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statistics principles and methods
Statistics The Exploration And Analysis Of Data 6th Edition John M Scheb, Jay Devore, Roxy Peck - Solutions
=+a. Compute the mean, the standard deviation, and the interquartile range for sodium content of these chocolate puddings.
=+4.26 ● The paper referenced in Exercise 4.25 also gave summary quantities for sodium content (in milligrams per kilogram) of chocolate pudding made from instant mix:3099 3112 2401 2824 2682 2510 2297 3959 3068 3700
=+4.25 ● ▼ The paper “Total Diet Study Statistics on Element Results” (Food and Drug Administration, April 25, 2000) gave information on sodium content for various types of foods. Twenty-six tomato catsups were analyzed.Data consistent with summary quantities given in the paper were
=+e. Write a few sentences comparing repair cost for moderately priced and inexpensive midsize cars. Be sure to include information about both center and variability.
=+d. Compute the mean repair cost for each of the two types of cars.
=+c. Is there more variability in the repair cost for the moderately priced cars or for the inexpensive midsize cars?Justify your choice.
=+b. Compute the standard deviation and the interquartile range for the repair cost of the inexpensive midsize cars.
=+4.23 ● In 1997 a woman sued a computer keyboard manufacturer, charging that her repetitive stress injuries were caused by the keyboard (Genessey v. Digital Equipment Corporation). The jury awarded about $3.5 million for pain and suffering, but the court then set aside that award as being
=+27 similar cases and specified a reasonable award as one within 2 standard deviations of the mean of the awards in the 27 cases. The 27 award amounts were (in thousands of dollars)37 60 75 115 135 140 149 150 238 290 340 410 600 750 750 750 1050 1100 1139 1150 1200 1200 1250 1576 1700 1825 2000
=+What is the maximum possible amount that could be awarded under the “2-standard deviations rule”?
=+4.24 ● The Highway Loss Data Institute reported the following repair costs resulting from crash tests conducted in October 2002. The given data are for a 5-mph crash into a flat surface for both a sample of 10 moderately priced midsize cars and a sample of 14 inexpensive midsize
=+a. Compute the standard deviation and the interquartile range for the repair cost of the moderately priced midsize cars.
=+c. Which graphing method—the pie chart or the segmented bar chart—do you think does a better job of conveying information about response? Explain.
=+Data for 11 G-rated animated films showing tobacco use that were produced by MGM/United Artists, Warner Brothers, Universal, and Twentieth Century Fox were also given. The tobacco exposure times (in seconds) for these films was as follows:205 162 6 1 117 5 91 155 24 55 17 Construct a comparative
=+in 56% of the reviewed films. Data on the total tobacco exposure time (in seconds) for films with tobacco use produced by Walt Disney, Inc., were as follows:223 176 548 37 158 51 299 37 11 165 74 92 6 23 206 9
=+3.50 ● The article “Tobacco and Alcohol Use in G-Rated Children’s Animated Films” (Journal of the American Medical Association [1999]: 1131–1136) reported exposure to tobacco and alcohol use in all G-rated animated films released between 1937 and 1997 by five major film studios. The
=+Construct a comparative bar chart for this data set.Remember to use relative frequency when constructing the bar chart because the two group sizes are not the same.
=+3.48 Each student in a sample of 227 boys and 251 girls was asked what he or she thought was most important: getting good grades, being popular, or being good at sports.The resulting data, from the paper “The Role of Sport as a Social Determinant for Children” (Research Quarterly for
=+A language other than English 521 Construct a comparative bar chart for the average verbal and math scores for the three language groups. Write a few sentences describing the differences and similarities between the three language groups as shown in the bar chart.
=+3.47 The report referenced in Exercise 3.46 also gave average math SAT scores for the three language groups, as shown in the following table.First Language Learned Average Math SAT English 521 English and another language 513
=+3.46 Each year the College Board publishes a profile of students taking the SAT. In the report “2005 College Bound Seniors: Total Group Profile Report,” the average SAT scores were reported for three groups defined by first language learned. Use the data in the accompanying table to construct
=+6. Explain why looking at the distribution of the differences (Step 5) provides more information than the comparative stem-and-leaf display (Step 4). What information is lost in the comparative display that is retained in the display of the differences?
