Question: The first two columns of the following
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 estimate the sample mean and sample standard deviation of the days-to-maturity data. Round your final answers to one decimal place.
b. The following table gives the raw days-to-maturity data.
Using Definitions, respectively, gives the true sample mean and sample standard deviation of the days-to-maturity data as 68.3 and 16.7, respectively, rounded to one decimal place. Compare these actual values of x¯ and s to the estimates from part (a). Explain why the grouped-data formulas generally yield only approximations to the sample mean and sample standard deviation for non–single-value grouping.
> Determine the linear correlation coefficient by using a. Definition 4.8. b. Formula 4.3. Compare your answers in parts (a) and (b).
> Determine the linear correlation coefficient by using a. Definition 4.8. b. Formula 4.3. Compare your answers in parts (a) and (b).
> A quantitative data set has mean 30 and standard deviation 4. At least what percentage of the observations lie between 10 and 50?
> Use the specified grouping method to a. determine a frequency distribution. b. obtain a relative-frequency distribution. c. construct a frequency histogram based on your result from part (a). d. construct a relative-frequency histogram based on your resu
> The coefficient of determination of a set of data points is 0.709 and the slope of the regression line is −3.58. Determine the linear correlation coefficient of the data.
> The linear correlation coefficient of a set of data points is 0.846. a. Is the slope of the regression line positive or negative? Explain your answer. b. Determine the coefficient of determination.
> Answer true or false to the following statement and provide a reason for your answer: If there is a very strong positive correlation between two variables, a causal relationship exists between the two variables.
> Determine whether r is positive, negative, or zero.
> y = 1.5x 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.
> Determine whether r is positive, negative, or zero.
> When the behavior of the interviewer or respondent results in inaccurate responses, we have response bias. a. Explain why a survey question “Do you smoke marijuana” might result in response bias? b. Provide some additional survey situations that might be
> Determine whether r is positive, negative, or zero.
> Fill in the blanks: 1. The symbol that is used for the linear correlation coefficient is ____. 2. A value of r close to ±1 indicates that there is a ___ linear relationship between the variables. 3. A value of r close to ___ indicates that there is eithe
> y = −3x 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.
> A quantitative data set has mean 15 and standard deviation 2. At least what percentage of the observations lie between 7 and 23?
> The linear correlation coefficient is also known by another name. What is it?
> What is one purpose of the linear correlation coefficient?
> As we noted, because of the regression identity, we can express the coefficient of determination in terms of the total sum of squares and the error sum of squares as r2 = 1 − SSE/SST. a. Explain why this formula shows that the coefficient of determinatio
> What can you say about SSE, SSR, and the utility of the regression equation for making predictions if a. r2 = 1? b. r2 = 0?
> J. Greene and J. Touchstone conducted a study on the relationship between the estriol levels of pregnant women and the birth weights of their children. Their findings, “Urinary Tract Estriol: An Index of Placental Function,” were published in the America
> In the paper “Total Body Composition by Dual-Photon (153Gd) Absorptiometry” (American Journal of Clinical Nutrition, Vol. 40, pp. 834–839), R. Mazess et al. studied methods for quantifying body composition. Eighteen randomly selected adults were measured
> The data from Exercise 4.80 for volume, in cubic feet, and diameter at breast height, in inches, for 70 shortleaf pines are on the WeissStats site. a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b)–(d).
> When responses are not obtained from some of the individuals in the sample because either those individuals cannot be reached or refuse to participate, we have nonresponse bias. a. Discuss some of the dangers of nonresponse. b. Many sample surveys that a
> The data for gas mileage and engine displacement for 121 vehicles from Exercise 4.78 are provided on the WeissStats site. a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b)–(d). b. Obtain the coefficient
> The data for per capita income and per capita beer consumption for the 50 states and Washington, D.C., from Exercise 4.77 are on the WeissStats site. a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b)–(d
> We have provided simple data sets for you to practice the basics of finding measures of center. 1, 2, 4, 4 a. mean. b. median. c. mode(s).
> The data for shell thickness and concentration of PCBs for 60 Anacapa pelican eggs from Exercise 4.76 are on the WeissStats site. a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b)–(d). b. Obtain the coe
> y = 2 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.
> The data from Exercise 4.75 for average high and low temperatures in January for a random sample of 50 cities are on the WeissStats site. a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b)–(d). b. Obtain
> The data from Exercise 4.74 for home size (in square feet) and assessed value (in thousands of dollars) for the same homes as in Exercise 4.107 are on the WeissStats site. a. Decide whether finding a regression line for the data is reasonable. If so, the
> The data from Exercise 4.73 for lot size (in acres) and assessed value (in thousands of dollars) for a sample of homes in a particular area are on the WeissStats site. a. Decide whether finding a regression line for the data is reasonable. If so, then al
> The data from Exercise 4.72 on domestic and overseas grosses for a random sample of 50 movies are on the WeissStats site. a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b)–(d). b. Obtain the coefficient
> The data from Exercise 4.71 for the ages at inauguration and of death for the presidents of the United States are on the WeissStats site. a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b)–(d). b. Obtain
> The data from Exercise 4.70 for number of birdies during a tournament and final score for 63 women golfers are on the WeissStats site. a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b)–(d). b. Obtain th
> Oftentimes, an accurate and complete list of the population is unavailable. In such cases, one or more groups will be omitted from the sampling process because they are not listed as part of the population. This type of bias is called under coverage. a.
> At the beginning of this chapter, we discussed a freight study commissioned by the Chesapeake and Ohio Railroad Company (C&O). A sample of 2072 waybills from a population of 22,984 waybills was used to estimate the total revenue due C&O. The estimate arr
> 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
> 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
> 2, 5, 0, −1 Determine the a. range. b. sample standard deviation.
> 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.
