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Understanding Basic Statistics 6th Edition Charles Henry Brase, Corrinne Pellillo Brase - Solutions

Wetlands offer a diversity of benefits. They provide a habitat for wildlife, spawning grounds for U.S. commercial fish, and renewable timber resources. In the last 200 years, the United States has lost more than half its wetlands. Environmental Almanac gives the percentage of wetlands lost in each
The American Medical Association€™s Center for Health Policy Research, in its publication State Health Care Data: Utilization, Spending, and Characteristics, included data, by state, on the number of community hospitals and the average length of a patient stay (in days). The data are shown in
Using the number of hospitals per state listed in the table in Problem 3, make a stem-and-leaf display for the number of community hospitals per state. Which states have an unusually high number of hospitals?
The Boston Marathon is the oldest and best-known U.S. marathon. It covers a route from Hopkinton, Massachusetts, to downtown Boston. The distance is approximately 26 miles. Visit the Brase/Brase statistics site at www.cengagebrain.com and find the link to the Boston Marathon. Search the marathon
The U.S. Open Championship golf tournament was played at Congressional Country Club, Bethesda, Maryland, with prizes ranging from $465,000 for first place to $5000. Par for the course was 70. The tournament consisted of four rounds played on different days. The scores for each round of the 32
Use the data in Table 2-16 to make a stem-and-leaf display for milligrams of tar per cigarette smoked. Are there any outliers?
Use the data in Table 2-16 to make a stem-and-leaf display for milligrams of carbon monoxide per cigarette smoked. Are there any outliers?
Use the data in Table 2-16 to make a stem-and-leaf display for milligrams of nicotine per cigarette smoked. In this case, truncate the measurements at the tenths position and use two lines per stem. (See Problem 5, part (a).)
Many people say the civil justice system is overburdened. Many cases center on suits involving businesses. The following data are based on a Wall Street Journal report. Researchers conducted a study of lawsuits involving 1908 businesses ranked in the Fortune 1000 over a 20-year period. They found
The Sand Canyon Archaeological Project edited by W. D. Lipe and published by Crow Canyon Archaeological Center contains the stem-and-leaf diagram shown in Figure 2-19. The study uses tree rings to accurately determine the year in which a tree was cut. The figure gives the treering- cutting dates
A Harris Poll surveyed 2085 U.S. adults regarding use of cell phones while driving. All the adults were asked their opinion regarding how dangerous it is for a driver to use a cell phone while driving. Graph (a) shows the percentage responding €œvery dangerous€ by age group.
Solve the focus problem at the beginning of this chapter.
The time plot in Figure 2-18 gives the number of state and federal prisoners per 100,000 population (Source: Statistical Abstract of the United States, 120th edition).(a) Estimate the number of prisoners per 100,000 people for 1980 and for 1997.(b) Interpretation During the time period shown, there
Almost everyone files (or will someday file) a federal income tax return. A research poll for TurboTax (a computer software package to aid in tax-return preparation) asked what aspect of filing a return people thought to be the most difficult. The results showed that 43% of the respondents said
Driving under the influence of alcohol (DUI) is a serious offense. The following data give the ages of a random sample of 50 drivers arrested while driving under the influence of alcohol. This distribution is based on the age distribution of DUI arrests given in the Statistical Abstract of the
The following data represent trunk circumferences (in mm) for a random sample of 60 four-year-old apple trees at East Malling Agriculture Research Station in England (Reference: S. C. Pearce, University of Kent at Canterbury).(a) Make a frequency table with seven classes showing class limits, class
Consider two data sets.(a) Suppose the number 20 is included as an additional data value in Set A. data set, add 20 to ˆ‘x for the original data set and divide by 6. (b) Suppose the number 20 is included as an additional data value in Set B. (c) Why does the addition of the number 20 to
A job-performance evaluation form has these categories: 1= excellent; 2 = good; 3 = satisfactory; 4 = poor; 5 = unacceptable Based on 1= client reviews, one employee had median rating of 4; mode rating of 1. The employee was pleased that most clients had rated her as excellent. The supervisor said
In this problem, we explore the effect on the mean, median, and mode of adding the same number to each data value. Consider the data set 2, 2, 3, 6, 10.(a) Compute the mode, median, and mean.(b) Add 5 to each of the data values. Compute the mode, median, and mean.(c) Compare the results of parts
