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Fundamentals Of Statistics 4th Edition Michael Sullivan III - Solutions

The weight, in grams, of the pair of kidneys in adult males between the ages of 40 and 49 has a bell-shaped distribution with a mean of 325 grams and a standard deviation of 30 grams. (a) About 95% of kidney pairs will be between what weights? (b) What percentage of kidney pairs weighs between 235
The distribution of the length of bolts has a bell shape with a mean of 4 inches and a standard deviation of 0.007 inch. (a) About 68% of bolts manufactured will be between what lengths? (b) What percentage of bolts will be between 3.986 inches and 4.014 inches? (c) If the company discards any
Suppose Professor Alpha and Professor Omega each teach Introductory Biology. You need to decide which professor to take the class from and have just completed your Introductory Statistics course. Records obtained from past students indicate that students in Professor Alpha’s class have a mean
Lawrence Summers (former secretary of the treasury and former president of Harvard) infamously claimed that women have a lower standard deviation IQ than men. He went on to suggest that this was a potential explanation as to why there are fewer women in top math and science positions. Suppose an IQ
In December 2010, 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
According to the U.S. Census Bureau, the mean of the commute time to work for a resident of Boston, Massachusetts's 27.3 minutes. Assume that the standard deviation of the commute time is 8.1 minutes to answer the following: (a) What minimum percentage of commuters in Boston has a commute time
The standard deviation of batting averages of all teams in the American League is 0.008. The standard deviation of all players in the American League is 0.02154. Why is there less variability in team batting averages?
Benjamin owns a small Internet business. Besides himself, he employs nine other people. The salaries earned by the employees are given next in thousands of dollars (Benjamin€™s salary is the largest, of course):(a) Determine the range, population variance, and population standard
Each of the following three data sets represents the IQ scores of a random sample of adults. IQ scores are known to have a mean and median of 100. For each data set, determine the sample standard deviation. Then recompute the sample standard deviation assuming that the individual whose IQ is 106 is
Another measure of variation is the mean absolute deviation. It is computed using the formulaCompute the mean absolute deviation of the data in Problem 11 and compare the results with the sample standard deviation.
Karl Pearson developed a measure that describes the skewness of a distribution, called the coefficient of skewness. The formula is Skewness = 3(mean — median) /standard deviation The value of this measure generally lies between -3 and +3. The closer the value lies to -3, the more the distribution
A popular theory in investment states that you should invest a certain amount of money in foreign investments to reduce your risk. The risk of a portfolio is defined as the standard deviation of the rate of return. Refer to the following graph, which depicts the relation between risk (standard
The data set on the left represents the annual rate of return (in percent) of eight randomly sampled bond mutual funds, and the data set on the right represents the annual rate of return (in percent) of eight randomly sampled stock mutual funds.(a) Determine the mean and standard deviation of each
What is meant by the phrase degrees of freedom as it pertains to the computation of the sample standard deviation?
In one of Sullivan’s statistics sections, the standard deviation of the heights of all students was 3.9 inches. The standard deviation of the heights of males was 3.4 inches and the standard deviation of females was 3.3 inches. Why is the standard deviation of the entire class more than the
Explain how standard deviation measures spread. In your explanation include the computation of the same standard deviation for two data sets:Data set 1:3,4,5;Data set 2:0,4,8.
Draw two histograms with different standard deviations and label them I and II. Which histogram has the larger standard deviation?
