
Is there a relation between the age difference between husband/wives and the percent of a country that is literate. Researchers found the least-squares regression between age difference (husband age minus wife age), y, and literacy rate (percent of the population that is literate), x, is ŷ =
The least squares regression equation ŷ = 0.7676x - 52.6841 relates the carbon dioxide emissions (in hundred thousands of tons), y, and energy produced (hundred thousands of megawatts), x, for all countries in the world. (a) Interpret the slope. (b) Is the y-intercept of the model reasonable?
An engineer wants to determine how the weight of a car, x, affects gas mileage, y. The following data represent the weights of various domestic cars and their miles per gallon in the city for the 2015 model year. (Refer to Problem 29, Section 4.1.)(a) Find the least-squares regression line treating
The following data represent the maximum wind speed (in knots) and atmospheric pressure (in millibars) for a random sample of hurricanes that originated in the Atlantic Ocean. (Refer to Problem 30, Section 4.1)(a) Find the least-squares regression line treating atmospheric pressure as the
The following data represent the total compensation for 12 randomly selected chief executive officers (CEO) and the company's stock performance in 2013. Based on the analysis from Problem 31 in Section 4.1, what would be the predicted stock return for a company whose CEO made $15 million? What
A bear market in the stock market is defined as a condition in which market declines by 20% or more over the course of at least two months. The following data represent the number of months and percentage change in the S&P500 (a group of 500 stocks). Based on the analysis from Problem 32 in
The following data represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. (Refer to Problem 34, Section 4.1.)(a) Find the least-squares regression line for males treating number of licensed drivers as the explanatory
The variable "2013 Cost" represents the four-year cost including tuition, supplies, room and board. The variable "Annual ROI" represents the return on investment for graduates of the school. It essentially represents how much you would earn on the investment of attending the school. The variable
One of the biggest factors in determining the value of a home is the square footage. The following data represent the square footage and selling price (in thousands of dollars) for a random sample of homes for sale in Naples, Florida in January 2015. Square Footage, x Selling Price ($000s),
What is a residual? What does it mean when a residual is positive?

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