2, 5, 0, −1 Determine the a. range. b. sample standard deviation.
> A quantitative data set has mean 25 and standard deviation 5. Fill in the following blanks: a. At least 89% of the observations lie between and ___. b. At least % of the observations lie between 15 and 35.
> Following are the data on study time and score for calculus students. a. compute SST, SSR, and SSE. b. compute the coefficient of determination, r 2. c. determine the percentage of variation in the observed values of the response variable explained by th
> Following are the data on age and crown-rump length for fetuses. a. compute SST, SSR, and SSE. b. compute the coefficient of determination, r 2. c. determine the percentage of variation in the observed values of the response variable explained by the reg
> Following are the data on plant weight and quantity of volatile emissions. a. compute SST, SSR, and SSE. b. compute the coefficient of determination, r 2. c. determine the percentage of variation in the observed values of the response variable explained
> Following are the size and price data for custom homes. a. compute SST, SSR, and SSE. b. compute the coefficient of determination, r 2. c. determine the percentage of variation in the observed values of the response variable explained by the regression,
> y = −0.75x − 5 a. find the y-intercept and slope. b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation. c. use two points to graph the equation.
> Regarding linear equations with one independent variable, answer the following questions: a. What is the general form of such an equation? b. In your expression in part (a), which letters represent constants and which represent variables? c. In your expr
> What does Chebyshev’s rule say about the percentage of observations in any data set that lie within a. four standard deviations to either side of the mean? b. 2.5 standard deviations to either side of the mean?
> Apply Chebyshev’s rule with k = 3 to verify that at least 89% of the observations in any data set lie within three standard deviations to either side of the mean, that is, between x¯ − 3s and x¯ + 3s.
> If the condition for using the empirical rule is met, why should that rule be used instead of Chebyshev’s rule?
> Discuss the pros and cons of Chebyshev’s rule.
> Provide a scenario of your own in which a sample is not representative.
> In the article “Element Hunters” (National Geographic, Vol. 233, No. 5, pp. 112−120), R. Dunn reports about the search for new undiscovered elements. Since 1940, scientists have been synthesizing elements one by one. The first was neptunium (Np), element
> The first two columns of the following table provide a frequency distribution, using limit grouping, for the days to maturity of 40 short-term investments, as found in BARRON’S. The third column shows the class marks. a. Use the grouped-data formulas to
> In the following table, we repeat the salary data in Data Set II. a. Use Definitions, respectively, to obtain the sample mean and sample standard deviation of this (ungrouped) data set. b. A frequency distribution for Data Set II, using single-value grou
> We discussed outliers, or observations that fall well outside the overall pattern of the data. The following table contains two data sets. Data Set II was obtained by removing the outliers from Data Set I. a. Compute the sample standard deviation of each
> 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
> Use the technology of your choice to determine and interpret the range and sample standard deviation for those data sets to which those concepts apply. If those concepts don’t apply, explain why. A study by researchers at the University of Maryland addre
> We have provided simple data sets for you to practice the basics of finding measures of center. 4, 0, 5 a. mean. b. median. c. mode(s).
> Use the technology of your choice to determine and interpret the range and sample standard deviation for those data sets to which those concepts apply. If those concepts don’t apply, explain why. As reported by the U.S. Census Bureau in Educational Attai
> Use the technology of your choice to determine and interpret the range and sample standard deviation for those data sets to which those concepts apply. If those concepts don’t apply, explain why. As reported by the U.S. Census Bureau in Educational Attai
> A quantitative data set has mean 10 and standard deviation 3. Fill in the following blanks: a. At least 75% of the observations lie between and ___. b. At least % of the observations lie between 1 and 19.
> Use the technology of your choice to determine and interpret the range and sample standard deviation for those data sets to which those concepts apply. If those concepts don’t apply, explain why. In the article, “Length of The Beatles’ Songs” (Chance, Vo
> In an issue of Discover (Vol. 26, No. 5, p. 14), A. Casselman looked at the natural-hazards risk index of megacities to evaluate potential loss from catastrophes such as earthquakes, storms, and volcanic eruptions. Urban areas have more to lose from natu
> Use the technology of your choice to determine and interpret the range and sample standard deviation for those data sets to which those concepts apply. If those concepts don’t apply, explain why. In an article titled “Great White, Deep Trouble” (National
> Use the technology of your choice to determine and interpret the range and sample standard deviation for those data sets to which those concepts apply. If those concepts don’t apply, explain why. In Issue 338 of the Amstat News, then president of the Ame
> Use the technology of your choice to determine and interpret the range and sample standard deviation for those data sets to which those concepts apply. If those concepts don’t apply, explain why. Research by W. Clark and L. Midanik (Alcohol Consumption a
> Use the technology of your choice to determine and interpret the range and sample standard deviation for those data sets to which those concepts apply. If those concepts don’t apply, explain why. The American Hospital Association conducts annual surveys
> Use the technology of your choice to determine and interpret the range and sample standard deviation for those data sets to which those concepts apply. If those concepts don’t apply, explain why. The Japan Automobile Manufacturer’s Association provides d
> 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 resulting from motorcycle accidents in Scotland for built-up roads and non– built-up roads were as foll
> The Board of Governors of the Federal Reserve System publishes information on family net worth in the Survey of Consumer Finances. In 2010, the mean net worth of families in the United States was $498.8 thousand and the median net worth was $77.3 thousan
> In this exercise, you will compare Chebyshev’s rule and the empirical rule. a. Compare the estimates given by the two rules for the percentage of observations that lie within two standard deviations to either side of the mean. Comment on the differences.
