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Statistics The Exploration And Analysis Of Data 6th Edition John M Scheb, Jay Devore, Roxy Peck - Solutions
=+a. What is the smallest flow rate in the sample?
=+3.56 The accompanying stem-and-leaf display shows observations on average shower flow rate (in liters per minute) for a sample of 129 houses in Perth, Australia (“An Application of Bayes Methodology to the Analysis of Diary Records from a Water Use Study,” Journal of the American
=+Construct a time-series plot that shows the insured catastrophic loss over time. What do you think causes the peaks in the graph?
=+3.59 ● Each observation in the following data set is the number of housing units (homes or condominiums) sold during November 1992 in a region corresponding to a particular Orange County, California, ZIP code:25 18 16 6 26 11 29 7 5 15 12 37 35 11 16 35 20 27 17 30 10 16 28 13 26 11 12 8 9 29
=+3.63 ● Many nutritional experts have expressed concern about the high levels of sodium in prepared foods. The following data on sodium content (in milligrams) per frozen meal appeared in the article “Comparison of ‘Light’Frozen Meals” (Boston Globe, April 24, 1991):720 530 800 690 880
=+b. Use the data from 1994 and 2001 to construct a comparative bar chart for the type of donation (relative or unrelated). Write a few sentences commenting on your display.
=+a. Construct a time-series plot for the number of livingdonor kidney transplants where the donor is a relative of the recipient. Describe the trend in this plot.
=+3.62 ● Living-donor kidney transplants are becoming more common. Often a living donor has chosen to donate a kidney to a relative with kidney disease. The following data appeared in a USA Today article on organ transplants(“Kindness Motivates Newest Kidney Donors,” June 19, 2002):Number of
=+c. Do these data suggest that a murder is more likely to be committed on some days than on other days? Explain your reasoning.
=+b. What proportion of these murders was committed on a weekend day—that is, Friday, Saturday, or Sunday?
=+a. Construct the corresponding frequency distribution.
=+in the following frequencies: Sunday, 109; Monday, 73;Tuesday, 97; Wednesday, 95; Thursday, 83; Friday, 107;Saturday, 100.
=+3.60 Each murder committed in Utah during the period 1978–1990 was categorized by day of the week, resulting
=+Construct a stem-and-leaf display, and comment on any interesting features.
=+b. Summarize the given data using a segmented bar chart.
=+b. Write a sentence or two commenting on the difference in average number of fatalities for the days of the week.
=+3.30 ● The paper “Lessons from Pacemaker Implantations” (Journal of the American Medical Association[1965]: 231–232) gave the results of a study that followed 89 heart patients who had received electronic pacemakers.The time (in months) to the first electrical malfunction of the
=+i. Approximately what proportion of commute times were less than 50 min?
=+e. Use the cumulative relative frequency plot constructed in Part (d) to answer the following questions.
=+d. Compute the cumulative relative frequencies, and construct a cumulative relative frequency plot.
=+c. Use the densities computed in Part (b) to construct a histogram for this data set. (Note: The newspaper displayed an incorrectly drawn histogram based on frequencies rather than densities!) Write a few sentences commenting on the important features of the histogram.
=+b. Construct a table that adds a relative frequency and a density column to the given frequency distribution.
=+a. Notice that not all intervals in the frequency distribution are equal in width. Why do you think that unequal width intervals were used?
=+3.26 ● U.S. Census data for San Luis Obispo County, California, were used to construct the following frequency distribution for commute time (in minutes) of working adults (the given frequencies were read from a graph that appeared in the San Luis Obispo Tribune [September 1, 2002] and so are
=+e. Estimate the proportion of women that average 450 minutes or more per month.
=+d. Estimate the proportion of men that average less than 500 minutes per month.
=+c. What proportion of men average less than 400 minutes per month?
=+b. Construct a relative frequency histogram for average number of minutes used per month for women. Is the distribution for average number of minutes used per month similar for men and women? Explain.
=+ii. Approximately what proportion of commute times were greater than 22 min?
=+iii. What is the approximate commute time value that separates the shortest 50% of commute times from the longest 50%?