=+5. For each observation in the data set, compute the difference dominant-hand count 2 nondominant-hand count Construct a stem-and-leaf display of the differences. Comment on the interesting features of this display.
=+3.51 ● The accompanying data on household expenditures on transportation for the United Kingdom appeared in “Transport Statistics for Great Britain: 2002 Edition”(in Family Spending: A Report on the Family Expenditure Survey [The Stationary Office, 2002]). Expenditures (in pounds per week)
=+a. Construct time-series plots of the transportation expense data and the percent of household expense data.
=+b. Construct a segmented bar chart for these data.
=+a. Summarize these data using a pie chart.
=+3.54 The article “The Healthy Kids Survey: A Look at the Findings” (San Luis Obispo Tribune, October 25, 2002)gave the accompanying information for a sample of fifth graders in San Luis Obispo County. Responses are to the question:“After school, are you home alone without adult
=+d. Write a brief paragraph describing the difference between women and men with respect to the way they answered this question.
=+c. Is it easier to compare the responses of women and men by looking at the comparative bar chart or the two pie charts? Explain.
=+b. Construct two pie charts, one summarizing the responses for women and one summarizing the responses for men.
=+a. Construct a comparative bar chart that allows the responses for women and men to be compared.
=+3.53 The same poll described in Exercise 3.52 also asked the question, “What about salaries? These days, if a man and a woman are doing the same work, do you think the man generally earns more, the woman generally earns more, or that both earn the same amount?” The resulting data are shown in
=+write a few sentences describing the differences in the response distribution for men and women.
=+3.52 The web site PollingReport.com gave data from a CBS news poll conducted in December 1999. In the survey described, people were asked the following question:“All things considered, in our society today, do you think there are more advantages in being a man, more advantages in being a
=+b. Do the time-series plots of Part (a) support the statement that follows? Explain why or why not. Statement:Although actual expenditures have been increasing, the percentage of the total household expenditures that was for transportation has remained relatively stable.
=+4. Now construct a comparative stem-and-leaf display that allows you to compare dominant-hand count to nondominant-hand count. Does the display support the theory that dominant-hand count tends to be higher than nondominant-hand count?
=+3. Using the class data set, construct a comparative stemand-leaf display with the right-hand counts displayed on the right and the left-hand counts displayed on the left of the stem-and-leaf display. Comment on the interesting features of the display and include a comparison of the righthand
=+2. Use the sampling method from Step 1 to obtain the subjects for this study. Subjects should be shown the accompanying map of the United States and asked to point out the state of Vermont. After the subject has given his or her answer, ask the subject to point out the state of Nebraska. For
=+1. Working as a class, decide how you will select a sample that you think will be representative of the students from your school.
=+■ Is there much variability in the data values? What does this say about the variable being summarized?
=+■ Where do most of the data values fall? What is a typical value for the data set?What does this say about the variable being summarized?
=+■ Are there any outliers (noticeably unusual values) in the data set? Is there any plausible explanation for why these values differ from the rest of the data? (The presence of outliers often leads to further avenues of investigation.)
=+the shape of the distribution, and what does this say about the variable being summarized?
=+■ For graphical displays of univariate numerical data, how would you describe
=+■ Is the chosen display appropriate for the type of data collected?
=+called seasonal patterns. Describe any seasonal patterns that you see in the summer box office data. Hint: Look for patterns that seem to be consistent from year to year.
=+3.45 The accompanying time-series plot of movie box office totals (in millions of dollars) over 18 weeks of summer for both 2001 and 2002 appeared in USA Today (September 3, 2002):Patterns that tend to repeat on a regular basis over time are
=+c. Write a sentence or two commenting on the change in average number of fatalities over time. What is one possible reason for the change?
=+3. When the data collection process is complete, summarize the resulting data in a table like the one shown here:Response Frequency Correctly identified both states Correctly identified Vermont but not Nebraska Correctly identified Nebraska but not Vermont Did not correctly identify either state
=+4. Construct a pie chart that summarizes the data in the table from Step 3.