In 2000, the Walt Disney Company created the “fast pass.” A fast-pass ticket is issued to a rider for the popular rides and the rider is told to return at a specific time during the day. At that time, the rider is allowed to by-pass the regular line, thereby reducing the wait time for that
The following frequency distribution represents the birth weight of all babies born in the United States in 2004. Approximate the mean and standard deviation birth weight.Weight (grams) ....Number of Babies (thousands)0-999 ........ 301000-1999 ...... 972000-2999 ....... 9353000-3999
The frequency distribution below represents the square footage of a random sample of 500 houses that are owner occupied year round. Approximate the mean and standard deviation square footage.Square Footage ....Frequency0-499 .......... 5500-999 ........ 171000-1499 ....... 361500-1999
Often, frequency distributions are reported using unequal class widths because the frequencies of some groups would otherwise be small or very large. Consider the following data, which represent the daytime household temperature the thermostat is set to when someone is home for a random sample of
The frequency distribution on the following page represents the age of people living in poverty in 2009 (in thousands). In this frequency distribution, the class widths are not the same for each class. Approximate the mean and standard deviation age of a person living in poverty. For the open-ended
The following data represent the number of live multiple-delivery births in 2007 for women 15 to 54 years old.Age .....Number of Multiple Births15–19 ..... 10020-24 ..... 46725–29 ....162030-34 ....226235–39 ...154540-44 .... 32845–49 .... 8550-54 ... 20(a) Approximate the mean and standard
The following data represent SAT Mathematics scores for 2010.SAT Math Score ....Number200-299 ....... 36,305300-399 ....... 193,968400-499 ....... 459,010500-599 ....... 467,855600-699 ...... 286,518700-800 .... 104,334(a) Approximate the mean and standard deviation of the score.(b) Draw a
Use the frequency distribution whose class width is 0.5 obtained in Problem 37 in Section 2.2 to approximate the mean and standard deviation for cigarette tax rate& Comparel these results to the actual mean and standard deviation.
Use the frequency distribution whose class width is 0.4 obtained in Problem 38 in Section 2.2 to approximate the mean and standard deviation of the dividend yield. Compare these results to the actual mean and standard deviation.
Marissa has just completed her second semester in college. She earned a B in her 5-hour calculus course, an A in her 3-hour social work course, an A in her 4-hour biology course, and a C in her 3-hour American literature course. Assuming that an A equals 4 points, a B equals 3 points, and a C
In Marissa's calculus course, attendance counts for 5% of the grade, quizzes count for 10% of the grade, exams count for 60% of the grade, and the final exam counts for 25% of the grade. Marissa had a 100% average for attendance, 93% for quizzes, 86% for exams, and 85% on the final. Determine
Michael and Kevin want to buy chocolates. They can't agree on whether they want chocolate—covered almonds, chocolate-covered peanuts, or chocolate-covered raisins.They agree to create a mix. They bought 4 pounds of chocolate-covered almonds at $3.50 per pound, 3 pounds of chocolate-covered
Michael and Kevin return to the candy store, but this time they want to purchase nuts. They can't decide among peanuts, cashews, or almonds. They again agree to create a mix. They bought 2.5 pounds of peanuts for $1.30 per pound, 4 pounds of cashews for $4.50 per pound, and 2 pounds of almonds for
The following data represent the male and female population, by age, of the United States in 2008.(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 2007.(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 2007. (c) Which year has the higher mean age?
Approximate the median of the frequency distribution in Problem 1.Weight (grams) ....Number of Babies (thousands)0-999 ........ 301000-1999 ...... 972000-2999 ....... 9353000-3999 .......26984000-4999 ....... 3445000-5999 ....... 5Use the following steps to approximate the median from grouped
Approximate the median of the frequency distribution in Problem 2.Square Footage .... Frequency0-499 .......... 5500-999 ........ 171000-1499 ....... 361500-1999 ....... 1212000-2499 ...... 1192500-2999 ....... 813000-3499 ....... 473500-3999 ...... 454000-4499 ....... 224500-4999
Approximate the median of the frequency distribution in Problem 3.Temperature (Â°F) ....Frequency61-64 ......... 3165-67 ......... 6768-69 .......19870 .........19571-72 ........12073-76 ......... 8977-80 ......... 50Use the following steps to approximate the median from grouped
Approximate the median of the frequency distribution in Problem 4.Age .....Frequency0-17 ......15,45118â€“24 ..... 607125â€“34 .... 612335â€“44 .... 475645â€“54 .... 442155â€“59 ..... 179260-64 .... 152065 and older .. 3433Use the following steps to approximate the median
Determine the modal class of the frequency distribution in Problem 1.Weight (grams) ....Number of Babies (thousands)0-999 ........ 301000-1999 ...... 972000-2999 ....... 9353000-3999 .......26984000-4999 ....... 3445000-5999 ....... 5Use the following definition of the modal class. The modal class
Determine the modal class of the frequency distribution in Problem 2. Weight (grams) .... Number of Babies (thousands) 0-999 ........ 30 1000-1999 ...... 97 2000-2999 ....... 935 3000-3999 ....... 2698 4000-4999 ....... 344 5000-5999 ....... 5 Use the following definition of the
In 2010, babies born after a gestation period of 32 to 35 weeks had a mean weight of 2600 grams and a standard deviation of 660 grams. In the same year, babies born after a gestation period of 40 weeks had a mean weight of 3500 grams and a standard deviation of 470 gram& Suppose a 34-week gestation
In 2010, babies born after a gestation period of 32 to 35 weeks had a mean weight of 2600 grams and a standard deviation of 660 grams. In the same year, babies born after a gestation period of 40 weeks had a mean weight of 3500 grams and a standard deviation of 470 grams. Suppose a 34-week
The average 20-to-29 year old man is 69.6 inches tall, with a standard deviation of 3.0 inches, while NW the average 20- to 29-year-old woman is 64.1 inches tall, with a standard deviation of 3.8 inches. Who is relatively taller, a 75-inch man or a 70-inch woman?
