Question: Consider a data set with m observations.

> Some data sets contain outliers, observations that fall well outside the overall pattern of the data. Suppose, for instance, that you are interested in the ability of high school algebra students to compute square roots. You decide to give a square-root

> As you discovered earlier, ordinal data are data about order or rank given on a scale such as 1, 2, 3, or A, B, C,.... Most statisticians recommend using the median to indicate the center of an ordinal data set, but some researchers also use the mean. In

> Anthropologists are still trying to unravel the mystery of the origins of the Etruscan empire, a highly advanced Italic civilization formed around the eighth century B.C. in central Italy. Were they native to the Italian peninsula or, as many aspects of

> L. Petersen et al. evaluated the effects of integrated treatment for patients with a first episode of psychotic illness in the paper “A Randomised Multicentre Trial of Integrated Versus Standard Treatment for Patients with a First Episode of Psychotic Il

> A study by researchers at the University of Maryland addressed the question of whether the mean body temperature of humans is 98.6◦F. The results of the study by P. Mackowiak et al. appeared in the article “A Critical Appraisal of 98.6◦F, the Upper Limit

> Refer to Exercise 1.44. a. List the 20 possible samples (without replacement) of three artists that can be selected from the six. b. Describe a procedure for taking a simple random sample of three artists from the six. c. If a simple random sampling proc

> Consider the data set 1, 2, 3, 4, 5, 6, 7, 8, 9. a. Obtain the mean and median of the data. b. Replace the 9 in the data set by 99 and again compute the mean and median. Decide which measure of center works better here and explain your answer. c. For the

> As reported by the U.S. Census Bureau in Educational Attainment in the United States, the percentage of adults in each state and the District of Columbia who have completed a bachelor’s degree is provided on the WeissStats site. Use the technology of you

> As reported by the U.S. Census Bureau in Educational Attainment in the United States, the percentage of adults in each state and the District of Columbia who have completed high school is provided on the WeissStats site. Use the technology of your choice

> In the article, “Length of The Beatles’ Songs” (Chance, Vol. 25, No. 1, pp. 30–33), T. Koyama discusses aspects and interpretations of the lengths of songs by The Beatles. Data on the length, in seconds, of 229 Beatles’ songs are presented on the WeissSt

> Consider the following data set. a. Draw a graph. b. Compare the percentage of the observations that actually lie within two standard deviations to either side of the mean with that given by Chebyshev’s rule with k = 2. c. Repeat part (b) with k = 3.

> On the Celebrity Net Worth website, we found the article “The 10 Highest Earning Dead Celebrities” by G. Golden. According to the article, the highest earning dead celebrities in 2012 are as shown in the following table. What type of data is presented in

> In an article titled “Great White, Deep Trouble” (National Geographic, Vol. 197(4), pp. 2–29), Peter Benchley—the author of JAWS—discussed various aspects of the Great White Shark (Carcharodon carcharias). Data on the number of pups borne in a lifetime b

> In Issue 338 of the Amstat News, then president of the American Statistical Association Fritz Scheuren reported the results of a survey on how members would prefer to receive ballots in annual elections. On the WeissStats site, you will find data for pre

> Research by W. Clark and L. Midanik (Alcohol Consumption and Related Problems: Alcohol and Health Monograph 1. DHHS Pub. No. (ADM) 82–1190) examined, among other issues, alcohol consumption patterns of U.S. adults by marital status. Data for marital stat

> The American Hospital Association conducts annual surveys of hospitals in the United States and publishes its findings in AHA Hospital Statistics. Data on hospital type for U.S. registered hospitals can be found on the WeissStats site. For convenience, w

> The Japan Automobile Manufacturer’s Association provides data on exported vehicles in Motor Vehicle Statistics of Japan. In 2010, cars, trucks, and buses constituted 88.3%, 9.3%, and 2.4% of vehicle exports, respectively. A random sample of last year’s e