=+Explain your reasoning in each case.
=+c. half the students in the class have had calculus, the other half have had no prior college math courses, and the exam emphasizes mathematical manipulation?
=+3.29 An exam is given to students in an introductory statistics course. What is likely to be true of the shape of the histogram of scores if:a. the exam is quite easy?b. the exam is quite difficult?
=+c. Based on the histogram of Part (b), write a few sentences describing the educational debt of medical students completing their residencies.
=+b. Suppose that no student had an educational debt of$150,000 or more upon completion of his or her residency, so that the last class in the relative frequency distribution would be 100,000 to ,150,000. Summarize this distribution graphically by constructing a histogram of the educational debt
=+a. What are two reasons that it would be inappropriate to construct a histogram using relative frequencies to determine the height of the bars in the histogram?
=+3.28 Student loans can add up, especially for those attending professional schools to study in such areas as medicine, law, or dentistry. Researchers at the University of Washington studied medical students and gave the following information on the educational debt of medical students on
=+c. What proportion of subdivisions has total length less than 2000? between 2000 and 4000?
=+b. Construct a histogram using class boundaries of 0 to 1000, 1000 to 2000, and so on. How would you describe the shape of the histogram?
=+a. Construct a stem-and-leaf display for these data using the thousands digit as the stem. Comment on the various features of the display.
=+3.27 ● The article “Determination of Most Representative Subdivision” (Journal of Energy Engineering [1993]: 43–55) gave data on various characteristics of subdivisions that could be used in deciding whether to provide electrical power using overhead lines or underground lines. Data on
=+a. Construct a relative frequency histogram for average number of minutes used per month for men. How would you describe the shape of this histogram?
=+3.25 ● ▼ USA Today (July 2, 2001) gave the following information regarding cell phone use for men and women:Average Number of Minutes Used Relative Frequency per Month Men Women 0 to ,200 .56 .61 200 to ,400 .18 .18 400 to ,600 .10 .13 600 to ,800 .16 .08
=+a. Use class intervals of $0 to ,$3, $3 to ,$6, $6 to,$9 etc., to create a relative frequency distribution for these data.
=+New Mexico 10.65 New York 4.10 North Carolina 13.27 North Dakota 1.87 Ohio 14.43 Oklahoma 10.07 Oregon 6.93 Pennsylvania 10.14 Rhode Island 7.32 South Carolina 16.57 South Dakota 1.87 Tennessee 14.08 Texas 10.31 Utah 6.33 Vermont 7.32 Virginia 8.81 Washington 6.93 West Virginia 10.14 Wisconsin
=+3.22 ● Medicare’s new medical plans offer a wide range of variations and choices for seniors when picking a drug plan (San Luis Obispo Tribune, November 25, 2005). The monthly cost for a stand-alone drug plan varies from plan to plan and from state to state. The accompanying table gives the
=+accommodate the leaves of 8 and 9. Construct a stem-andleaf display for this data set that uses stems 0f, 0s, 0*, 1., 1t, 1f, and 1s. Comment on the important features of the display
=+five parts: 0 and 1, 2 and 3, 4 and 5, 6 and 7, and 8 and 9.Then, for example, stem 1 could be repeated as 1. with leaves 0 and 1 1t with leaves 2 and 3 1f with leaves 4 and 5 1s with leaves 6 and 7 If there had been any dropout rates as large as 18 or 19 in the data set, we would also need to
=+data, if we regard each dropout rate as a two-digit number and use the first digit for the stem, then there are only two possible stems, 0 and 1. One solution is to use repeated stems. Consider a scheme that divides the leaf range into
=+3.21 ● High school dropout rates (percentages) for the period 1997–1999 for the 50 states were given in The Chronicle of Higher Education (August 31, 2001) and are shown in the following table:State Rate Alabama 10 Alaska 7 Arizona 17 Arkansas 12 California 9 Colorado 13 State Rate
=+c. Now construct a comparative stem-and-leaf display for the eastern and western states. Write a few sentences comparing the percentage growth distributions for eastern and western states.