The average 20- to 29-year-old man is 69.6 inches tall, with a standard deviation of 3.0 inches, while the average 20- to 29-year-old woman is 64.1 inches tall, with a standard deviation of 3.8 inches. Who is relatively taller, a 67-inch man or a 62-inch woman?
In 2010, Josh Johnson of the Florida Marlins 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 2.30. Also in 2010, Felix Hernandez of the Seattle Mariners had the lowest ERA of any
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 2010, Josh Hamilton was the American League batting champion, with a batting average of 0.359.
The 2010 Indianapolis 500 was a very competitive race with 1 minute separating the time between the winning car and fourteenth car to finish the race. The mean finishing time of cars in the Indy 500 was 186.15 minutes with a standard deviation of 0.359 minute. The winning car, driven by Dario
Roberto finishes a triathlon (750-meter swim, 5-kilometer run, and 20-kilometer bicycle) in 63.2 minutes. Among all men in the race, the mean finishing time was 69.4 minutes with a standard deviation of 8.9 minutes. Zandra finishes the same triathlon in 79.3 minutes. Among all women in the race,
A highly selective boarding school will only admit students who place at least 1.5 standard deviations above the mean on a standardized test that has a mean of 200 and a standard deviation of 26. What is the minimum score that an applicant must make on the test to be accepted?
A manufacturer of bolts has a quality- control policy that requires it to destroy any bolts that are more than 2 standard deviations from the mean. The quality-control engineer knows that the bolts coming off the assembly line have a mean length of 8 cm with a standard deviation of 0.05 cm. For
Explain the meaning of the following percentiles. Source: Advance Data from Vital and Health Statistics(a) The 15th percentile of the head circumference of males 3 to 5 months of age is 41.0 cm.(b) The 90th percentile of the waist circumference of females 2 years of age is 52.7 cm.(c) Anthropometry
Explain the meaning of the following percentiles. (a) The 5th percentile of the weight of males 36 months of age is 12.0 kg. (b) The 95th percentile of the length of newborn females is 53.8 cm.
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 2009.(a) Provide an interpretation of these results. (b) Determine and interpret
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 2010 semester in a College Algebra class at Joliet
The following graph is an ogive of IQ scores. The vertical axis in an ogive is the cumulative relative frequency and can also be interpreted as a percentile.(a) Find and interpret the percentile rank of an individual whose IQ is 100. (b) Find and interpret the percentile rank of an individual whose
The following graph is an ogive of the, mathematics scores on the SAT for the class of 2010. The vertical axis in an ogive is the cumulative relative frequency and can also be interpreted as a percentile.(b) Find and interpret the percentile rank of a student who scored 750 on the SAT mathematics
The following data represent the miles per gallon of a random sample of SMART cars with a three-cylinder, 1.0-liter engine.(a) Compute the z-score corresponding to the individual who obtained 36.3 miles per gallon. Interpret this result. (b) Determine the quartiles. (c) Compute and interpret the
The following data represent the hemoglobin (in g/dL) for 20 randomly selected cats.(a) Compute the z-score corresponding to the hemoglobin of Blackie, 7.8 g/dL. Interpret this result. (b) Determine the quartiles. (c) Compute and interpret the interquartile range, IQR. (d) Determine the lower and
In sports betting, Las Vegas sports books establish winning margins for a team that is favored to win a game. An individual can place a wager on the game and will win if the team bet upon wins after accounting for the spread. For example, if Team A is favored by 5 points and wins the game by 7
A nutritionist was interested in developing a model that describes the relation between the amount of fat (in grams) in cheeseburgers at fast-food restaurants and the number of calories. She obtains the following data from the Web sites of the companies.(a) The researcher wants to use fat content
The following data represent the square footage and rent for apartments in the borough of Queens and Nassau County, New York.(a) On the same graph, draw a scatter diagram for both Queens and Nassau County apartments treating square footage as the explanatory variable. Be sure to use a different
Using the data and results from Problem 2, do the following:(a) Find the least-squares regression line treating fat content as the explanatory variable. (b) Draw the least-squares regression line on the scatter diagram. (c) Interpret the slope and y-intercept, if appropriate. (d) Predict the number
Using the Queens data and results from Problem 3, do the following:(a) Find the least-squares regression line, treating square footage as the explanatory variable.(b) Interpret the slope and y-intercept, if appropriate.(c) Is the rent on the 825-square-foot apartment in the data above or below
(a) Draw a scatter diagram treating x as the explanatory variable and y as the response variable.(b) Select two points from the scatter diagram, and ï¬nd the equation of the line containing the points selected.(c) Graph the line found in part (b) on the scatter diagram.(d) Determine the
Use the results from Problem 2 to compute and interpret R2.