=+2. Create a class data set by recording the values of the three variables listed in Step 1 for each student in your class.
=+4 without any beans falling before you can determine the number grabbed. Repeat the process with the other hand, and then record the following information: (1) right-hand number, (2) left-hand number, and (3) dominant hand(left or right, depending on whether you are left- or
=+the beans onto a piece of paper and record the number of beans grabbed. If any beans drop during the count, restart the count. That is, you must hold the beans for a count of
=+1. Flip a coin to determine which hand you will measure first. If the coin lands heads side up, start with the right hand. If the coin lands tails side up, start with the left hand.With the designated hand, reach into the bowl and grab as many beans as possible. Raise the hand over the bowl and
=+10. Would you be comfortable generalizing your conclusions in Step 8 to the population of students at your school? Explain why or why not.
=+9. Write a paragraph commenting on the level of knowledge of U.S. geography demonstrated by the students participating in this study.
=+do you think that the students at your school were better able to identify the state that was closer than the one that was farther away? Justify your answer.
=+8. Which state, Vermont or Nebraska, is closer to the state in which your school is located? Based on the pie chart,
=+7. Construct a comparative bar chart that shows the proportion correct and the proportion incorrect for each of the two states considered.
=+6. What proportion of sampled students were able to correctly identify Nebraska on the map?
=+5. What proportion of sampled students were able to correctly identify Vermont on the map?
=+What is one possible reason for the differences?
=+a. Construct a pie chart to summarize this data set, and write a sentence or two summarizing how people responded to this question.
=+Bold exercises answered in back ● Data set available online but not required ▼ Video solution available Embankment (11.0%)Other (11.0%)Bridge Rail (1.0%)Concrete Bar (2.0%)Tree (28.0%)Fence (4.0%)Sign or Post (6.0%) Culvert (5.0%)Curb (6.0%)Ditch (8.0%)Utility Pole(9.0%)Guardrail (9.0%)
=+data using repeated stems 1H, 2L, 2H, . . . , 4L. For example, the first observation, 29, would have a stem of 2 and a leaf of 9. It would be entered into the display for the stem 2H, because it is a “high” 2—that is, it has a leaf that is on the high end (5, 6, 7, 8, 9).
=+3.18 ● Many states face a shortage of fully credentialed teachers. The percentages of teachers who are fully credentialed for each county in California were published in the San Luis Obispo Tribune (July 29, 2001) and are given in the following table:Percentage County Credentialed Alameda 85.1
=+a. Construct a stem-and-leaf display for this data set using stems 7, 8, 9, and 10. Truncate the leaves to a single digit. Comment on the interesting features of the display.
=+b. Construct a stem-and-leaf display using repeated stems.Are there characteristics of the data set that are easier to see in the plot with repeated stems, or is the general shape of the two displays similar?3.19 ● ▼ A report from Texas Transportation Institute
=+(Texas A&M University System, 2005) titled “Congestion Reduction Strategies” included the accompanying data on extra travel time for peak travel time in hours per year per traveler for different sized urban areas.Extra Hours Very Large per Year Urban Areas per Traveler Los Angeles, CA 93 San
=+Very Large per Year Urban Areas per Traveler Atlanta, GA 67 Houston, TX 63 Dallas, Fort Worth, TX 60 Chicago, IL-IN 58 Detroit, MI 57 Miami, FL 51 Boston, MA, NH, RI 51 New York, NY-NJ-CT 49 Phoenix, AZ 49 Philadelphia, PA-NJ-DE-MD 38 Extra Hours per Year Large Urban Areas per Traveler Riverside,
=+a. Construct a back-to-back stem-and-leaf plot for annual delay per traveler for each of the two different sizes of urban areas.
=+b. Is the following statement consistent with the display constructed in part (a)? Explain.The larger the urban areas, the greater the extra travel time during peak period travel.
=+b. Write a short description of the important features of the shape of the histogram.
=+a. Construct a frequency distribution for these data, and draw the corresponding histogram.