> An American roulette wheel contains 18 red numbers, 18 black numbers, and 2 green numbers. The following table shows the frequency with which the ball landed on each color in 200 trials. a. determine the mode of the data. b. decide whether it would be ap

> Refer to Exercise 1.44. a. List the 15 possible samples (without replacement) of four artists that can be selected from the six. b. Describe a procedure for taking a simple random sample of four artists from the six. c. If a simple random sampling proced

> The Association of American Medical Colleges (AAMC) compiles data on medical school faculty and publishes the results in AAMC Faculty Roster. The following table presents a frequency distribution of rank for medical school faculty during one year. a. det

> True or false: The mean, median, and mode can all be used with quantitative data. Explain your answer.

> The Higher Education Research Institute of the University of California, Los Angeles, publishes information on characteristics of incoming college freshmen in The American Freshman. In 2000, 27.7% of incoming freshmen characterized their political views

> Consider the following data set. a. Draw a graph similar to Fig. 3.5 on page 111. b. Compare the percentage of the observations that actually lie within two standard deviations to either side of the mean with that given by Chebyshev’s rule with k = 2. c.

> The Department of Justice and the Federal Bureau of Investigation publish a compilation on crime statistics for the United States in Crime in the United States. The following table provides a frequency distribution for robbery type during a one-year peri

> From Wikipedia, we found that the law schools of the justices of the U.S. Supreme Court, as of September 9, 2013, are as follows. a. determine the mode of the data. b. decide whether it would be appropriate to use either the mean or the median as a measu

> The report Controlling Road Rage: A Literature Review and Pilot Study was prepared for the AAA Foundation for Traffic Safety by D. Rathbone and J. Huckabee. The authors discussed the results of a literature review and pilot study on how to prevent aggres

> From NCAA.com—the official Web site for NCAA sports—we obtained the National Collegiate Athletic Association wrestling champions for the years 1989–2013 in the document “Championship History”. They are displayed in the following table. a. determine the m

> From the TVbytheNumbers website, we obtained the networks for the top 20 primetime broadcast TV shows by total viewership for the week ending August 18, 2013. a. determine the mode of the data. b. decide whether it would be appropriate to use either the

> From Wikipedia, we found that the ages of the justices of the U.S. Supreme Court, as of September 9, 2013, are as follows, in years. a. Find n. b. Compute Σxi . c. Determine the sample mean. Round your answer to one more decimal place than that used for

> Pesticides are chemicals often used in agriculture to control pests. In Pakistan, 70% of the population depends on agriculture, and pesticide use there has increased rapidly. In the article, “Monitoring Pesticide Residues in Fresh Fruits Marketed in Pesh

> The Recording Industry Association of America provides data on the best-selling albums of all time. As of May 28, 2013, the top six best-selling albums of all time (U.S. sales only), are by the artists the Eagles (E), Michael Jackson (M), Pink Floyd (P),

> In 1908, W. S. Gosset published the article “The Probable Error of a Mean” (Biometrika, Vol. 6, pp. 1–25). In this pioneering paper, written under the pseudonym “Student,” Gosset introduced what later became known as Student’s t-distribution, which we di

> Popular destinations for the newlyweds of today are the Caribbean and Hawaii. According to a recent American Wedding Study by the Conde Nast Bridal Group, a honeymoon, on average, lasts 9.4 days and costs $5111. A sample of 12 newlyweds reported the foll

> Apply Chebyshev’s rule with k = 5 and interpret your answer.

> Of the mean, median, and mode, which is the only one appropriate for use with qualitative data?

