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A Pathway To Introductory Statistics 1st Edition Jay Lehmann - Solutions
The author surveyed one of his statistics classes about the numbers of friends they had in high school and the numbers of those high school friends they still consider to be friends. A scatterplot compares the two variables in Fig. 17a. Identify the explanatory and response variables.b. Is the
The scatterplot in Fig. 18 compares the temperatures and relative humidities in Seattle, Washington, for approximately every hour, from 12:53 a.m. to 11:53 p.m. on June 1, 2014.a. There were 24 pairs of temperatures and relative humidities recorded. Why are there only 19 dots in the scatterplot?b.
The scatterplot in Fig. 19 compares the temperatures and relative humidities in Atlanta, Georgia, for every hour, from 12:52 a.m. to 11:52 p.m. on June 1, 2014.a. There were 24 pairs of temperatures and relative humidities recorded. Why are there only 15 dots in the scatterplot? b. Identify the
Let x be the explanatory variable and y be the response variable. Construct a scatterplot of the ordered pairs listed in Table 8.Table 8 Some Ordered Pairsx y2…………………………….57…………………………….911…………………………
Let x be the explanatory variable and y be the response variable. Construct a scatterplot of the ordered pairs listed in Table 9.Table 9 some Ordered Pairsx y-5…………………… 2-4…………………… 3-1…………………… 54……………………. 911…………………..15
The number of pages in each of the books in the Harry Potter series is listed in Table 10.Table 10 Number of pages in the Book of the Harry Potter SeriesBook NumberNumber of
The mean life-spans of various denominations of bills are shown in Table 11. For example, the mean life-span of a $1 bill is 1.5 years before it is taken out of circulation due to wear and tear.Table 11 Mean Life-Spans of Denominations of BillsValue of Bill (dollars)Life-span
Woods€™s golf tournament earnings and numbers of wins are shown in Table 12 for various years.Let E be Tiger Woods€™s tournament earnings (in millions of dollars) in the year that is t years since 2000. For example, t = 0 represents 2000, and t = 6 represents 2006.a. Identify the
The mean price per barrel of crude oil and the total fuel cost for the global airline industry are shown in Table 13 for various years.Let C be the total airline fuel cost (in billions of dollars) in the year that is t years since 2005, For example, t = 0 represents 2005, and t = 2 represents
The total costs to individuals and companies to prepare their taxes are shown in Table 14 for various years.Table 14 Total costs to individuals and Companies to prepare taxesYearTotal Cost (billions of
The mean hourly manufacturing pay is shown in Table 15 for various years.Table 15 Mean Hourly Manufacturing PayYearMean Hourly Pay
The numbers of automobile accidents per 1000 licensed drivers per year are shown in Table 16 for various age groups.Let r be the automobile accident rate (number of accidents per 1000 licensed drivers per year) for licensed drivers at age a years.a. Construct a scatterplot.b. Which age group shown
The percentages of Americans of various age groups who are ordering more takeout food than they did two years ago are shown in Table 17.Let p be the percentage of Americans at age a year€™s who are ordering more takeout food than they did two years ago.a. Construct a scatterplot.b. Is the
Several inventions are listed in Table 18, along with the years they were invented and how long it took for one-quarter of the U.S. population to use them (€œmass use€).Let M be the number of years elapsed until an invention reached mass use if it was invented at t years since 1870.a.
Let n be the number of hours a student studies for a quiz, and let s be the student’s score (in points) on the quiz. Identify the explanatory and the response variables. Which variable should be described by the horizontal axis of a coordinate system? How about the vertical axis?
The percentages of adults of various age groups who ap- prove of single men raising children on their own are shown in Table 19.Let p be the percentage of adults at age a years who approve of single men raising children on their own.a. Construct a scatterplot.b. Is the association positive,
Data about existing home sales in area 232 of Palo Alto, California, in 2007 are shown in Table 20.Let F be the square footage of a home, and let P be the home€™s sales price (in thousands of dollars).a. Construct a scatterplot that describes the association between square footage and sales
Data about existing home sales in area 232 of Palo Alto, California, in 2007 are shown in Table 20. A list price is the price an owner originally requested before negotiations began. Let L be the list price (in thousands of dollars) of a home, and let S be the home’s sales price (in thousands of
Data about existing home sales in area 232 of Palo Alto, California, in 2007 are shown in Table 20 on page 379. Let x be the number of bedrooms in a home, and let y be the number of baths in the home.a. Construct a scatterplot that describes the association between number of bedrooms and number of
Data about existing home sales in area 232 of Palo Alto, California, in 2007 are shown in Table 20 on page 379. Let B be the number of bedrooms in a home, and let S be the home’s sales price (in thousands of dollars).a. Construct a scatterplot that describes the association between number of
On the basis of 18 LCD TVs, the mean annual costs to operate LCD TVs are shown in Table 21 for various sizes.A student lets C be the mean annual cost (in dollars) to run a LCD TV of size S inches. The student tries to construct a scatterplot (see Fig. 20). Describe all the errors made by the
In a study, the explanatory variable is the number of milligrams of an experimental drug that a person ingests per day, and the response variable is the person’s blood pressure. Because the number of milligrams of the drug is the explanatory variable, does that mean that the drug definitely
The author surveyed his algebra students about their favorite music genres. The students€™ responses are summarized in the bar graph in Fig. 21. A student says there is a negative association between favorite music genre and frequency. What would you tell the student?