In this problem, we explore the effect on the mean, median, and mode of multiplying each data value by the same number. Consider the data set 2, 2, 3, 6, 10.(a) Compute the mode, median, and mean.(b) Multiply each data value by 5. Compute the mode, median, and mean.(c) Compare the results of parts
Consider a data set of 15 distinct measurements with mean A and median B. (a) If the highest number is increased, what is the effect on the median and mean? Explain. (b) If the highest number is decreased to a value still larger than B, what is the effect on the median and mean? Explain. (c) If the
How hot does it get in Death Valley? The following data are taken from a study conducted by the National Park System, of which Death Valley is a unit. The ground temperatures (oF) were taken from May to November in the vicinity of Furnace Creek.Compute the mean, median, and mode for these ground
How large is a wolf pack? The following information is from a random sample of winter wolf packs in regions of Alaska, Minnesota, Michigan, Wisconsin, Canada, and Finland (Source: The Wolf by L. D. Mech, University of Minnesota Press). Winter pack size:Compute the mean, median, and mode for the
The Grand Canyon and the Colorado River are beautiful, rugged, and sometimes dangerous. Thomas Myers is a physician at the park clinic in Grand Canyon Village. Dr. Myers has recorded (for a 5-year period) the number of visitor injuries at different landing points for commercial boat trips down the
How old are professional football players? The 11th edition of The Pro Football Encyclopedia gave the following information. Random sample of pro football players€™ ages in years:(a) Compute the mean, median, and mode of the ages.(b) Interpretation Compare the averages. Does one seem to
How expensive is Maui? If you want a vacation rentalcondominium (up to four people), visit the Brase/Brase statistics site atwww.cengagebrain.com, find the link to Maui, and then search for accommodations.The Maui News gave the following costs in dollars per day for a randomsample of condominiums
Find the weighted average of a data set where 10 has a weight of 5; 20 has a weight of 3; 30 has a weight of 2
Find the weighted average of a data set where 10 has a weight of 2; 20 has a weight of 3; 30 has a weight of 5
In your biology class, your final grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. There are 100 points available for each score. The lab score is worth 25% of your total grade, each major test is worth 22.5%, and the final exam is worth
At General Hospital, nurses are given performance evaluations to determine eligibility for merit pay raises. The supervisor rates the nurses on a scale of 1 to 10 (10 being the highest rating) for several activities: promptness, record keeping, appearance, and bedside manner with patients. Then an
Where does all the water go? According to the Environmental Protection Agency (EPA), in a typical wetland environment, 38% of the water is outflow, 47% is seepage, 7% evaporates, and 8% remains as water volume in the ecosystem (Reference: Environmental Protection Agency Report EPA 832-R-93-005).
When data consist of rates of change, such as speeds, the harmonic mean is an appropriate measure of central tendency. For n data values, Harmonic mean = n/∑1/x, assuming no data value is 0 Suppose you drive 60 miles per hour for 100 miles, then 75 miles per hour for 100 miles. Use the harmonic
When data consist of percentages, ratios, growth rates, or other rates of change, the geometric mean is a useful measure of central tendency. For n data values, Geometric mean = n√ product of the n data values, assuming all data values are positive To find the average growth factor over 5 years
If a data set has an even number of data, is it true or false that the median is never equal to a value in the data set? Explain.
Consider the following types of data that were obtained from a random sample of 49 credit card accounts. Identify all the averages (mean, median, or mode) that can be used to summarize the data. (a) Outstanding balance on each account (b) Name of credit card (e.g., MasterCard, Visa, American
Consider the numbers(a) Compute the mode, median, and mean.(b) If the numbers represent codes for the colors of T-shirts ordered from a catalog, which average(s) would make sense?(c) If the numbers represent one-way mileages for trails to different lakes, which average(s) would make sense?(d)
In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. Consider the data set 5, 9, 10, 11, 15. (a) Use the defining formula, the computation formula, or a calculator to compute s. (b) Add 5 to each data value to get the new
In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 5, 9, 10, 11, 15. (a) Use the defining formula, the computation formula, or a calculator to compute s. (b) Multiply each data value by 5 to
One indicator of an outlier is that an observation is more than 2.5 standard deviations from the mean. Consider the data value 80. (a) If a data set has mean 70 and standard deviation 5, is 80 a suspect outlier? (b) If a data set has mean 70 and standard deviation 3, is 80 a suspect outlier?