> The Scottish Executive, Analytical Services Division Transport Statistics, compiles data on motorcycle accidents. During one year, the numbers of motorcycle accidents in Scotland were tabulated by day of the week for built-up roads and non–built-up roads

> The Scottish Executive, Analytical Services Division Transport Statistics, compiles data on motorcycle casualties. During one year, monthly casualties from motorcycle accidents in Scotland for built-up roads and non–built-up roads were as follows. a. Fin

> In the article “Material Culture as Memory: Combs and Cremations in Early Medieval Britain” (Early Medieval Europe, Vol. 12, Issue 2, pp. 89–128), H. Williams discussed the frequency of cremation burials found in 17 archaeological sites in eastern Englan

> In the article “Router Roundup” (Popular Mechanics, Vol. 180, No. 12, pp. 104–109), T. Klenck reported on tests of seven fixed-base routers for performance, features, and handling. The following table gives the horsepower (hp) for each of the seven route

> The English rock band, The Beatles, was formed in Liverpool in 1960. There are 12 studio albums that are considered part of their core catalogue. In the article, “Length of The Beatles’ Songs” (Chance, Vol. 25, No. 1, pp. 30–33), T. Koyama lists the albu

> Tablet personal computers such as iPad and Kindle Fire are one-piece portable computers that typically offer a touchscreen. Tablets are available in different sizes but generally offer a screen that is greater than 7 inches diagonally. Consumer Reports r

> Each year, Forbes magazine compiles a list of the 400 richest Americans. As of September 19, 2012, the top 10 on the list are as shown in the following table. Find the a. mean. b. median. c. mode(s). For the mean and the median, round each answer to on

> The five top Oklahoma state officials are displayed in Table 1.2 on page 11. Use that table to solve the following problems. a. List the 10 possible samples (without replacement) of size 3 that can be obtained from the population of five officials. b. If

> S. Fearn et al. compare two types of snakes in the article “Body Size and Trophic Divergence of Two Large Sympatric Elapic Snakes in Tasmania” (Australian Journal of Zoology, Vol. 60, No. 3, pp. 159–165). Tiger snakes and lowland copperheads are both lar

> What does Chebyshev’s rule say about the percentage of observations in any data set that lie within a. 1.25 standard deviations to either side of the mean? b. 3.5 standard deviations to either side of the mean?

> Each year, thousands of high school students bound for college take the Scholastic Assessment Test (SAT). This test measures the verbal and mathematical abilities of prospective college students. Student scores are reported on a scale that ranges from a

> Suppose that you are thinking of buying a resale home in a large tract. The owner is asking $205,500. Your realtor obtains the sale prices of comparable homes in the area that have sold recently. The mean of the prices is $220,258 and the standard deviat

> A company produces cans of stewed tomatoes with an advertised weight of 14 oz. The standard deviation of the weights is known to be 0.4 oz. A quality-control engineer selects a can of stewed tomatoes at random and finds its net weight to be 17.28 oz. a.

> From the ESPN website, in the Dallas Mavericks Roster, we obtained the following weights, in pounds, for the players on that basketball team for the 2013–2014 season. Use the technology of your choice to determine a. the population mean weight. b. the po

> In one Winter Olympics, Michelle Kwan competed in the Short Program ladies singles event. From nine judges, she received scores ranging from 1 (poor) to 6 (perfect). The following table provides the scores that the judges gave her on technical merit, fou

> You examine the numerical relationship between the population standard deviation and the sample standard deviation computed from the same data. This relationship is helpful when the computer or statistical calculator being used has a built-in program for

> Consider the following three data sets. a. Assuming that each of these data sets is sample data, compute the standard deviations. b. Assuming that each of these data sets is population data, compute the standard deviations. (Round your final answers to t

> Suppose you buy a new car whose advertised mileage is 25 miles per gallon (mpg). After driving your car for several months, you find that its mileage is 21.4 mpg. You telephone the manufacturer and learn that the standard deviation of gas mileages for al

> The five top Oklahoma state officials are displayed in Table 1.2 on page 11. Use that table to solve the following problems. a. List the possible samples of size 1 that can be obtained from the population of five officials. b. What is the difference betw

> We have provided simple data sets for you to practice the basics of finding measures of center. 3, 5, 7 a. mean. b. median. c. mode(s).