=+b. Comment on any interesting features of the data set.Do any of the observations appear to be outliers?
=+single digit; for example, a leaf of 8.5 could be truncated to 8 for purposes of constructing the display.
=+a. Construct a stem-and-leaf display for percentage growth for the data set consisting of all 50 states. Hints:Regard the observations as having two digits to the left of the decimal place. That is, think of an observation such as 8.5 as 08.5. It will also be easier to truncate leaves to a
=+b. Construct a histogram and comment on its shape.
=+c. Using the relative frequency distribution or the histogram, determine the proportion of the states that have a minimum monthly plan of less than $13.00 a month.
=+d. What proportion of the patients had at least four impairments?
=+c. Use the result of Part (b) to determine what proportion of patients had more than two impairments.
=+b. What proportion of these patients had at most two impairments?
=+a. Determine the relative frequencies that correspond to the given frequencies.
=+3.24 ● People suffering from Alzheimer’s disease often have difficulty performing basic activities of daily living(ADLs). In one study (“Functional Status and Clinical Findings in Patients with Alzheimer’s Disease,” Journal of Gerontology [1992]: 177–182), investigators focused on six
=+d. Do you think the high nonresponse rate for the survey may have contributed to the observed differences in the two histograms? Explain.
=+c. Comment on the similarities and differences in the histograms from Parts (a) and (b).
=+b. Construct a histogram for the survey data. Use the same scale that you used for the histogram in part (a) so that it will be easy to compare the two histograms.
=+a. Construct a histogram for the credit bureau data. For purposes of constructing the histogram, assume that none of the students in the sample had a balance higher than 15,000 and that the last interval can be regarded as 7000 to , 15,000. Be sure to use the density scale when constructing the
=+a survey completed by 132 of the 1260 college students who received the survey.Credit Card Balance (dollars)—Credit Bureau Data Relative Frequency 0 to ,100 .18 100 to ,500 .19 500 to ,1000 .14 1000 to ,2000 .16 2000 to ,3000 .10 3000 to ,7000 .16 7000 or more .07 Credit Card Balance
=+3.23 ● The following two relative frequency distributions were constructed using data that appeared in the report“Undergraduate Students and Credit Cards in 2004 (Nellie Mae, May 2005). One relative frequency distribution is based on credit bureau data for a random sample of 1413 college
=+State Change East/West Arkansas 13.7 E Utah 29.6 W Nevada 66.3 W New Mexico 20.1 W West Virginia 0.8 E Nebraska 8.4 W Idaho 28.5 W Maine 3.9 E New Hampshire 11.4 E Hawaii 9.3 W Rhode Island 4.5 E Montana 12.9 W Delaware 17.6 E South Dakota 8.5 W North Dakota 0.5 W Alaska 14.0 W Vermont 8.2 E
=+a. Summarize these data in the form of a frequency dis tributio so on.b. Co tive fre distrib
=+shows the average fatalities over time for each day of the week. Be sure to label each line clearly as to which day of the week it represents.
=+3.41 ● The National Telecommunications and Information Administration published a report titled “Falling Through the Net: Toward Digital Inclusion” (U.S. Department of Commerce, October 2000) that included the following information on access to computers in the home:Percentage of
=+c. Does an increase in plasma cortisol concentration appear to be accompanied by a change in oxygen consumption rate? Comment.
=+b. Construct a scatterplot of the data.
=+2-min disturbances were read from a graph in the paper“Metabolic Cost of Acute Physical Stress in Juvenile Steelhead” (Transactions of the American Fisheries Society[1987]: 257–263). The paper also included data for unstressed fish.x 25 36 48 59 62 72 80 100 100 137 y 155 184 180 220 280
=+3.40 ● Stress can affect the physiology and behavior of animals, just as it can with humans (as many of us know all too well). The accompanying data on x 5 plasma cortisol concentration (in milligrams of cortisol per milliliter of plasma) and y 5 oxygen consumption rate (in milligrams per
=+resonance frequency (in hertz) and y 5 sum of peak-topeak accelerations (a characteristic of arm vibration, in meters per second per second) for n 5 23 different rackets(“Transfer of Tennis Racket Vibrations into the Human Forearm,” Medicine and Science in Sports and Exercise[1992]:
=+3.39 ▼ One factor in the development of tennis elbow, a malady that strikes fear into the hearts of all serious players of that sport (including one of the authors), is the impact-induced vibration of the racket-and-arm system at ball contact. It is well known that the likelihood of getting
=+d. Comment on the similarities and differences in the two scatterplots of Parts (a) and (b).