Determine whether a scatterplot can describe the given types of variables. If it is not possible, explain why by describing how we construct axes of a scatterplot.a. Two categorical variablesb. A categorical variable and a numerical variablec. two numerical variables
Let n be the number of office parties an employer hosts per year, and let p be the percentage of employees who say they enjoy working at the company. Identify the explanatory and the response variables. Which variable should be described by the horizontal axis of a coordinate system? How about the
Let h be the height (in inches) of a girl, and let a be the age (in years) of the girl. Identify the explanatory and the response variables. Which variable should be described by the horizontal axis of a coordinate system? How about the vertical axis?
Let p be the percentage of colleges that would accept a student whose grade point average (GPA) is G points. Identify the explanatory and the response variables. Which variable should be described by the horizontal axis of a coordinate system? How about the vertical axis?
Let I be a student’s IQ (in points), and let G be the student’s GPA (in points) in college. Identify the explanatory and the response variables. Which variable should be described by the horizontal axis of a coordinate system? How about the vertical axis?
Some ordered pairs are shown in Table 23. Let x be the explanatory variable and y be the response variable.Table 23 Values of x and yx y1…………………….23…………………….64…………………….46…………………….87……………………10a. Construct a
Some ordered pairs are shown in Table 24. Let x be the explanatory variable and y be the response variable.Table 24 Values of x and yxy0……………………182……………………162……………………134……………………116…………………… 8a. Construct a scatterplot.b.
The scatterplot in Fig. 58 compares the number of seats in the House of Representatives with the population for each of the 50 states.a. Describe the four characteristics of the association. You do not have to compute r. b. What does the positive association mean in this situation? c.
The heights and weights of the 60 players picked in the 2014 draft for NBA basketball teams are described by the scatter- plot in Fig. 59.a. Describe the four characteristics of the association. You do not have to compute r. b. Estimate the weight of 2014 draft pick Alec Brown, who is 85 inches
The scatterplot in Fig.60 describes the ages and years of experience of NFL football players. To enter the NFL, a player must be at least three years removed from completing high school, or the player must have completed at least three years of college.a. Explain why the red dot is an outlier.
Figure 61 displays a scatterplot that compares the percentage of adults who exercise with the percentage of adults who are obese for each of the 50 states, Puerto Rico, and District of Columbia.a. Explain why the red dot in the scatterplot might be considered an outlier. What does this mean in this
A planet€™s orbital velocity is the speed that a planet travels around the Sun. The orbital velocities and the mean distances from the Sun of the 8 planets in our solar system are shown in Table 25.Let v be the orbital velocity (in km/s) of a planet, and let d be the planet€™s mean distance
Escape velocity is the initial velocity that an object needs in order to break free of a planet€™s gravitational pull. The mass of a planet can be used to help find the weight of an object on that planet. The escape velocities and the masses of 7 of the 8 planets in our solar system are shown
The scatterplot in Fig. 62 compares the prices of hot dogs and soft drinks at all the Major League Baseball (MLB) stadiums.a. Describe the four characteristics of the association. You do not have to compute r.b. The correlation coefficient is 0.83. Does this support your analysis of the strength of
Figure 64 displays a scatterplot that compares the mean lengths with the mean heights of 51 types of dinosaurs. There are two main categories (called orders) of dinosaurs: Saurischians and Ornithischians. Saurischians had a pelvis also found in modern lizards, whereas Ornithischians had a pelvis
A football fan says Super Bowl games should be hosted only at indoor stadiums and at outdoor stadiums with warm January climates so the games will all be high-scoring. The scatterplot in Fig. 65 describes the temperature on the field and the total score from both teams in each of the 48 Super
A study was based on the records of 6789 patients in 369 hospitals in which the patients’ hearts stopped because of conditions that could have been reversed by an electrical shock from a defibrillator. The percentages of patients who survived at least until being discharged from the hospital are
The probability that a randomly selected newborn is a boy is actually more than 1/2.The number of newborn boys for every 100 newborn girls is called the sex ratio at birth. The birth order of a first child is 1, the birth order of a second child is 2, and so on. The sex ratios at birth are shown in
The tank and aircraft productions in Germany and the United States during World War II are shown in Table 29.Let T be a country€™s annual tank production, and let A be the country€™s annual aircraft production. Treat T as the explanatory variable and A as the response variable.a. Construct