=+3.64 ● Americium 241 ( 241Am) is a radioactive material used in the manufacture of smoke detectors. The article“Retention and Dosimetry of Injected 241Am in Beagles”(Radiation Research [1984]: 564–575) described a study in which 55 beagles were injected with a dose of 241Am(proportional
=+3.17 The stem-and-leaf display of Exercise 3.16 uses only four stems. Construct a stem-and-leaf display for these
=+4. Write a sentence or two describing the calorie content of light beers.
=+a. Do you think this is an effective use of a pie chart?Why or why not?
=+b. Construct a bar chart to show the distribution of deaths by object struck. Is this display more effective than the pie chart in summarizing this data set? Explain.
=+3.14 The article “Death in Roadwork Zones at Record High” (San Luis Obispo Tribune, July 25, 2001) included a bar chart similar to this one:’91 ’92 ’93 ’94 ’95 ’96 ’97 ’98 ’99 Year Number of deaths 900 800 700 600 500 400 300 200 100 0Copyright 2008 Thomson Learning, Inc.
=+a. Comment on the trend over time in the number of people killed in highway work zones.
=+b. Would a pie chart have also been an effective way to summarize these data? Explain why or why not.
=+3.15 ● ▼ The National Survey on Drug Use and Health, conducted in 2002 and 2003 by the Office of Applied Studies, led to the following state estimates of the total number of people (ages 12 and older) who had smoked within the last month).Number of People State (in thousands)Alabama 976
=+a. Construct a stem-and-leaf display using hundreds (of thousands) as the stems and truncating the leaves to the tens (of thousands) digit.
=+b. Write a few sentences describing the shape of the distribution and any unusual observations.
=+c. The three largest values were for California, New York, and Texas. Does this indicate that tobacco use is more of a problem in these states than elsewhere? Explain.
=+d. If you wanted to compare states on the basis of the extent of tobacco use, would you use the data in the given table? If yes, explain why this would be reasonable.If no, what would you use instead as the basis for the comparison?
=+3.16 ● The Connecticut Agricultural Experiment Station conducted a study of the calorie content of different types of beer. The calorie content (calories per 100 ml) for 26 brands of light beer are (from the web site brewery.org):29 28 33 31 30 33 30 28 27 41 39 31 29 23 32 31 32 19 40 22 34 31
=+b. Use each histogram to determine approximately the proportion of observations that are less than 800, and compare to the actual proportion.
=+a. Do the two histograms give different impressions about the distribution of values?
=+3.58 ● 2005 was a record year for hurricane devastation in the United States (San Luis Obispo Tribune, November 30, 2005). Of the 26 tropical storms and hurricanes in the season, 4 hurricanes hit the mainland: Dennis, Katrina, Rita, and Wilma. The U.S. insured catastrophic losses since 1989
=+North Dakota 130.49 Missouri 91.93 Mississippi 40.22 Kentucky 85.21 Michigan 154.75 Maine 150.12 Massachusetts 200.99 New York 193.48 West Virginia 82.94 Virginia 97.98 Georgia 91.31
=+State Average Welfare Payment ($)Texas 56.79 Nebraska 115.15 Minnesota 171.75 Arkansas 65.96 Alabama 39.62 Illinois 112.28 Indiana 92.43 New Hampshire 164.20 Rhode Island 179.37 New Jersey 121.99 Delaware 113.66 North Carolina 91.95 Florida 95.43 Washington 160.41 Idaho 97.93 Utah 118.36 Colorado
=+relative frequency distribution for these data using equal interval widths. Draw the histogram corresponding to your frequency distribution.State Average Welfare Payment ($)Alaska 244.90 California 218.31 Arizona 93.57 Montana 114.95
=+3.57 ● Disparities among welfare payments by different states have been the source of much political controversy.The accompanying table reports average payment per person (in dollars) in the Aid to Families with Dependent Children Program for the 1990 fiscal year. Construct a
=+e. Does the distribution of values in the display appear to be reasonably symmetric? If not, how would you describe the departure from symmetry?f. Does the data set appear to contain any outliers (observations far removed from the bulk of the data)?
=+d. Does the display appear to be highly concentrated, or quite spread out?
=+c. What is a typical, or representative, flow rate?
=+b. If one additional house yielded a flow rate of 8.9, where would this observation be placed on the display?
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