Use Queens data and the results from Problems 3 and 5 to compute and interpret R2.
The correlation between the number of visitors to the state of Florida and the number of shark attacks since 1990 is 0.946. Should the number of visitors to Florida be reduced in an attempt to reduce shark attacks? Explain your reasoning.
Are you more likely to be satisï¬ed with your automobile purchase when it is new or used? The following data represent the level of satisfaction of the buyer for both new and used cars.(a) How many were extremely satisï¬ed with their automobile purchase?(b) Construct a relative frequency
Recessions are an economic phenomenon that are often deï¬ned as two consecutive quarters of reduced national output. One measure to assess the severity of a recession is the rate of unemployment. The table shows the number of employed and unemployed residents of the United States at the peak of
(a) The correlation between number of married residents and number of unemployed residents in 2008 for the 50 states and Washington, DC, is 0.922. A scatter diagram of the data drawn in MINITAB is shown on the following page. What type of relation appears to exist between number of marriages and
List the eight properties of the linear correlation coefﬁcient.
In a newspaper article written in the Chicago Tribune on September 29, 2002, it was claimed that poorer school districts have shorter school days.(a) The least-squares regression line between length, y, and income, x, is y-hat = -0.0102 x + 7.11. Interpret the slope of this regression line. Does it
Crickets make a chirping noise by sliding their wings rapidly over each other. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following data list the temperature (in degrees Fahrenheit) and the number of chirps per second for the striped ground
What is the relationship between education and belief in Heaven? The data on the following page represent the highest level of education and belief in Heaven for a random sample of adult Americans.(a) Construct a relative frequency marginal distribution. (b) What proportion of adult Americans in
Consider the following contingency table, which relates the number of applicants accepted to a college and gender.(a) Construct a conditional distribution of acceptance status by gender.(b) What proportion of males was accepted? What proportion of females was accepted?(c) What might you conclude
What does it mean if a linear correlation coefﬁcient is close to zero? Draw two scatter diagrams for which the linear correlation coefﬁcient is close to zero.
Match the linear correlation coefï¬cient to the scatter diagrams. The scales on the x- and y-axes are the same for each diagram.(a) r = 0.787(b) r = 0.523(c) r = 0.053(d) r = 0.946
Match the linear correlation coefï¬cient to the scatter diagram. The scales on the x- and y-axes are the same for each diagram.(a) r = -0.969(b) r = -0.049(c) r = -1(d) r = -0.992
The scatter diagram drawn in MINITAB shows the relation between the percentage of the population of astate plus Washington, DC, that has at least a bachelor€™s degree and the median income (in dollars) of the state for 2009. (a) Describe any relation that exists between level of
The following scatter diagram drawn in StatCrunch shows the relation between median income (in dollars) in a state and birthrate (births per 1000 women 15 to 44 years old).(a) Describe any relation that exists between median income and birthrate. (b) One observation sticks out from the rest. Which
(a) Draw a scatter diagram of the data,(b) By hand, compute the correlation coefï¬cient, and(c) Determine whether there is a linear relation between x and y.
(a) Draw a scatter diagram of the data,(b) By hand, compute the correlation coefï¬cient, and(c) Determine whether there is a linear relation between x and y.
(a) Draw a scatter diagram of the data,(b) By hand, compute the correlation coefï¬cient, and(c) Determine whether there is a linear relation between x and y.