Given the sample data(a) Find the range. (b) Verify that ˆ‘x 5 110 and ˆ‘x2 5 2568. (c) Use the results of part (b) and appropriate computation formulas to compute the sample variance s2 and sample standard deviation s. (d) Use the defining formulas to compute the sample
(a) Compute the coefficient of variation.(b) Compute a 75% Chebyshev interval around the sample mean.
Consider population data with μ = 20 and σ = 2. (a) Compute the coefficient of variation. (b) Compute an 88.9% Chebyshev interval around the population mean.
Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Market Index Fund (all stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index Fund (60% stocks and 40%
Kevlar epoxy is a material used on the NASA space shuttles. Strands of this epoxy were tested at the 90% breaking strength. The following data represent time to failure (in hours) for a random sample of 50 epoxy strands (Reference: R. E. Barlow, University of California, Berkeley). Let x be a
The Hill of Tara in Ireland is a place of great archaeological importance. This region has been occupied by people for more than 4000 years. Geomagnetic surveys detect subsurface anomalies in the earth€™s magnetic field. These surveys have led to many significant archaeological discoveries.
For mallard ducks and Canada geese, what percentage of nests are successful (at least one offspring survives)? Studies in Montana, Illinois, Wyoming, Utah, and California gave the following percentages of successful nests (Reference: The Wildlife Society Press, Washington, D.C.):x: Percentage
Pax World Balanced is a highly respected, socially responsible mutual fund of stocks and bonds (see Viewpoint €œSocially Responsible Investing€). Vanguard Balanced Index is another highly regarded fund that represents the entire U.S. stock and bond market (an index fund). The
In some reports, the mean and coefficient of variation are given. For instance, in Statistical Abstract of the United States, 116th edition, one report gives the average number of physician visits by males per year. The average reported is 2.2, and the reported coefficient of variation is 1.5%. Use
What was the age distribution of prehistoric Native Americans? Extensive anthropological studies in the southwestern United States gave the following information about a prehistoric extended family group of 80 members on what is now the Navajo Reservation in northwestern New Mexico (Source: Based
What is the age distribution of adult shoplifters (21 years of age or older) in supermarkets? The following is based on information taken from the National Retail Federation. A random sample of 895 incidents of shoplifting gave the following age distribution: align="center">Estimate the mean
Alexander BorbÃ©ly is a professor at the University of Zurich Medical School, where he is the director of the sleep laboratory. The histogram in Figure 3-2 is based on information from his book Secrets of Sleep. The histogram displays hours of sleep per day for a random sample of 200
What are the big corporations doing with their wealth? One way to answer this question is to examine profits as percentage of assets. A random sample of 50 Fortune 500 companies gave the following information (Source: Based on information from Fortune, Vol. 135, No. 8):Estimate the sample mean,
You do not need a lot of money to invest in a mutual fund. However, if you decide to put some money into an investment, you are usually advised to leave it in for (at least) several years. Why? Because good years tend to cancel out bad years, giving you a better overall return with less risk. To
If you like mathematical puzzles or love algebra, try this! Otherwise, just trust that the computational formula for the sum of squares is correct. We have a sample of x values. The sample size is n. Fill in the details for the following steps.
Consider the data set(a) Find the range.(b) Use the defining formula to compute the sample standard deviation s.(c) Use the defining formula to compute the population standard deviation Ïƒ.
Consider the data set(a) Find the range. (b) Use the defining formula to compute the sample standard deviation s. (c) Use the defining formula to compute the population standard deviation Ïƒ.
For a given data set in which not all data values are equal, which value is smaller, s or σ? Explain.
(i) 8 9 10 11 12(ii) 7 9 10 11 13(iii) 7 8 10 12 13(a) Without doing any computations, order the data sets according to increasing value of standard deviations.(b) Why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard
What percentage of the general U.S. population are high school dropouts? The Statistical Abstract of the United States, 120th edition, gives the percentage of high school dropouts by state. For convenience, the data are sorted in increasing order.(a) Make a box-and-whisker plot and find the
Consumer Reports rated automobile insurance companies and listed annual premiums for top-rated companies in several states. Figure 3-9 shows box-and-whisker plots for annual premiums for urban customers (a married couple with one 17-year-old son) in three states. The box-and-whisker plots in Figure
Some data sets include values so high or so low that they seem to stand apart from the rest of the data. These data are called outliers. Outliers may represent data collection errors, data entry errors, or simply valid but unusual data values. It is important to identify outliers in the data set
Consider the following ordered data:(a) Find the low, Q1, median, Q3, and high. (b) Find the interquartile range. (c) Make a box-and-whisker plot.
