ࡱ>  Fbjbjvv "d<<4Ӵ̗̗̗^``````ɵk`-̗̗̗̗З`ttttԗ^t̗^tto/Xj žL0Ӵʞ,tt̗̗̗~ o:   Assignment 2.1 Statistical Methods Descriptive Statistics M&S 50, 59-60 PART I NAME: 2.25 (3 points) Consider the stem-and-leaf display shown here: StemLeaf51445730003621134599122480012 a. How many observations were in the original data set? b. In the bottom row of the stem-and-leaf display, identify the stem, the leaves, and the number in the original data set represented by its stem and its leaves. c. Re-create all the numbers in the data set, and construct a dot plot. ANSWERS 23 In the bottom row, stem is 0 and the leaves are 0, 1, 2. The original data are 0, 0.1, and 0.2 . 2.38 (3 points) Research on eating disorders. Data from a psychology experiment were reported and analyzed in The American Statistician (May 2001). Two samples of female students participated in the experiment. One sample consisted of 11 students known to suffer from the eating disorder bulimia; the other sample consisted of 14 students with normal eating habits. Each student completed a questionnaire from which a fear of negative evaluation (FNE) score was produced. (The higher the score, the greater was the fear of negative evaluation.) The data are displayed in the following table: BULIMIA Bulimic Students:2113102025191621241314Normal Students: 1361613819231811197101520 a. Construct a dot plot or stem-and-leaf display for the FNE scores for all 25 female students. b. Highlight the bulimic students on the graph you made in part a. Does it appear that bulimics tend to have a greater fear of negative evaluation? Explain. c. Why is it important to attach a measure of reliability to the inference made in part b? ANSWERS  2.42 (5 points) A data set contains the observations 5,1,3,2,1. Find a. " x b. " x c. " (x  1) d. " (x-1) e. (" x) ANSWERS  2.58 (3 points) Most powerful women in America. Fortune (Oct. 14, 2002) published a list of the 50 most powerful women in America. The data on age (in years) and title of each of these 50 women are stored in the WPOWER50 file. a. Find the mean, median, and modal age of these 50 women. b. What do the mean and median indicate about the skewness of the age distribution? c. Construct a relative frequency histogram for the age data. What is the modal age class? ANSWERS   RankNameAgeCompanyTitle1Carly Fiorina48Hewlet-PackardCEO2Betsy Holden 46Kraft Foods CEO3Meg Whitman 46eBayCEO4Indra Nooyi 46PepsiCoCEO5Andrea Jung 44Avon Products CEO6Anne Mulcahy 49XeroxCEO7Karen Katen 53Pfizer EVP8Pat Woertz 49ChevronTexacoEVP9Abigail Johnson 40Fidelity M&R President10Oprah Winfrey48Harpo EntertainmentChairman11Ann Moore52AOL Time WarnerCEO12Judy McGrath50ViacomPresident13Colleen Barrett58Southwest AirlinesCOO14Shelly Lazarus55Ogilvy & MatherCEO15Pat Russo50Lucent Tech.CEO16Betsy Bernard47AT&TCEO17Amy Brinkley46Bank of AmericaCRO18Lois Juliber53Colgate-PalmoliveCOO19Sherry Lansing58ViacomChairman20Stacey Snider41Vivendi UniversalChairman21Judy Lewent53MerckEVP22Marjorie Magner53CitigroupCOO23Ann Livermore44Hewlett-PackardPresident24Cathleen Black58Hearst MagazinesPresident25Doreen Toben52VerizonEVP26Amy Pascal44SonyChairman27Vivian Banta52Prudential Fin.Vice Chair28Janet Robinson52New York TimesSVP29Pam Strobel50ExelonEVP30Dina Dublon49J.P. Morgan ChaseEVP31Nancy Peretsman48Allen & Co.EVP32Susan Arnold48Procter & GamblePresident33Mary Kay Haben46Kraft FoodsEVP34Deb Henretta41Procter & GamblePresident35Carole Black59Lifetime EntertainmentCEO36Jamie Gorelick52Fannie MaeVice Chair37Marce Fuller42MirantCEO38Kathi Seifert53Kimberly-ClarkEVP39Anne Sweeney44Walt DisneyPresident40Marilyn C. Nelson63Carlson Cos.CEO41Anne Stevens53Ford MotorEVP42Sallie Krawcheck37Sanford BernsteinCEO43Carol Tome45Home DepotEVP44Marion Sandler71Golden West Fin.CEO45Louise Francesconi49RaytheonEVP46Vanessa Castagna53J.C. PenneyCEO47Larree Renda44SafewayEVP48Dawn Lepore48Charles SchwabVice Chair49Fran Keeth56Royal Dutch PetrolCEO50Heidi Miller49Bank OneEVP 2.61 (2 points) Radioactive lichen. Refer to the University of Alaska study to monitor the level of radioactivity in lichen, Exercise 2.34 (p. 51). The amount of the radioactive element sesium-137 (measured in microcuries per milliliter) for each of nine lichen specimens is repeated in the table. LocationBethel-5.50-5.00Eagle Summit-4.15-4.85Moose Pass-6.05Turnagain Pass-5.00Wickersham Dome-4.10-4.50-4.60 a. Find the mean, median, and mode of the radioactivity levels. ANSWER