> We presented a frequency distribution for data on chest circumference, in inches, for 5732 Scottish militiamen. As mentioned there, Adolphe Quetelet used a procedure for fitting a normal curve to the data based on the binomial distribution. Here you are

> Data on low-birth weight babies were collected over a 2-year period by 14 participating centers of the National Institute of Child Health and Human Development Neonatal Research Network. Results were reported by J. Lemons et al. in the on-line paper “Ver

> W. Duellman and J. Kohler explore a new species of frog in the article “New Species of Marsupial Frog (Hylidae: Hemiphractinae: Gastrotheca) from the Yungas of Bolivia” (Journal of Herpetology, Vol. 39, No. 1, pp. 91–100). These two museum researchers co

> Gestation periods of humans have a mean of 266 days and a standard deviation of 16 days. Let y denote the variable “gestation period” for humans. a. Find the standardized variable corresponding to y. b. What are the mean and standard deviation of the sta

> According to Compendium of Federal Justice Statistics, published by the Bureau of Justice Statistics, the mean time served to first release by Federal prisoners is 32.9 months. Assume the standard deviation of the times served is 17.9 months. Let x denot

> The top two players in the 2001–2002 Professional Darts Corporation World Championship were Phil Taylor and Peter Manley. Taylor and Manley dominated the competition with a record number of doubles. A double is a throw that lands in either the outer ring

> The Centers for Disease Control and Prevention compiles reported cases and rates of diseases in United States cities and outlying areas. In a document titled Sexually Transmitted Disease Surveillance, the number of reported cases of all stages of syphili

> From the ESPN website, in the Dallas Mavericks Roster, we obtained the following ages, in years, for the players on that basketball team for the 2013–2014 season. Obtain the following parameters for these ages. Use the appropriate mathematical notation f

> Each year, tornadoes that touch down are recorded by the Storm Prediction Center and published in Monthly Tornado Statistics. The following table gives the number of tornadoes that touched down in the United States during each month of one year. Find the

> The Tropical Cyclone Report, a publication of the National Hurricane Center, contains comprehensive information on each tropical cyclone, including synoptic history, meteorological statistics, casualties, and damages. A hurricane is a tropical cyclone wi

> In sampling, explain why obtaining a representative sample is important.

> The family of mammals called Chinchillidae contains the chinchilla and viscachas, which are large South American rodents. The article, “Species Richness and Distribution of Neotropical Rodents, with Conservation Implications” (Mammalia, Vol. 77, Issue 1,

> Explain why a sample of 30 dentists from Seattle taken to estimate the median income of all Seattle residents is not representative.

> The U.S. Census Bureau collects information about the ages of people in the United States. Results are published in Current Population Reports. a. Identify the variable and population under consideration. b. A sample of six U.S. residents yielded the fol

> 4, 2, 0, 2, 2 a. population mean. b. population standard deviation.

> 1, 9, 8, 4, 3 a. population mean. b. population standard deviation.

> 2, 5, 0, −1 a. population mean. b. population standard deviation.

> 1, 2, 4, 4 a. population mean. b. population standard deviation.

> 3, 5, 7 a. population mean. b. population standard deviation.

> 4, 0, 5 a. population mean. b. population standard deviation.

> We found that, considering the five starting players on Team II a sample of all male starting college basketball players, the mean and standard deviation of the heights are 75 inches and 6.2 inches, respectively. Explain why, numerically, the sample mean

> Explain in detail the purpose of a measure of center.

> An article by D. Schaefer et al. (Journal of Tropical Ecology, Vol. 16, pp. 189–207) reported on a long-term study of the effects of hurricanes on tropical streams of the Luquillo Experimental Forest in Puerto Rico. The study shows that Hurricane Hugo ha

> Name and describe the three most important measures of center.

> In the year 2000, an on-line poll was conducted over Memorial Day weekend that asked people what they were doing to observe the holiday. The choices were: (1) stay home and relax, (2) vacation outdoors over the weekend, or (3) visit a military cemetery.

