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

If the linear correlation coefficient is 0, what is the equation of the least-squares regression line?
1. The _____ _____ _____, R2, measures the proportion of total variation in the response variable that is explained by the leastsquares regression line. 2. Total deviation = _____ deviation + _____ deviation 3. A _____ _____ is a scatter diagram with the residuals on the vertical axis and the
Use the linear correlation coefficient given to determine the coefficient of determination, R2. Interpret each R2. (a) r = -0.32 (b) r = 0.13 (c) r = 0.40 (d) r = 0.93
A scatter diagram is given with one of the points drawn in blue. In addition, two least-squares regression lines are drawn: The line drawn in red is the least-squares regression line with the point in blue excluded. The line drawn in blue is the least-squares regression line with the point in blue
Perhaps you are familiar with the famous Old Faithful geyser in Yellowstone National Park. Another Old Faithful geyser is located in Calistoga in California's Napa Valley. The following data represent the time (in minutes) between eruptions and the length of eruption for 9 randomly selected
As concrete cures, it gains strength. The following data represent the 7-day and 28-day strength (in pounds per square inch) of a certain type of concrete.(a) A scatter diagram of the data is shown next. What type of relation appears to exist between 7-day strength and 28-day strength? (b) The
The following data represent the number of calories per serving and the number of grams of sugar per serving for a random sample of high-fiber cereals.(a) Draw a scatter diagram of the data treating calories as the explanatory variable. What type of relation appears to exist between calories and
The scatter diagram represents the percentage of the population with a bachelor's degree, x, and teen birthrates (births per 1000 15- to 19-year-olds), y, for the 50 states and Washington, DC, in 2013.(a) The least-squares regression with Washington, DC, included is yÌ‚ = -0.8276 x +
The time it takes for a planet to complete its orbit around the sun is called the planet's sidereal year. In 1618, Johannes Kepler discovered that the sidereal year of a planet is related to the distance the planet is from the sun. The following data show the distances of the planets, and the dwarf
The wind chill factor depends on wind speed and air temperature. The following data represent the wind speed (in mph) and wind chill factor at an air temperature of 15° Fahrenheit.(a) Draw a scatter diagram of the data treating wind speed as the explanatory variable. (b) Determine the
Suppose that we add the Dodge Viper to the data in Problem 21 in Section 4.2. A Dodge Viper weighs 3425 pounds and gets 11 miles per gallon. (a) Compute the coefficient of determination of the expanded data set. What effect does the addition of the Viper to the data set have on R2? (b) Is the point
The following data represent the carbon dioxide emissions (in thousands of tons), y, and energy generated (thousands of megawatts), x, for a random sample of 14 power plants in Oregon. Is there anything unusual about the Boardman Power Plant, which produces 4618 thousand megawatts of energy and
Professor Katula feels that there is a relation between the number of hours a statistics student studies each week and the student's age. She conducts a survey in which 26 statistics students are asked their age and the number of hours they study statistics each week. She obtains the following
Is the width of a tornado related to the amount of distance for which the tornado is on the ground? Go www.pearsonhighered.com/sullivanstats to obtain the data file 4_3_31 using the file format of your choice for the version of the text you are using. The data represent the width (yards) and length
Go to www.pearsonhighered.com/ sullivanstats to obtain the data file SullivanStatsSurveyII using the file format of your choice for the version of the text you are using. One question asked in this survey is, "What percent of income do you believe individuals should pay in federal income tax?" (a)
Analyze the residual plots and identify which, if any, of the conditions for an adequate linear model is not met.1.2. 3. 4.
Match the coefficient of determination to the scatter diagram in the next column. The scales on the horizontal and vertical axis are the same for each scatter diagram.(a) R2 = 0.58(b) R2 = 0.90(c) R2 = 1(d) R2 = 0.12
(a) Create a relative frequency distribution for political philosophy. What percent of the respondents are moderate? (b) Draw a relative frequency bar graph for political philosophy. (c) The column "GenderIncomeInequality" represents the response to the question, "Do you believe there is an income
Use the results from Problems 2 and 4 for the following:(a) Compute and interpret R2.(b) Plot the residuals against fat content.(c) Based on the residual plot drawn in part (b), is a linear model appropriate for describing the relation between fat content and calories?(d) Are there any outliers or
Use Queens data and the results from Problems 3 and 5 for the following: (a) Compute and interpret R2. (b) Plot the residuals against square footage. (c) For the graph obtained in part (b), is a linear model appropriate? (d) Are there any outliers or influential observations?