mean = - 4.86; median = -4.85; mode = -5.00 b. Interpret the value of each measure of central tendency, part a. 2.65 (7 points) Childrens use of pronouns. Clinical observations suggest that specifically language-impaired (SLI) children have a great difficulty with the proper use of pronouns. This phenomenon was investigated and reported in the Journal of Communication Disorders (Mar. 1995). Thirty children, all from low-income families, participated in the study. Ten were 5-year-old SLI children, ten were younger (3-yer-old) normally developing (YND) children, and ten were older (5-year-old) normally developing (OND) children. The table contains the gender, deviation intelligence quotient (DIQ), and percentage of pronoun errors observed for each of the 30 subjects. SubjectGenderGroupDIQPronoun Errors (%)1FYND11094.402FYND9219.053FYND9262.504MYND10018.755FYND8606FYND10555.007FYND90100.008MYND9686.679MTND9032.4310FTND92011FSLI8660.0012MSLI8640.0013MSLI9431.5814MSLI9866.6715FSLI8942.8616FSLI8427.2717MSLI11033.3318FSLI107019FSLI87020MSLI95021MOND110022MOND113023MOND113024FOND109025MOND92026FOND108027MOND95028FOND87029FOND94030FOND980 a. Identify the variables in the data set as quantitative or qualitative. b. Why is it nonsensical to compute numerical descriptive measure for qualitative variables? c. Compute measure of central tendency for DIQ for the ten SLI children. d. Compute measures of central tendency for DIQ for the ten YND children. e. Compute measures of central tendency for DIQ for the ten OND children. f. Use the results, parts c-e, to compare the DIQ central tendencies of the three groups of children. Is it reasonable to use a single number (e.g., mean or median) to describe the center of the DIQ distribution? Or should three centers be calculated, one for each of the three groups of children? Explain. g. Repeat parts c-f for the percentage of pronoun errors. ANSWERS a. qualitative, qualitative, quantitative, quantitative c. mean = 93.6; median = 91.5; mode = 86 d. mean = 95.3; median = 92; mode = 92 e. mean = 101.9; median = 103; mode = 113 f. three centers g. YND: mean = 46.88, median = 43.7, mode = 0; SLI: mean = 30.17, median = 32.5, mode = 0; OND: mean = 0, median = 0, mode = 0 2.66 (5 points) Mongolian desert ants. The Journal of Biogeography (Dec. 2003) published an article on the first comprehensive study of ants in Mongolia (Central Asia). Botanists placed seed baits at 11 study sites and observed the ant species attracted to each site. Some of the data recorded at each study site are provided below. SiteRegionAnnual Rainfall (mm)Max. Daily Temp. (C)Total Plant Cover (%)Number of Ant SpeciesSpecies Diversity Index1Dry Steppe1965.7403.892Dry Steppe1965.7523.833Dry Steppe1797.040521.314Dry Steppe1978.04371.485Dry Steppe1498.5275.976Gobi Desert11210.73049.467Gobi Desert12511.41651.238Gobi Desert9910.93049Gobi Desert12511.4564.7610Gobi Desert8411.42251.2611Gobi Desert11511.4144.69 a. Find the mean, median, and mode for the number of ant species discovered at the 11 sites. Interpret each of these values. ANSWER b. Which measures of central tendency would you recommend to describe the center of the number of ant species distribution? Explain. ANSWER c. Find the mean, median, and mode for the total plant cover percentage at the 5 Dry Steppe sites only. ANSWER d. Find the mean, median, and mode for the total plant cover percentage at the 6 Gobi Desert sites only. ANSWER e. Based on the results, parts c and d, does the center of the total plant cover percentage distribution appear to be different at the two regions? ANSWER   2.75 (3 points) Calculate the range, variance, and standard deviation for the following samples: a. 39, 42, 40, 37, 41 b. 100, 4, 7, 96, 80, 3, 10, 2 c. 100, 4, 7, 30, 80, 30, 42, 2 ANSWERS a. 5, 3.7, 1.92 b. 99, 1949.25, 44.15 c. 98,1307.84, 36.16 2.80 (4 points) Compute s2 , and s for each of the data sets listed. Where appropriate, specify the units in which your answer is expressed. a. 3, 1, 10, 10, 4 b. 8 feet, 10 feet, 32 feet, 5 feet c. -1, -4, -3, 1, -4, -4 d. 1/5 ounce, 1/5 ounce, 1/5 ounce, 2/5 ounce, 1/5 ounce, 4/5 ounce ANSWERS    2.81 (3 points) Reading Japanese books. Refer to the Reading in a foreign language (Apr. 2004) experiment to improve the Japanese reading comprehension levels of 14 University of Hawaii students, presented in exercises 2.31 and 2.57 (pp. 46 and 58). The data on number of books read and grade