The number of math degrees granted by Northwestern University are shown in Table 30 for various years.Let n be the number of math degrees granted by Northwestern University in the year that is t years since 2000.a. Construct a scatterplot.b. Is there a linear association, a nonlinear association,
Women€™s winning times in Olympic 500-meter speed skating are shown in Table 31 for various years.Let w be the women€™s winning time (in seconds) at t years since 1970.a. Construct a scatterplot.b. Is there a linear association, a nonlinear association, or no association?c. Compute r. On
Men€™s 400-meter record times are shown in Table 32 for various years.Let r be the men€™s 400-meter record time (in seconds) at t years since 1900.a. Construct a scatterplot.b. Is there a linear association, a nonlinear association, or no association?c. Compute r. On the basis of the
The percentages of Americans who believe marriages between same-sex couples should be recognized by the law as valid are shown in Table 33 for various age groups.Let p be the percentage of Americans at age a years who believe marriages between same-sex couples should be recognized by the law as
The percentages of adult women who are overweight (including obese) are shown in Table 34 for various age groups.Let p be the percentage of women at age a years who are obese.a. Construct a scatterplot.b. Is there a linear association, a nonlinear association, or no association?c. Is the
The sea ice extent is the area of the ocean with at least 15% sea ice. The association between years since 1970 and the mean sea ice extent in the northern hemisphere in March is described by the scatterplot in Fig. 69. The association between years since 1970 and the mean sea ice extent in the
The association between years since 1995 and the numbers of fires in California within CAL FIRE jurisdiction is described by the scatterplot in Fig. 73. The association between years since 1995 and the numbers of thousands of acres burned is described by the scatterplot in Fig. 74.a. Is there a
a. Construct a scatterplot and compute r for the association of the variables x and y described in Table 35.b. Add 10 to each of the x values in Table 35. Then construct a scatterplot and compute r. How do the scatterplot and r com- pare to your results in part (a)? Why does this make sense?c. Add
a. Find r for the association of the variables x and y described in Table 36.b. Subtract 5 from each of the x values in Table 36. Then construct a scatterplot and compute r. How do the scatterplot and r compare to your results in part (a)? Why does this make sense?c. Subtract 2 from each of the y
A student says that if r = 0 for two variables, then there is no association between the variables. What would you tell the student?
State the four characteristics of an association and describe each one.
Some ordered pairs are listed in Table 46.Table 46 Some Ordered PairsXy1……………………133…………………….95…………………….87…………………….49…………………….2a. Construct a scatterplot by hand.b. Is there a linear association, a nonlinear association,
Some ordered pairs are listed in Table 47.Table 47 Some Ordered Pairsxy2……………………..43……………………..65……………………..67…………………….1110……………………13a. Construct a scatterplot by hand.b. Is there a linear association, a nonlinear
Some ordered pairs are listed in Table 48.Table 48 Some Ordered Pairsx
Some ordered pairs are listed in Table 49.Table 49 Some Ordered Pairsxy-10………………………….4-7…………………………..1-3………………………….-3-1………………………….-22……………………………-5a. Construct a scatterplot by hand.b. Is there a
Let n be the number (in thousands) of ride-related injuries at fixed-site amusement parks in the year that is t years since 2000. A scatterplot of some data and a linear model are sketched in Fig. 95.a. Use the linear model to estimate the number of ride- related injuries in 2004.b. What was the
Refer to Exercise 21, including Fig. 95.a. Use the linear model to estimate the number of ride-related injuries in 2002.b. What was the actual number of ride-related injuries in 2002?c. Is your result in part (a) an underestimate or an overestimate? Explain how you can tell this from the graph of
The scatterplot and linear model in Fig. 96 describe the prices of hot dogs and soft drinks at all Major League Baseball (MLB) stadiums.a. Use the linear model to predict the soft drink price at an MLB stadium that charges $4 for a hot dog.b. Use the linear model to predict the hot dog price at an
Figure 97 displays a scatterplot that compares the mean lengths and mean heights of 51 types of dinosaurs. There are two main categories (called orders) of dinosaurs: Saurischians and Ornithischians. Saurischians had a pelvis also found in modern lizards, whereas Ornithischians had a pelvis that
A scatterplot and linear model comparing the highway mile- ages and city mileages of 1159 conventional cars (neither hybrid nor electric) are displayed in Fig. 98.a. Use the linear model to predict the city mileage for a car with highway mileage 20 miles per gallon.b. Use the linear model to