Consider the following ordered data:(a) Find the low, Q1, median, Q3, and high.(b) Find the interquartile range.(c) Make a box-and-whisker plot.
At Center Hospital there is some concern about the high turnover of nurses. A survey was done to determine how long (in months) nurses had been in their current positions. The responses (in months) of 20 nurses wereMake a box-and-whisker plot of the data. Find the interquartile range.
Another survey was done at Center Hospital to determine how long (in months) clerical staff had been in their current positions. The responses (in months) of 20 clerical staff members were(a) Make a box-and-whisker plot. Find the interquartile range. (b) Compare this plot with the one in Problem 7.
What percentage of the general U.S. population have bachelor€™s degrees? The Statistical Abstract of the United States, 120th edition, gives the percentage of bachelor€™s degrees by state. For convenience, the data are sorted in increasing order:(a) Make a box-and-whisker plot
The pathogen Phytophthora capsici causes bell-pepper plants to wilt and die. A research project was designed to study the effect of soil water content and the spread of the disease in fields of bell peppers (Source: Journal of Agricultural, Biological, and Environmental Statistics, Vol. 2, No. 2).
A performance evaluation for new sales representatives at Office Automation Incorporated involves several ratings done on a scale of 1 to 10, with 10 the highest rating. The activities rated include new contacts, successful contacts, total contacts, dollar volume of sales, and reports. Then an
Look at the two histograms shown. Each involves the same number of data. The data are all whole numbers, so the height of each bar represents the number of values equal to the corresponding midpoint shown on the horizontal axis. Notice that both distributions are symmetrical.(a) Estimate the mode,
Consider the following Minitab display of two data sets: (a) What are the respective means? the respective ranges? (b) Which data set seems more symmetrical? Why? (c) Compare the interquartile ranges of the two sets. How do the middle halves of the data sets compare?
€œRadon: The Problem No One Wants to Face€ is the title of an article appearing in Consumer Reports. Radon is a gas emitted from the ground that can collect in houses and buildings. At certain levels it can cause lung cancer. Radon concentrations are measured in picocuries per
How Democratic is Georgia? County-by-county results are shown for a recent election. For your convenience, the data have been sorted in increasing order (Source: County and City Data Book, 12th edition, U.S. Census Bureau).Percentage of Democratic Vote by County in Georgia(a) Make a box-and-whisker
Professor Cramer determines a final grade based on attendance, two papers, three major tests, and a final exam. Each of these activities has a total of 100 possible points. However, the activities carry different weights. Attendance is worth 5%, each paper is worth 8%, each test is worth 15%, and
The following data represent weights in kilograms of maize harvested from a random sample of 72 experimental plots on St. Vincent, an island in the Caribbean (Reference: B. G. F. Springer, Proceedings of the Caribbean Food Crops Society, Vol. 10, pp. 147€“152).(a) Compute the five-number
Solve the focus problem at the beginning of this chapter. Discuss.