for each student are saved in the JAPANESE file. a. Find the range, variance, and standard deviation of the number of books read by students who earned an A grade. b. Find the range, variance, and standard deviation of the number of books read by students who earned either a B or C grade. c. Refer to parts a and b. which of the two groups of students has a more variable distribution for number of books read? ANSWERS a. 29, 75.7, 8.70 b. 24, 72.7, 8.53 c. A students 2.93 (3 points) Sanitation inspection of cruise ships. Refer to exercise 2.32 (p.46) and the Centers for Disease Control and Prevention listing of the May 2006 sanitation scores for 169 cruise ships. The data are saved in the SHIPSANT file. a. Find the mean and standard deviation of the sanitation scores. b. Calculate the intervals c. Find the percentage of measurements in the data set that fall within each of the intervals in part b. Do these percentages agree with either Chebyshevs rule or the empirical rule? ANSWERS a. (x = 94.91, s = 4.83 b. (90.08, 99.74): (85.25, 104.570; (80.42, 109.40) c. 81.1%, 97.6%, 98.2%: yes 2.97 (3 points) Hand washing versus hand rubbing. In hospitals, washing the hands with soap is emphasized as the single most important measure in the prevention of infections. As an alternative to hand washing, some hospitals allow health workers to rub their hands with an alcohol-based antiseptic. The British medical Journal (Aug. 17 2002) reported on a study to compare the effectiveness of washing the hands with soap and rubbing alcohol. One group of health care workers used hand rubbing, while a second group of used hand washing to clean their hands. The bacterial count (number of colony-forming units) on the hand of each worker was recorded. The table gives descriptive statistics on bacteria counts for the two groups of health care workers. --------------------------------------------------------------------------------------------------------- Mean Standard Deviation --------------------------------------------------------------------------------------------------------- Hand rubbing 35 59 Hand washing 69 106 --------------------------------------------------------------------------------------------------------- a. for hand rubbers, form an interval that contains about 95% of the bacterial counts. (Note: The bacterial count cannot be less than 0.) b. Repeat part a for hand washers. c. On the basis of your results in parts a and b, make an inference about the effectiveness of the two hand-cleaning methods ANSWERS a. (0, 300.5) b. (0, 546) c. hand rubbing appear to be more effective 2.99 (2 points) Velocity of Winchester bullets. The American Rifleman (June 1993) reported on the velocity of ammunition fired from the FEG P9R pistol, a 9-mm gun manufactured in Hungary. Field tests revealed that Winchester bullets fired from the pistol had a mean velocity (at 15 feet) of 936 feet per second and a standard deviation of 10 feet per second. Tests were also conducted with Uzi and black Hills ammunition. a. Describe the velocity distribution of Winchester bullets fired from the FEG P9R pistol. b. A bullet whose brand is unknown is fired from the FEG P9R pistol. Suppose the velocity (at 15 feet) of the bullet is 1,000 feet per second. Is the bullet likely to be manufactured by Winchester? Explain. ANSWERS a. at least 8/9 of the velocities will fall within 936 ( 3(10) b. No 2.101 (3 points) Improving SAT scores. The National Education Longitudinal Survey (NELS) tracks a nationally representative sample of U.S. students from eight grade through high school and college. Research published in chance (winter 2001) examined the SAT scores of 265 NELS students who paid a private tutor to help them improve their scores. The table summarizes the damages in both the SAT-Mathematics and SAT-verbal scores for these students. SAT-Math SAT-Verbal Mean change in score 19 7 Standard deviation of scores changes 65 49 a. Suppose one of the 265 students who paid a private tutor is selected at random. Give an interval that is likely to contain the change in this students SAT-Math score. b. Repeat part a for the SAT-Verbal score. c. Suppose the selected students score increased on one of the SAT tests by 140 points. Which test, the SAT-Math or SAT-Verbal, is the one most likely to have had the 140- point increase? Explain. ANSWERS a. 19 ( 195 b. 7 ( 147 c. 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