=+c. Do age and emissions appear to be related? If so, in what way?
=+b. Construct a scatterplot of emissions versus age for the reformulated gasoline.
=+a. Construct a scatterplot of emissions versus age for the baseline gasoline.
=+a. Construct a time-series plot for these data. Be careful—the observations are not equally spaced in time. The points in the plot should not be equally spaced along the x axis.b. Comment on any trend over time.
=+3.42 According to the National Association of Home Builders, the average size of a home in 1950 was 983 ft2.The average size increased to 1500 ft2 in 1970, 2080 ft2 in 1990; and 2330 ft2 in 2003 (San Luis Obispo Tribune, October 16, 2005).
=+a. Using the midpoint of each year range (e.g., 1980 for the 1978–1982 range), construct a time-series plot that
=+Bold exercises answered in back ● Data set available online but not required ▼ Video solution available Average Fatalities per Day(day of the week)Mon Tue Wed Thurs Fri Sat Sun 1978–1982 103 101 107 116 156 201 159 1983–1987 98 96 99 108 140 174 140 1988–1992 97 94 97 106 139 168 135
=+3.44 ● Some days of the week are more dangerous than others, according to Traffic Safety Facts produced by the National Highway Traffic Safety Administration. Average number of fatalities per day for each day of the week are shown in the accompanying table.Good time Bad time 53%67%78%
=+c. Which graph, the given bar chart or the time-series plot, best shows the trend over time?
=+b. Add a new line to the plot from Part (a) showing the percentage that thought it was a bad time to buy a house over time. Be sure to label the lines clearly.
=+a. Construct a time-series plot that shows how the percentage that thought it was a good time to buy a house has changed over time.
=+and 2003 in which a sample of American adults were asked whether or not it was a good time or a bad time to buy a house.
=+3.43 An article that appeared in USA Today (September 3, 2003) included a graph similar to the one shown here summarizing responses from polls conducted in 1978, 1991,
=+what would you predict the average home size to be in 2010?
=+3.20 ● The article “A Nation Ablaze with Change” (USA Today, July 3, 2001) gave the accompanying data on percentage increase in population between 1990 and 2000 for the 50 U.S. states. Also provided in the table is a column that indicates for each state whether the state is in the eastern
=+a. Construct a time-series plot that shows how the average size of a home has changed over time.
=+Engine Age Baseline Reformulated 1 0 1.72 1.88 2 0 4.38 5.93 3 2 4.06 5.54 4 11 1.26 2.67 5 7 5.31 6.53 6 16 0.57 0.74 7 9 3.37 4.94 8 0 3.44 4.89 9 12 0.74 0.69 10 4 1.24 1.42
=+from a study in which both a baseline gasoline and a reformulated gasoline were used. Consider the following observations on age (in years) and NOx emissions (in grams per kilowatt-hour):
=+24–30). What are some interesting features of this histogram? What is a typical difference value? Roughly what proportion of the runners ran the late distance more quickly than the early distance?
=+the end of the race. The histogram on page 113 is based on times of runners who participated in several different Japanese marathons (“Factors Affecting Runners’ Marathon Performance,” Chance [Fall, 1993]:
=+3.32 How does the speed of a runner vary over the course of a marathon (a distance of 42.195 km)? Consider determining both the time to run the first 5 km and the time to run between the 35 km and 40 km points, and then subtracting the 5-km time from the 35–40-km time. A positive value of
=+b. Cloudy days are those with a clearness index smaller than 0.35. What proportion of the days was cloudy?c. Clear days are those for which the index is at least 0.65. What proportion of the days was clear?
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