> We analyzed the heights of the starting five players on each of two men’s college basketball teams. The heights, in inches, of the players on Team II are 67, 72, 76, 76, and 84. Regarding the five players as a population, solve the following problems. a.

> Earlier in this section, we found that the population standard deviation of the lengths of the holes at the Augusta National Golf Club is 132.0 yd. In this context, is the number 132.0 a parameter or a statistic? Explain your answer.

> Earlier in this section, we found that the population mean length of the holes at the Augusta National Golf Club is 413.1 yd. In this context, is the number 413.1 a parameter or a statistic? Explain your answer.

> Identify the statistic that is used to estimate a. a population mean. b. a population standard deviation.

> Fill in the following blanks. a. A standardized variable always has mean and standard deviation. b. The z-score corresponding to an observed value of a variable tells you. c. A positive z-score indicates that the observation is the mean, whereas a negati

> For a given brand of microwave popcorn, what property is desirable for the population standard deviation of the cooking time? Explain your answer.

> Although, in practice, sample data are generally analyzed in inferential studies, what is the ultimate objective of such studies?

> The number of patents a university receives is an indicator of the research level of the university. From a study titled Science and Engineering Indicators issued by the National Science Foundation, we found the number of U.S. patents awarded to a sample

> Identify each quantity as a parameter or a statistic. a. μ b. s c. x¯ d. σ

> Vitamin C (ascorbate) boosts the human immune system and is effective in preventing a variety of illnesses. In a study by E. Cameron and L. Pauling titled “Supplemental Ascorbate in the Supportive Treatment of Cancer: Reevaluation of Prolongation of Surv

> Advertising researchers F. Shuptrine and D. McVicker wanted to determine whether there were significant differences in the readability of magazine advertisements. Thirty magazines were classified based on their educational level high, mid, or low—and the

> The members of a population are numbered 1–50. a. Use Table I in Appendix A to obtain an SRS of size 6 from the population. Start at the two-digit number in line number 10 and column numbers 10−11, read down the column, up the next, and so on. b. If you

> In a study of the effects of radiation on amphibian embryos titled “Shedding Light on Ultraviolet Radiation and Amphibian Embryos” (BioScience, Vol. 53, No. 6, pp. 551–561), L. Licht recorded the time it took for a sample of seven different species of fr

> Anthropologists are still trying to unravel the mystery of the origins of the Etruscan empire, a highly advanced Italic civilization formed around the eighth century B.C. in central Italy. Were they native to the Italian peninsula or, as many aspects of

> L. Petersen et al. evaluated the effects of integrated treatment for patients with a first episode of psychotic illness in the paper “A Randomised Multicentre Trial of Integrated Versus Standard Treatment for Patients with a First Episode of Psychotic Il

> A study by researchers at the University of Maryland addressed the question of whether the mean body temperature of humans is 98.6◦F. The results of the study by P. Mackowiak et al. appeared in the article “A Critical Appraisal of 98.6◦F, the Upper Limit

> As reported by the U.S. Census Bureau in Educational Attainment in the United States, the percentage of adults in each state and the District of Columbia who have completed a bachelor’s degree is provided on the WeissStats site. a. obtain and interpret t

> As reported by the U.S. Census Bureau in Educational Attainment in the United States, the percentage of adults in each state and the District of Columbia who have completed high school is provided on the WeissStats site. a. obtain and interpret the quart

> R. Morris and E. Watson studied various aspects of process capability in the paper “Determining Process Capability in a Chemical Batch Process” (Quality Engineering, Vol. 10(2), pp. 389–396). In one part of the study, the researchers compared the variabi

> In the article, “Length of The Beatles’ Songs” (Chance, Vol. 25, No. 1, pp. 30–33), T. Koyama discusses aspects and interpretations of the lengths of songs by The Beatles. Data on the length, in seconds, of 229 Beatles’ songs are presented on the WeissSt