The scatterplot and linear model in Fig. 99 describe the ages and years of experience of NFL football playersa. Use the linear model to predict the years of experience of a 30-year-old player.b. Use the linear model to predict the age of a player with 5 years of experience.c. Use the linear model
The total numbers of animal and plant species in the United States that are listed as endangered or threatened are shown in Table 50 for various years.Let n be the number of species that are listed as endangered or threatened at t years since 1980.a. Construct a scatterplot by hand.b. Is there a
The percentages of Americans who say there should be a ban on the possession of handguns are shown in Table 51 for various years.Let p be the percentage of Americans who say there should be a ban on the possession of handguns at t years since 1990.a. Construct a scatterplot by hand.b. Is there a
Due to improved technology and public-service campaigns, the number of collisions at highway€“railroad crossings per year has declined since 1992 (see Table 52).Let n be the number of collisions (in thousands) for the year that is t years since 1990.a. Construct a scatterplot by hand.b. Draw a
For a situation that can be described by a model whose explanatory variable is x, we perform ____ when we use a part of the model whose x-coordinates are not between the x-coordinates of any two data points.
Repeat Exercise 29, but let n be the number of collisions (in thousands) for the year that is t years since 1985. Which of your responses for this exercise are the same as those for Exercise 29? Explain why it makes sense that these responses are the same. Explain why it makes sense that the other
The percentages of Americans who believe marriages between same-sex couples should be recognized by the law as valid are shown in Table 53 for various age groups.Let p be the percentage of Americans at age a years who believe marriages between same-sex couples should be recognized by the law as
The percentages of Americans who currently have a personal profile page on a social networking website such as Facebook are shown in Table 54 for various age groups.Let p be the percentage of Americans at age a years who have a personal profile page.a. Construct a scatterplot by hand.b. Draw a
The loudness of sound can be measured by using a decibel scale. Some examples of sounds at various sound levels are listed in Table 55.The sound level of music from a Pioneer MT-2000® stereo- CD-receiver system is controlled by the system€™s volume number. The sound levels of music for various
The temperature at which water boils (the boiling point) depends on elevation: The higher the elevation, the lower the boiling point will be. At sea level, water boils at 212°F; at an elevation of 10,000 meters, water boils at about 151°F. Boiling points are listed in Table 57 for various
The discounts State Farm® offers to customers who have insured a vehicle with the company are shown in Table 58 for various years of loyalty.Let p be the discount (in percent) for customers who have insured a vehicle with the company for t years.a. Construct a scatterplot by hand and draw a model
The discounts State Farm offers to customers who have insured a vehicle with the company are shown in Table 58 for various years of loyalty.Let p be the discount (in percent) for customers who have insured a vehicle with the company for t years.a. Construct a scatterplot by hand, and draw a linear
The percentages of Americans who are satisfied with the way things are in the United States are shown in Table 59 for various years.Let p be the percentage of Americans at t years since 1990 who are satisfied with the way things are.a. Construct a scatterplot by hand and draw a linear model on the
The percentages of Americans living below the poverty level are shown in Table 61 for various years.Let p be the percentage of Americans living below the poverty level at t years since 1990.a. Construct a scatterplot by hand.b. Draw a linear model on your scatterplot.c. Use your model to estimate
The annual profits of Alaska Air Group are shown in Table 63 for various years.Let p be the annual profit (in millions of dollars) at t years since 2002.a. Without graphing, estimate the coordinates of the t-intercept for a line that comes close to the data points. What does that point mean in this
The windchill (or windchill factor) is a measure of how cold you feel as a result of being exposed to wind. Table 64 pro- vides some data on windchills for various temperatures when the wind speed is 10 mph.Let w be the windchill (in degrees Fahrenheit) corresponding to a temperature of t degrees
President Obama€™s statewide approval ratings and Democratic candidates€™ shares of votes in Senate races in 2010 and 2012 are compared in Table 65 for 12 randomly selected Senate races in recent years.Let P be President Obama€™s statewide approval rating (in per- cent) and D be a
The mean annual U.S. per-person consumptions of lower fat and skim milk and the mean annual U.S. per-person consumptions of whole milk are shown in Table 66 for various years.Let L be the mean annual consumption of lower fat and skim milk, and let W be the mean annual consumption of whole milk,