Over the past 30 years in the United States, there has been a strong negative correlation between the number of infant deaths at birth and the number of people over age 65. (a) Is the fact that people are living longer causing a decrease in infant mortalities at birth? (b) What lurking variables
Trevor conducted a study and found that the correlation between the price of a gallon of gasoline and gasoline consumption has a linear correlation coefficient of −0.7. What does this result say about the relationship between price of gasoline and consumption? The study included gasoline prices
Do people who spend more time on social networking sites spend more time using Twitter? Megan conducted a study and found that the correlation between the times spent on the two activities was 0.8. What does this result say about the relationship between times spent on the two activities? If
How much should a healthy Shetland pony weigh? Let x be the age of the pony (in months) and let y be the average weight of the pony (in kilograms). The following information is based on data taken from The Merck Veterinary Manual (a reference used in most veterinary colleges):(a) Make a scatter
The following data are based on information from Domestic Affairs. Let x be the average number of employees in a group health insurance plan, and let y be the average administrative cost as a percentage of claims.(a) Make a scatter diagram and draw the line you think best fits the data. (b) Would
Can a low barometer reading be used to predict maximum wind speed of an approaching tropical cyclone? Data for this problem are based on information taken from Weatherwise (Vol. 46, No. 1), a publication of the American Meteorological Society. For a random sample of tropical cyclones, let x be the
Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Let x be the magnitude of an earthquake (on the Richter scale), and let y be the depth (in kilometers) of the quake below the surface at the epicenter. The following is based on information taken
In baseball, is there a linear correlation between batting average and home run percentage? Let x represent the batting average of a professional baseball player, and let y represent the player€™s home run percentage (number of home runs per 100 times at bat). A random sample of n = 7
Do larger universities tend to have more property crime? University crime statistics are affected by a variety of factors. The surrounding community, accessibility given to outside visitors, and many other factors influence crime rates. Let x be student enrollment (in thousands) on a university
The initial visual impact of a scatter diagram depends on the scales used on the x and y axes. Consider the following data:(a) Make a scatter diagram using the same scale on both the x and y axes (i.e., make sure the unit lengths on the two axes are equal). (b) Make a scatter diagram using a scale
Examine the computation formula for the sample correlation coefficient r [formulas (1) and (2)].(a) In the formula for r, if we exchange the symbols x and y, do we get a different result or do we get the same (equivalent) result? Explain.(b) If we have a set of x and y data values and we exchange
The correlation coefficient r is a sample statistic. What does it tell us about the value of the population correlation coefficient p (Greek letter rho)? We will build the formal structure of hypothesis tests of p in Section 11.4. However, there is a quick way to determine if the sample evidence
In this problem, we use Table 4-6 to explore the significance of r based on different sample sizes. (a) Is a sample correlation coefficient r = 0.820 significant at the α = 0.01 level based on a sample size of n = 7 data pairs? What about n = 9 data pairs? (b) Is a sample correlation coefficient
Fuming because you are stuck in traffic? Roadway congestion is a costly item, in both time wasted and fuel wasted. Let x represent the average annual hours per person spent in traffic delays and let y represent the average annual gallons of fuel wasted per person in traffic delays. A random sample
Describe the relationship between two variables when the correlation coefficient r is (a) near 21. (b) near 0. (c) near 1.
Look at the following diagrams. Does each diagram show high linear correlation, moderate or low linear correlation, or no linear correlation?(a)(b) (c)
Look at the following diagrams. Does each diagram show high linear correlation, moderate or low linear correlation, or no linear correlation?(a)(b) (c)
Over the past few years, there has been a strong positive correlation between the annual consumption of diet soda drinks and the number of traffic accidents. (a) Do you think increasing consumption of diet soda drinks causes traffic accidents? Explain. (b) What lurking variables might be causing
Over the past decade, there has been a strong positive correlation between teacher salaries and prescription drug costs. (a) Do you think paying teachers more causes prescription drugs to cost more? Explain. (b) What lurking variables might be causing the increase in one or both of the variables?
Over the past 50 years, there has been a strong negative correlation between average annual income and the record time to run 1 mile. In other words, average annual incomes have been rising while the record time to run 1 mile has been decreasing. (a) Do you think increasing incomes cause decreasing
Data for this problem are based on information from STATS Basketball Scoreboard. It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls that were more than (i.e., over and above) the number of fouls
Data for this problem are based on information taken from The Wall Street Journal. Let x be the age in years of a licensed automobile driver. Let y be the percentage of all fatal accidents (for a given age) due to speeding. For example, the first data pair indicates that 36% of all fatal accidents
Let x be the age of a licensed driver in years. Let y be the percentage of all fatal accidents (for a given age) due to failure to yield the right-of-way. For example, the first data pair states that 5% of all fatal accidents involving 37-year-olds are due to failure to yield the right-of-way. The
Let x be per capita income in thousands of dollars. Let y be the number of medical doctors per 10,000 residents. Six small cities in Oregon gave the following information about x and y (Based on information from The Rating Guide to Life in America€™s Small Cities by G. S. Thomas,
Does prison really deter violent crime? Let x represent percent change in the rate of violent crime and y represent percent change in the rate of imprisonment in the general U.S. population. For 7 recent years, the following data have been obtained (Source: The Crime Drop in America, edited by

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