Using the Nassau County apartment rent data and the results of Problem 3, do the following:(a) Find the least-squares regression line treating square footage as the explanatory variable. (b) Are there any outliers or influential observations?
The following data represent the price of a random sample of used Chevy Camaros, by age.(a) Draw a scatter diagram treating the age of the car as the explanatory variable and price as the response variable. (b) Find the correlation coefficient between age and price. Based on the correlation
In a newspaper article written in the Chicago Tribune, it was claimed that poorer school districts have shorter school days.(a) The least-squares regression line between length, y, and income, x, is yÌ‚ = -0.0102 x + 7.11. Interpret the slope of this regression line. Does it make sense
A residual plot is given. From the residual plot, determine whether or not a linear model is appropriate. If not, state your reason.1.2. 3.
(a). Read the article Food, Land, Population, and the American Economy from Carrying Capacity Network. (b). Use the historic census data from the U.S. Census Bureau at www.census.gov for the United States for the years 1790 to present to find an exponential model of the form P = a ∙ bt, where t
According to Nate Silver, the probability of a senate candidate winning his/her election with a 5% lead in an average of polls with a week until the election is 0.89. Interpret this probability.
The Wall Street Journal regularly publishes an article entitled "The Count." In one article, The Count looked at 1000 randomly selected home runs in Major League Baseball. (a) Of the 1000 homeruns, it was found that 85 were caught by fans. What is the probability that a randomly selected homerun is
A gene is composed of two alleles, either dominant or recessive. Suppose that a husband and wife, who are both carriers of the sickle-cell anemia allele but do not have the disease, decide to have a child. Because both parents are carriers of the disease, each has one dominant normal-cell allele
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
You suspect a 6-sided die to be loaded and conduct a probability experiment by rolling the die 400 times. The outcome of the experiment is listed in the table below. Do you think the die is loaded? Why? Value of Die
1. In probability, a(n) _________ is any process that can be repeated in which the results are uncertain. 2. A(n) ________ is any collection of outcomes from a probability experiment.
In 2013, the median income of families in the United States was $52,250. What is the probability that a randomly selected family has an income greater than $52,250?
The middle 50% of enrolled freshmen at Washington University in St. Louis had SAT math scores in the range 700-780. What is the probability that a randomly selected freshman at Washington University has an SAT math score of 700 or higher?
Each year the National Football League (NFL) runs a combine in which players who wish to be considered for the NFL draft must participate in a variety of activities. Go to www.pearsonhighered.com/sullivanstats to obtain the data file 5_1_53 using the file format of your choice for the version of
Suppose you live in a town with two hospitals-one large and the other small. On a given day in one of the hospitals, 60% of the babies who were born were girls. Which one do you think it is? Or, is it impossible to tell. Support your decision?
1. If E and F are disjoint events, then P(E or F) = ________. 2. If E and F are not disjoint events, then P(E or F) = ________.
A golf ball is selected at random from a golf bag. If the golf bag contains 9 Titleists, 8 Maxflis, and 3 Top-Flites, find the probability that the golf ball is: 1. A Titleist or Maxfli. 2. A Maxfli or Top-Flite. 3. Not a Titleist. 4. Not a Top-Flite.