> 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
> Determine the range and sample standard deviation for data sets. For the sample standard deviation, round each answer to one more decimal place than that used for the observations. In the article “Router Roundup” (Popular Mechanics, Vol. 180, No. 12, pp.
> Each year, Fortune Magazine publishes an article titled “The International 500” that provides a ranking by sales of the top 500 firms outside the United States. Suppose that you want to examine various characteristics of successful firms. Further suppose
> Determine the range and sample standard deviation for data sets. For the sample standard deviation, round each answer to one more decimal place than that used for the observations. The English rock band, The Beatles, was formed in Liverpool in 1960. Ther
> Determine the range and sample standard deviation for data sets. For the sample standard deviation, round each answer to one more decimal place than that used for the observations. Tablet personal computers such as iPad and Kindle Fire are one-piece port
> Determine the range and sample standard deviation for data sets. For the sample standard deviation, round each answer to one more decimal place than that used for the observations. Each year, Forbes magazine compiles a list of the 400 richest Americans.
> Determine the range and sample standard deviation for data sets. For the sample standard deviation, round each answer to one more decimal place than that used for the observations. In one Winter Olympics, Michelle Kwan competed in the Short Program ladie
> Determine the range and sample standard deviation for data sets. For the sample standard deviation, round each answer to one more decimal place than that used for the observations. Each year, tornadoes that touch down are recorded by the Storm Prediction
> Determine the range and sample standard deviation for data sets. For the sample standard deviation, round each answer to one more decimal place than that used for the observations. An article by D. Schaefer et al. (Journal of Tropical Ecology, Vol. 16, p
> Determine the range and sample standard deviation for data sets. For the sample standard deviation, round each answer to one more decimal place than that used for the observations. In a study of the effects of radiation on amphibian embryos titled “Shedd
> What is another name for the empirical rule? Why is that name appropriate?
> 4, 2, 0, 2, 2 Determine the a. range. b. sample standard deviation.
> The U.S. Department of Housing and Urban Development compiles information on new, privately owned single family houses. According to the document Characteristics of New Housing, in 2012 the mean floor space of such homes was 2505 sq ft and the median was
> 1, 9, 8, 4, 3 Determine the a. range. b. sample standard deviation.
> In the game of keno, 20 balls are selected at random from 80 balls numbered 1–80. a. Use Table I in Appendix A to simulate one game of keno by obtaining 20 random numbers between 1 and 80. Start at the twodigit number in line number 5 and column numbers
> 1, 2, 4, 4 Determine the a. range. b. sample standard deviation.
> 3, 5, 7 Determine the a. range. b. sample standard deviation.
> 4, 0, 5 Determine the a. range. b. sample standard deviation.
> Consider the data set 3, 3, 3, 3, 3, 3. a. Guess the value of the sample standard deviation without calculating it. Explain your reasoning. b. Use the defining formula to calculate the sample standard deviation. c. Complete the following statement and ex
> The U.S. Census Bureau publishes information about ages of people in the United States in Current Population Reports. A sample of five U.S. residents have the following ages, in years. a. Determine the range of these ages. b. Find the sample standard dev
> Each of the following smooth curves represents the shape of a data set. In each case, decide whether application of the empirical rule to the data set is appropriate. Explain your answers.
> Consider the following four data sets. a. Compute the mean of each data set. b. Although the four data sets have the same means, in what respect are they quite different? c. Which data set appears to have the least variation? the greatest variation? d. C
> Consider the data set 1, 2, 3, 4, 5, 6, 7, 8, 9. a. Use the defining formula to obtain the sample standard deviation. b. Replace the 9 in the data set by 99, and again use the defining formula to compute the sample standard deviation. c. Compare your ans
> The following dartboards represent darts thrown by two players, Tracey and Joan. For the variable “distance from the center,” which player’s board represents data with a smaller sample standard deviation? Explain your answer.
> Complete the following statement: A descriptive measure is resistant if.
> From Wikipedia.com, we obtained the top seven major active social networking websites in the United States, excluding dating websites. Ranked according to registered users, as of April 2013, from most popular to least popular, they are Facebook (F), Twit
> When you use the standard deviation as a measure of variation, what is the reference point?
> Why is the standard deviation preferable to the range as a measure of variation?
> Explain the purpose of a measure of variation.
> Explain the difference between the quantities Σxi yi and (Σxi)(Σyi). Provide an example to show that, in general, those two quantities are unequal.
> Explain the difference between the quantities (Σxi)2 and Σx2i . Construct an example to show that, in general, those two quantities are unequal.
> What condition on a data set is required to apply the empirical rule?
> 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.
