AP® Statistics 2005 Scoring Guidelines The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the association is composed of more than 4,700 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three and a half million students and their parents, 23,000high schools, and 3,500 colleges through major programs and services in college admissions, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT®, the PSAT/NMSQT®, and the Advanced Placement Program® (AP®). The College Board is committed to the principles of excellence and equity, and that commitment is embodied in all of its programs, services, activities, and concerns. Copyright © 2005 by College Board. All rights reserved. College Board, AP Central, APCD, Advanced Placement Program, AP, AP Vertical Teams, Pre-AP, SAT, and the acorn logo are registered trademarks of the College Entrance Examination Board. Admitted Class Evaluation Service, CollegeEd, Connect to college success, MyRoad, SAT Professional Development, SAT Readiness Program, and Setting the Cornerstones are trademarks owned by the College Entrance Examination Board. PSAT/NMSQT is a registered trademark of the College Entrance Examination Board and National Merit Scholarship Corporation. Other products and services may be trademarks of their respective owners. Permission to use copyrighted College Board materials may be requested online at: http://www.collegeboard.com/inquiry/cbpermit.html. Visit the College Board on the Web: www.collegeboard.com. AP Central is the official online home for the AP Program and Pre-AP: apcentral.collegeboard.com. www.mymathscloud.com
AP® STATISTICS 2005 SCORING GUIDELINES Copyright © 2005 by College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). 2 Question 1 SolutionPart (a): The mean (40.45 cal/kg) and median (41 cal/kg) daily caloric intake of ninth-grade students in the rural school are higher than the corresponding measures of center, mean (32.6 cal/kg) and median (32 cal/kg), for ninth-graders in the urban school. There is also more variability or spread in the daily caloric intake for students in the rural school (Range=19, SD=6.04, IQR=10) than in the daily caloric intake for students in the urban school (Range=16, SD=4.67, IQR=7). The shapes of the two distributions are also different. The distribution of daily caloric intake for rural students is more uniformly distributed (symmetric) between 32 cal/kg and 51 cal/kg while the distribution of daily caloric intake for urban students appears to be skewed toward the larger values. Part (b): No, the samples include students from only one rural and one urban high school so it is not reasonable to generalize the findings from these two schools to all rural and urban ninth-grade students in the United States. Part (c): Since we are assuming that students keep accurate records, Plan II will do a better job of comparing the daily caloric intake of adolescents living in rural areas with the daily caloric intake of adolescents living in urban areas. Both plans take body weight into account by converting to food consumed per kilogram of body weight. Plan II includes a 7-day period (possibly days in school and days at home on the weekend), and there are differences in caloric intake among days. It would therefore be better to average over the 7-day period rather than considering only the food consumed in one day, as is the case with Plan I. Plan II would provide a more precise estimate of the average daily intake. ScoringParts (a) and (c) are scored as essentially correct (E), partially correct (P), or incorrect (I). Part (b) is scored as essentially correct (E) or incorrect (I). Part (a) is essentially correct (E) if the student correctly compares center, shape, and spread of the two distributions. Specific numerical values are not required. Part (a) is partially correct (P) if the student correctly compares any two of the three characteristics (center, shape, or spread) of the two distributions. Part (a) is incorrect (I) if the student correctly compares no more than one characteristic. www.mymathscloud.com
AP® STATISTICS 2005 SCORING GUIDELINES Copyright © 2005 by College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). 3 Question 1 (continued) Part (b) is essentially correct (E) if the student realizes that these findings cannot be generalized because the students were selected from only one rural and one urban high school. Part (b) is incorrect (I) if the student argues that these findings: • cannot be generalized with no explanation given; OR • cannot be generalized with an invalid explanation (e.g., the response indicates that the student sample size (n=20) is not big enough); OR • can be generalized because the randomly selected students from these two schools may represent all urban and rural ninth-grade students in the United States. Part (c) is essentially correct (E) if Plan II is chosen and a correct justification involving day-to-day variability is provided. Part (c) is partially correct (P) if Plan II is chosen, but a weak statistical justification that includes a discussion of day-to-day variability is provided. Part (c) is incorrect (I) if: • Plan I is chosen; OR • Plan II is chosen and a correct justification is not provided. 