The following probability model shows the distribution of murders by type of weapon for murder cases in 2013. Weapon Probability Handgun.................................0.472 Rifle........................................0.023 Shotgun..................................0.025 Unknown
The following probability model shows the distribution of family structure among families with at least one child younger than 18 years of age in 2013.Family Structure ProbabilityTwo married parents, first marriage..............................0.46Two married parents, one or both
In an effort to reduce the number of hospital-acquired conditions (such as infection resulting from the hospital stay), Medicare officials score hospitals on a 10-point scale with a lower score representing a better patient track record. The federal government plans to reduce Medicare payments to
The following data represents the number of rooms in a random sample of U.S. housing units.Rooms
The following data represent the number of drivers involved in fatal crashes in the United States in 2013 by day of the week and gender.(a) Determine the probability that a randomly selected fatal crash involved a male. (b) Determine the probability that a randomly selected fatal crash occurred on
The variable "Text while Driving" represents the response to the question, "Have you ever texted while driving?" The variable "Tickets" represents the response to the question, "How many speeding tickets have you received in the past 12 months?" Treat the individuals in the survey as a random
1. Two events E and F are _____ if the occurrence of event E in a probability experiment does not affect the probability of event F. 2. The word and in probability implies that we use the _____ Rule. 3. The word or in probability implies that we use the _____ Rule.
In finance, a derivative is a financial asset whose value is determined (derived) from a bundle of various assets, such as mortgages. Suppose a randomly selected mortgage has a probability of 0.01 of default. (a) What is the probability a randomly selected mortgage will not default (that is, pay
In airline applications, failure of a component can result in catastrophe. As a result, many airline components utilize something called triple modular redundancy. This means that a critical component has two backup components that may be utilized should the initial component fail. Suppose a
Suppose a particular airline component has a probability of failure of 0.03 and is part of a triple modular redundancy system. In airline applications, failure of a component can result in catastrophe. As a result, many airline components utilize something called triple modular redundancy. This
Ken and Dorothy like to fly to Colorado for ski vacations. Sometimes, however, they are late for their flight. On the air carrier they prefer to fly, the probability that luggage gets lost is 0.012 for luggage checked at least one hour prior to departure. However, the probability luggage gets lost
The probability that a randomly selected individual in the United States 25 years and older has at least a bachelor's degree is 0.094. The probability that an individual in the United States 25 years and older has at least a bachelor's degree, given that the individual lives in Washington DC, is,
According to the U.S. National Center for Health Statistics, 0.15% of deaths in the United States are 25- to 34-year-olds whose cause of death is cancer. In addition, 1.71% of all those who die are 25-34 years old. What is the probability that a randomly selected death is the result of cancer if
According to the U.S. Census Bureau, 8.0% of 16- to 24-year-olds are high school dropouts. In addition, 2.1% of 16- to 24-year-olds are high school dropouts and unemployed. What is the probability that a randomly selected 16- to 24-year-old is unemployed, given he or she is a dropout?
Adult Americans (18 years or older) were asked whether they used social media (Facebook, Twitter, and so on) regularly. The following table is based on the results of the survey.(a) What is the probability that a randomly selected adult American uses social media, given the individual is 18-34
The following data represent the number of drivers involved in fatal crashes in the United States in 2013 by day of the week and gender.(a) Among Sunday fatal crashes, what is the probability that a randomly selected fatality is female? (b) Among female fatalities, what is the probability that a
According to the U.S. Census Bureau, the probability that a randomly selected head of household in the United States earns more than $100,000 per year is 0.202. The probability that a randomly selected head of household in the United States earns more than $100,000 per year, given that the head of
1. A ________ is an ordered arrangement of r objects chosen from n distinct objects without repetition. 2. A ________ is an arrangement of r objects chosen from n distinct objects without repetition and without regard to order. 3. True or False: In a combination problem, order is not important. 4.
A man has six shirts and four ties. Assuming that they all match, how many different shirt-and-tie combinations can he wear?
A woman has five blouses and three skirts. Assuming that they all match, how many different outfits can she wear?
Suppose Dan is going to upload 12 songs to his digital music player. In how many ways can the 12 songs be played without repetition?
Suppose that a local area network requires eight letters for user names. Lower- and uppercase letters are considered the same. How many user names are possible for the local area network?
Find the value of each factorial. 1. 5! 2. 7! 3. 10! 4. 12! 5. 0! 6. 1!
A golf-course architect has four linden trees, five white birch trees, and two bald cypress trees to plant in a row along a fairway. In how many ways can the landscaper plant the trees in a row, assuming that the trees are evenly spaced?
A baseball team consists of three outfielders, four infielders, a pitcher, and a catcher. Assuming that the outfielders and infielders are indistinguishable, how many batting orders are possible?