(a) Draw a scatter diagram of the data,(b) By hand, compute the correlation coefï¬cient, and(c) Determine whether there is a linear relation between x and y.
For each of the following statements, explain whether you think the variables will have positive correlation, negative correlation, or no correlation. Support your opinion. (a) Number of children in the household under the age of 3 and expenditures on diapers (b) Interest rates on car loans and
For each of the following statements, explain whether you think the variables will have positive correlation, negative correlation, or no correlation. Support your opinion. (a) Number of cigarettes smoked by a pregnant woman each week and birth weight of her baby (b) Years of education and annual
The Trends in International Mathematics and Science (TIMMS) is a mathematics and science achievement exam given internationally. On each exam, students are asked to respond to a variety of background questions. For the 41 nations that participated in TIMMS, the correlation between the percentage of
The Gallup Organization regularly surveys adult Americans regarding their commute time to work. In addition, they administer a Well-Being Survey. According to the Gallup Organization, “The Gallup-Healthways Well-Being Index Composite Score is comprised of six sub-indices: Life Evaluation,
Fair Isaacs Corporation (FICO) credit score is used to determine your creditworthiness. It is used to help determine whether you qualify for a mortgage or credit and is even used to determine insurance rates. FICO scores have a range of 300 to 850, with a higher score indicating a better credit
The American black bear (Ursus americanus) is one of eight bear species in the world. It is the smallest North American bear and the most common bear species on the planet. In 1969, Dr. Michael R. Pelton of the University of Tennessee initiated a long-term study of the population in the Great Smoky
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 2011 model year.(a) Draw a scatter diagram treating the length of the right humerus as the explanatory variable
Research performed at NASA and led by Emily R. Morey-Holton measured the lengths of the right humerus and right tibia in 11 rats that were sent to space on Spacelab Life Sciences 2. The following data were collected.(a) Draw a scatter diagram treating the length of the right humerus as the
The data on the following page represent the total compensation for 10 randomly selected chief executive ofï¬cers (CEO) and the companyâ€™s stock performance in 2009.(a) One would think that a higher stock return would lead to a higher compensation. Based on this, what would likely be the
A doctor wanted to determine whether a relation exists between a male€™s age and his HDL (so-called good) cholesterol. He randomly selected 17 of his patients and determined their HDL cholesterol levels. He obtained the following data.(a) Draw a scatter diagram of the data treating age as
Researchers wondered whether the size of a personâ€™s brain was related to the individualâ€™s mental capacity. They selected a sample of right-handed introductory psychology students who had SAT scores higher than 1350. The subjects took the Wechsler Adult Intelligence Scale-Revised to
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.(a) On the same graph, draw a scatter diagram for both males and females. Be sure to use a different plotting symbol for each group. For example, use a
Miles per Gallon Suppose that we add the Ford Taurus to the data in Problem 29. A Ford Taurus weighs 3305 pounds and gets 19 miles per gallon.(a) Redraw the scatter diagram with the Taurus included.(b) Recompute the linear correlation coefï¬cient with the Taurus included.(c) Compare the results
The Web site that contained the American black bear data listed in Problem 28 actually had a bear whose height is 141.0 cm and weight is 100 kg incorrectly listed as 41.0 cm tall.Total Length (cm) .....Weight (kg)139.0 ..........110138.0 .......... 60139.0 .......... 90120.5 .......... 60149.0
Consider the four data sets shown below.(a) Compute the linear correlation coefï¬cient for each data set.(b) Draw a scatter diagram for each data set. Conclude that linear correlation coefï¬cients and scatter diagrams must be used together in any statistical analysis of bivariate data.
One basic theory of investing is diversiï¬cation. The idea is that you want to have a basket of stocks that do not all â€œmove in the same direction.â€ In other words, if one investment goes down, you don't want a second investment in your portfolio that is also likely to go down. One
Lyme disease is an inï¬‚ammatory disease that results in a skin rash and ï¬‚ulike symptoms. It is transmitted through the bite of an infected deer tick. The following data represent the number of reported cases of Lyme disease and thenumber of drowning deaths for a rural county in the
Based on data obtained from the CIA World Factbook, the linear correlation coefﬁcient between the number of television stations in a country and the life expectancy of residents of the country is 0.599. What does this correlation imply? Do you believe that the more television stations a country

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