4 Complete Response (3E) All three parts essentially correct 3 Substantial Response (2E 1P) Two parts essentially correct and one part partially correct 2 Developing Response (2E 0P or 1E 2P) Two parts essentially correct and zero parts partially correct OR One part essentially correct and two parts partially correct 1 Minimal Response ( 1E 1P or 1E 0P or 0E 2P) One part essentially correct and either zero parts or one part partially correct OR Zero parts essentially correct and two parts partially correct www.mymathscloud.com
AP® STATISTICS 2005 SCORING GUIDELINES Copyright © 2005 by College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). 4 Question 2 SolutionPart (a): The expected number of telephone lines in use by the technical support center at noon is: ()00.3510.220.1530.1540.150.051.6EX=¥+¥+¥+¥+¥+¥=Part (b): We would expect the average based on 1,000 days to be closer to 1.6 than the first average based on 20 days. Both averages have the same expected value (1.6), but the variability for sample averages based on 1,000 days is smaller than the variability for sample averages based on 20 days. Part (c): The median of X is 1. x()PX x£()PX x≥0 0.35 1.0 1 0.55 0.65 2 0.70 0.45 3 0.85 0.30 4 0.95 0.15 5 1.0 0.05 OR The median of X is 1 because ()10.550.50PX£=≥ and ()10.650.50PX≥=≥. Part (d): The probability histogram is clearly skewed to the right (or toward the larger values) so the mean (1.6) is larger than the median (1), as is typical for a right-skewed distribution. www.mymathscloud.com
AP® STATISTICS 2005 SCORING GUIDELINES Copyright © 2005 by College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). 5 Question 2 (continued) ScoringParts (a) and (c) are combined as one computational part. Each part is scored as essentially correct (E), partially correct (P), or incorrect (I). Collectively parts (a)and (c) are essentially correct (E) if both parts are calculated correctly, with the exception of minor arithmetic errors. Collectively parts (a) and (c) are partially correct (P) if one of the two parts is calculated correctly, with the exception of minor arithmetic errors. Collectively parts (a) and (c) are incorrect (I) if both parts are calculated incorrectly. Note: Unsupported answers in parts (a) and (c) are scored as incorrect. Part (b) is essentially correct (E) if the student: 1. States the new estimate based on 1,000 days should be closer to the expected value of 1.6; OR the new estimate will increase, or decrease if the answer in part (a) is less than 1.25. AND 2. Provides justification by stating the variability for sample averages based on 1,000 days will be smaller than the variability for sample averages based on 20 days; OR as the sample size increases the sample average approaches the expected value of X. Part (b) is partially correct (P) if the student provides one of the two items above. Part (d) is essentially correct (E) if the student states that since the distribution is skewed to the right, the mean is greater than the median; OR since the mean is greater than the median, the distribution is skewed to the right. Note: There must be evidence that the student looked at the given distribution. Part (d) is partially correct (P) if the student: • States that since the mean is greater than the median, the distribution is skewed to the right (with no evidence that the student looked at the given distribution); OR • Compares the two measures of center by referring to the inappropriate orincomplete shape of the distribution (e.g., “skewed to the left” or “skewed”); OR • Makes a correct statement about the measures of center and the shape without connecting the two. www.mymathscloud.com
AP® STATISTICS 2005 SCORING GUIDELINES Copyright © 2005 by College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). 6 Question 2 (continued) Part (d) is incorrect (I) if the student: • Compares the two measures of center without mentioning the shape of the distribution; OR • Correctly describes the shape without correct conclusions about the relative location of the mean and median; OR • Makes multiple “generic” statements about the relationship of mean, median, and shape with no reference to the given distribution. 4 Complete Response (3E) All three parts essentially correct 3 Substantial Response (2E 1P) Two parts essentially correct and one part partially correct 2 Developing Response (2E 0P or 1E 2P) Two parts essentially correct and zero parts partially correct OR One part essentially correct and two parts partially correct 1 Minimal Response ( 1E 1P or 1E 0P or 0E 2P) One part essentially correct and either zero parts or one part partially correct OR Zero parts essentially correct and two parts partially correct www.mymathscloud.com