Suppose a playlist you just created has 13 tracks. After listening to the playlist, you decide that you like 5 of the songs. The random feature on your music player will play each of the 13 songs once in a random order. Find the probability that among the first 4 songs played (a) You like 2 of
Follow the outline presented in Problem 67 to determine the probability of being dealt exactly one pair.
Evaluate each expression. 1. 6!2! 2. 7P3 3. 9C4
Shawn is planning for college and takes the SAT test. While registering for the test, he is allowed to select three schools to which his scores will be sent at no cost. If there are 12 colleges he is considering, how many different ways could he fill out the score report form?
According to the U.S. Census Bureau, 20.2% of American women aged 25 years or older have a Bachelor's Degree; 16.5% of American women aged 25 years or older have never married; among American women aged 25 years or older who have never married, 22.8% have a Bachelor's Degree; and among American
For Problems 5 and 6, let the sample space be S = 51, 2, 3, 4, 5, 6, 7, 8, 9, 106. Suppose that the outcomes are equally likely. Compute the probability of the event:1. E = 51, 3, 5, 106.2. F = "a number divisible by three."
In 2013, there were 32,719 traffic fatalities in the United States. Of these, 10,076 were alcohol related. (a) What is the probability that a randomly selected traffic fatality in 2013 was alcohol related? (b) What is the probability that a randomly selected traffic fatality in 2013 was not alcohol
The following data represent the birth weights (in grams) of babies born in 2013, along with the period of gestation.(a) What is the probability that a randomly selected baby born in 2013 was postterm?(b) What is the probability that a randomly selected baby born in 2013 weighed 3000-3999 grams?(c)
Let the sample space be S = 5red, green, blue, orange, yellow6. Suppose that the outcomes are equally likely. Compute the probability of the event: 1. F = {green or orange} 2. E = {red or blue or yellow}
In 1996, a New York couple won $2.5 million in the state lottery. Eleven years later, the couple won $5 million in the state lottery using the same set of numbers. The odds of winning the New York lottery twice are roughly 1 in 16 trillion, described by a lottery spokesperson as "galactically
1. Offender is at least 18.2. Offender is white.3. Offender is male.4. Victim is a white female.5. Victim is either white or female.6. Victim and offender are from the same age category.7. Victim and offender are from different age categories.8. Victim and offender are of the same race.9. Victim
In the following probability distribution, the random variable X represents the number of marriages an individual aged 15 years or older has been involved in.x
The following data represent the number of games played in each World Series from 1923 to 2014.x (games played)
The graph of the discrete probability distribution below represents the number of live births by a mother 50-54 years old who had a live birth in 2013.(a) What is the probability that a randomly selected 50- to 54-year-old mother who had a live birth in 2013 has had her fourth live birth?(b) What
The graph of the discrete probability distribution represents the number of rooms in rented housing units in 2013.(a) What is the probability that a randomly selected rental unit has five rooms? (b) What is the probability that a randomly selected rental unit has five or six rooms? (c) What is the
BlackJack is a popular casino game in which a player is dealt two cards where the value of the card corresponds to the number on the card, face cards are worth ten, and aces are worth either one or eleven. The object is to get as close to 21 as possible without going over and have cards whose value
In the 2014 election, Republicans took control of the Senate. A major theme during each senator's campaign was the popularity of President Obama (a Democrat). The scatter diagram below shows the presidential approval rating (percent of registered voters who approve of the job the president is
In your own words, provide an interpretation of the mean (or expected value) of a discrete random variable.
1. A binomial experiment is performed a fixed number of times. Each repetition of the experiment is called a _______.2. For each trial of a binomial experiment, there are two mutually exclusive outcomes: _______ or _______.3. True or False: In the binomial probability distribution function, nCx
In the Healthy Handwashing Survey conducted by Bradley Corporation, it was found that 64% of adult Americans operate the flusher of toilets in public restrooms with their foot. Suppose a random sample of n = 20 adult Americans is obtained and the number x who flush public toilets with their foot is
In the Healthy Handwashing Survey conducted by Bradley Corporation, it was found that 64% of adult Americans operate the flusher of toilets in public restrooms with their foot.(a) If 500 adult Americans are randomly selected, how many would we expect to flush toilets in public restrooms with their
Historically, the probability that a passenger will miss a flight is 0.0995. Source: Passenger-Based Predictive Modeling of Airline No-show Rates by Richard D. Lawrence, Se June Hong, and Jacques Cherrier. Airlines do not like flights with empty seats, but it is also not desirable to have
A probability distribution for the random variable X, the number of trials until a success is observed, is called the geometric probability distribution. It has the same criteria as the binomial distribution, except that the number of trials is not fixed. Its probability distribution function (pdf)
The negative binomial probability distribution can be used to compute the probability of the random variable X, the number of trials necessary to observe r successes of a binomial experiment. The probability distribution function is given byP(x) = (x - 1Cr - 1)pr(1 - p)x - rx = r, r + 1, r + 2, . .