The heights, lengths, and maximum speeds of 11 randomly selected U.S. wooden roller coasters are shown in Table 67.Let H be a roller coaster€™s height (in feet), and let S be the roller coaster€™s maximum speed (in mph).a. Compare the heights and maximum speeds of the roller coasters by
The heights, lengths, and maximum speeds of 11 randomly selected U.S. wooden roller coasters are shown in Table 67 on page 419. Let H be a roller coaster’s height (in feet), and let L be the roller coaster’s length (in feet).a. Compare the values of H with the values of L by constructing a
The heights, lengths, and maximum speeds of 11 randomly selected U.S. wooden roller coasters are shown in Table 67 on page 419. Let S be a roller coaster’s maximum speed (in mph), and let L be the roller coaster’s length (in ft).a. Compare the values of S with the values of L by constructing a
The pedestrian and bicyclist fatality rates in 10 randomly selected large cities are shown in Table 68.Let p be a city€™s pedestrian fatality rate (in number of deaths per 10,000 walking commuters), and let b be the city€™s bicyclist fatality rate (in number of deaths per 10,000 bicycling
Access the data about head sizes versus brain weights, which are available at MyMathLab and at the Pearson Downloadable Student Resources for Math & Stats website. Treat head size as the explanatory variable and brain weight as the response variable.a. Construct a scatterplot that describes the
Access the data about the San Mateo Real Estate, which are available at MyMathLab and at the Pearson Downloadable Student Resources for Math & Stats website.a. Construct a scatterplot that describes the association between the square footages and the sales prices of the homes.b. Describe the
a. Sketch a nonvertical line in a coordinate system. Find any outputs for the given input. State how many outputs there are for that single input.i. The input 2ii. The input 4iii. The input -3b. For your line, a single input leads to how many outputs? Explain.c. For any nonvertical line, a single
Let s be the mean salary (in dollars) for people with t years of education.
The median sales prices of vacation and investment homes are shown in Table 74 for various years.Let V be the median sales price (in thousands of dollars) of vacation homes in a certain year, and let I be the median sales price (in thousands of dollars) of investment homes in the same year.a.
Some ordered pairs are listed in Table 75a. Construct a scatterplot by hand.b. Is there a linear association, a nonlinear associations, or neither?c. Draw a line that comes close to the points in your scatterplot.d. Find y when x = 4.e. Find x when y = 7.
After gaining enough experience to advance through a first salary schedule (A), police officers at the Los Angeles Police Department are paid annual salaries as described in Table 76 (Schedule 2). As police officers gain more experience, they receive step increases.Let s be the annual salary (in
Let c be the mean number of calories that a person consumes daily, and let w be the person’s mean weight (in pounds).
Willie Mays, with all-around talent, was one of the greatest baseball players of all time. The numbers of stolen bases by Mays are shown in Table 77 for various years.Let n be the number of stolen bases by Mays in the year that is t years since 1955.a. Construct a scatterplot by hand.b. Draw a
Let M be the number of miles a person runs weekly, and let T be the person’s best marathon time (in minutes). A marathoner runs 110 miles weekly, and her best marathon time is 139 minutes.Describe the situation with an ordered pair. Which variable should be described by the horizontal axis of a
Let s be the number (in thousands) of Starbucks stores, and let t be the number of years since 2010. There were 21.4 thou- sand Starbucks stores in 2014.Describe the situation with an ordered pair. Which variable should be described by the horizontal axis of a coordinate system? How about the
Let x be the explanatory variable and y be the response variable. Construct a scatterplot of the ordered pairs listed in Table 71.
Sepsis is the presence of harmful bacteria in a patient€™s tissue. The numbers of Medicare sepsis patients discharged between October 1, 2012, and September 30, 2013, are shown in Table 72 for various lengths of stays.Let d be the number of Medicare sepsis patients discharged after staying for
The gauge of an extension cord measures the diameter (thickness) of the wires inside. The maximum rates (in amperes) at which electric current can safely flow through 16-gauge extension cords are shown in Table 73 for various lengths of cords. Not following these guidelines can cause a fire from
Let p be the percentage of Americans at age a years who own a home. Identify the explanatory and the response variables. Which variable should be described by the horizontal axis of a coordinate system? How about the vertical axis?
The number of spacecraft, rocket bodies, mission-related debris, and fragmentation debris orbiting the Earth has in- creased greatly since the beginning of the Space Age in 1957. The numbers of such debris larger than 10 cm are shown in Table 81 for various years.Let n be the number (in thousands)
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