Math 253 - Chapter 3 Problems

Math 253 - Chapter 3 Problems - Problem 8 Education Level...

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Unformatted text preview: Problem 8 Education Level No HS diploma HS diploma, no college Some college, no degree 2-year degree 4-year degree Master's degree Ph.D. or professional Total Count (thousands) 9945 11701 4481 1390 3133 1213 757 32620 Percent 30.5 35.9 13.7 4.3 9.6 3.7 2.3 100 40.0 Education Le 35.0 30.0 Relative Freqency (% of population) 25.0 20.0 15.0 10.0 5.0 Nearly a third did not graduate from high school. The total how did not attend college at all is about 2/3. And less than 1/6 got as far as completing a 4 year degree. 0.0 No HS diploma Problem 9 Phenomenon Psychic healing ESP Ghosts Astrology Channeling % Expressing Belief 54 50 38 28 15 60 50 % of Population 40 Population % Expressin 30 20 10 0 Psychic healing a) No! There might be as much . as a 10% overlap in the categories. b) No, because there is no way to tell how much overlap there is between categories. Problem 14 1. 2. 3. 4. 5. Display is tilted, giving excessive emphasis (area) to segments nearest the viewer. Pie charts work for mutually exclusive categories. These are not. The display is not labeled. Percentages add up to more than 100%. The arcs are not proportional to the percentages (85% should be much larger than 39%). Problem 18 Female Male L 35 50 85 M 36 44 80 C 6 21 27 77 115 192 B Column Percentages L M Female 41.2 45.0 Male 58.8 55.0 100 100 a) From Table C b) From Table C c) From Table A d) From Table C e) From Table f) From Table g) From Table C 22.2 77.8 100 108.4 191.6 300.0 59.90% 14.10% 18.30% 10.90% 45.50% 43.50% Not really, Table A shows about the same proportion of Liber but about twice the proportion of males as of females consid This difference is made up by differing proportions who consi Note that the first thing I did was to set up the three "daughter" contingency tables. to pick out the desired information. Problem 20 a) 50.0 Political Views of Class Members Percent of Class 40.0 30.0 20.0 10.0 Percent of Cla 10.0 0.0 Liberal Moderate Conservative Political Views b) Political Views of Male Class Members 50.0 45.0 40.0 % of Males in Class 35.0 30.0 25.0 20.0 15.0 10.0 5.0 0.0 Liberal Moderate Conservative c) 50.0 45.0 40.0 35.0 30.0 25.0 20.0 15.0 10.0 5.0 0.0 Political Views of Female Class Members % of Females in Class Liberal Moderate Conservative d) Political Views of Class Members, Separated by Gender 50.0 50.0 45.0 40.0 35.0 30.0 25.0 20.0 15.0 10.0 5.0 0.0 Liberal Moderate Conservative e) A larger proportion of the females tend to view themselves as moderate, while a larger proportion (more than twice) of the males tend to view themselves as conse Problem 27 Rain 27 7 34 No Rain 63 268 331 Rain No Rain 90 275 365 B Rain No Rain Column Percentages Rain No Rain 79.4 19.0 20.6 81.0 100.0 100.0 98.4 101.6 200.0 a) b) c) Table C. It rained on 9.3% of the days. Table C. Rain was predicted on 24.7 % of the days. Original Table. Rain was predicted and came on 27 days, no rain was predicted on 26 The forecast was correct on 100*(27+268)/365 percent of the days. The forecast was correct on 80.8% percent of the days. This information can also be obtained from Table C by adding the two diagonal cells d) When rain was predicted, the forecast was correct 30% of the time (Table B). When 97.5 of the time. This looks like a very strong association between type of weather a that when rain is predicted for an area it will not rain in all parts of the area. If the fo required to issue a prediction of rain, even though that will be incorrect for about ha Wrong Rain No Rain 30 2.5 Correct 70 97.5 Problem 32 a) The numbers cannot be table percentages, because they add up to more than 100%. add to 100% when adding across. But each of the three columns adds to 100%, so th Normal 23.8 27.8 31.6 16.8 Overweight 26 28.7 31.1 14.2 b) Inactive Irregular Activity Regular Activity Regular, Intense Obese 35.6 28.1 27.2 9.1 35 People with Normal BMI 35 % of Group with Normal BMI % of Overweight Group 30 25 20 15 10 5 30 25 Overweigh 20 15 10 5 0 Inactive 0 Inactive Irregular Activity Regular Activity Regular, Intense Note that the third diagram was expanded so that the scales are all the same. These data indicate, but do not prove, that lack of exercise causes obesity. There is n not mean the same for everyone. For someone who is really obese, walking up a ha likely not place a 10 mile bike ride in that category. The issue in answering the quest and obesity are not independent. Education Level of Citizens Over 65 No HS HS Some diploma diploma, no college, no college degree 2-year degree 4-year degree Master's Ph.D. or degree professional Maximum Educational Level Population % Expressing Belief in Supernatural Phenomena Psychic healing ESP Ghosts Phenomenon Astrology Channeling A Row Percentages L M Female 45.5 46.8 Male 43.5 38.3 88.9 85.0 C 7.8 18.3 26.1 100 100 200 C Percentages of Total L M Female 18.2 18.8 Male 26.0 22.9 44.3 41.7 C 3.1 10.9 14.1 40.1 59.9 100.0 e same proportion of Liberal males and females, males as of females consider themselves Conservatives. ring proportions who consider themselves Moderate. ghter" contingency tables. This makes it much easier Liberal Moderate Conservative embers These data are from the bottom margin of table C, above. Conservative mbers These data are from the "Male" row of Table A, above. Conservative s Members These data are from the "Female" row of Table A, above. Conservative rs, Separated These data are from both rows of Table A, above. Female Male es as moderate, while o view themselves as conservative. A Rain No Rain Row Percentages Rain No Rain 30.0 70.0 2.5 97.5 32.5 167.5 100 100 200 C Rain No Rain Total Percentages Rain No Rain 7.4 17.3 1.9 73.4 9.3 90.7 24.7 75.3 100.0 no rain was predicted on 268 days when it didn't rain. ding the two diagonal cells containing 7.4 and 73.4. the time (Table B). When No Rain was predicted, the forecast was correct between type of weather and accuracy of the prediction. However, most people don't realize parts of the area. If the forecaster knows that it will rain in 51% of an area, he/she is still l be incorrect for about half of the area. Accuracy of Prediction of Rain 120.0 100.0 80.0 60.0 Correct Incorrect 40.0 20.0 0.0 Rain No Rain dd up to more than 100%. Similarly, they cannot be row percentages because they don't olumns adds to 100%, so the numbers are column percentages. Overweight People % of Obese People Obese People 40 35 30 25 20 15 10 5 0 Inactive Irregular Activity Regular Activity Regular, Intense Inactive Irregular Activity Regular Activity Regular, Intense es are all the same. e causes obesity. There is no way of telling if everyone meant the same thing by "intense exercise", and in fact it does ally obese, walking up a half flight of stairs is very intense exercise, while someone with a normal BMI would sue in answering the question is not connection but causality. However, it is fairly obvious that lack of exercise Regular, Intense ...
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