One measure of successful investing is being able to "beat the market." To beat the market in any given year, an investor must earn a rate of return greater than the rate of return of some market basket of stocks, such as the Dow Jones Industrial Average (DJIA) or Standard and Poor's 500 (S&P 500).
Explain how the value of n, the number of trials in a binomial experiment, affects the shape of the distribution of a binomial random variable.
Assuming λ = 0.02 and t = 50, compute(a) P(2)(b) P(X < 2)(c) P(X ≥ 2)(d) P(1 ≥ X ≥ 3)(e) μX and σXThe random variable X follows a Poisson process with the given value of λ and t.
The number of hits to a website follows a Poisson process; hits occur at the rate of 1.4 per minute between 7:00 p.m. and 9:00 p.m. Compute the probability that the number of hits between 7:30 p.m. and 7:35 p.m. is(a) Exactly seven. Interpret the result.(b) Fewer than seven. Interpret the
The phone calls to a computer software help desk occur at the rate of 2.1 per minute between 3:00 p.m. and 4:00 p.m. Compute the probability that the number of calls between 3:10 p.m. and 3:15 p.m. is(a) Exactly eight. Interpret the result.(b) Fewer than eight. Interpret the result.(c) At least
The Food and Drug Administration sets a Food Defect Action Level (FDAL) for the various foreign substances that inevitably end up in the food we eat and liquids we drink. For example, the FDAL level for insect filth in peanut butter is 0.3 insect fragment (larvae, eggs, body parts, and so on) per
The potholes on a major highway in the city of Chicago occur at the rate of 3.4 per mile. Compute the probability that the number of potholes over 3 miles of randomly selected highway is(a) Exactly seven. Interpret the result.(b) Fewer than seven. Interpret the result.(c) At least seven. Interpret
According to www.meretrix.com, airline fatalities occur at the rate of 0.05 fatal accidents per 100 million miles. Find the probability that, during the next 100 million miles of flight, there will be(a) Exactly zero fatal accidents. Interpret the result.(b) At least one fatal accident. Interpret
According to www.meretrix.com, traffic fatalities occur at the rate of 1.32 fatal accidents per 100 million miles. Find the probability that, during the next 100 million vehicle miles, there will be(a) Exactly zero fatal accidents. Interpret the result.(b) At least one fatal accident. Interpret the
From 1900 to 2014 (115 years), Florida suffered 31 direct hits from major (category 3 to 5) hurricanes. Assume that this was typical and the number of hits per year follows a Poisson distribution.(a) What is the probability that Florida will not be hit by any major hurricanes in a single year?(b)
Officer Thompson of the Bay Ridge Police Department works the graveyard shift. He averages 4.5 calls per shift from his dispatcher. Assume the number of calls follows a Poisson distribution. Would it be unusual for Officer Thompson to get fewer than 2 calls in a shift?
Cars arrive at Wendy's drive-through at a rate of 0.2 car per minute between the hours of 11:00 p.m. and 1:00 a.m. on Saturday evening. Wendy's begins an advertising blitz that touts its late-night service. After one week of advertising, Wendy's officials count the number of cars, X, arriving at
Explain the role of λ and t in the Poisson probability formula.
A builder ordered two hundred 8-foot grade A 2-by-4s for a construction job. To qualify as a grade A board, each 2-by-4 will have no knots and will average no more than 0.05 imperfection per linear foot. The following table lists the number of imperfections per 2-by-4 in the 200 ordered:x (number

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