AP® Statistics 2008 Scoring Guidelines Form B 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 5,400 schools, colleges, universities, and other educational organizations. Each year, the College Board serves seven million students and their parents, 23,000 high 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. © 2008 The College Board. All rights reserved. College Board, AP Central, Advanced Placement Program, AP, SAT, and the acorn logo are registered trademarks of the College Board. PSAT/NMSQT is a registered trademark of the College Board and National Merit Scholarship Corporation. All other products and services may be trademarks of their respective owners. Permission to use copyrighted College Board materials may be requested online at: www.collegeboard.com/inquiry/cbpermit.html. Visit the College Board on the Web: www.collegeboard.com. AP Central is the online home for AP teachers: apcentral.collegeboard.com. www.mymathscloud.com
AP® STATISTICS 2008 SCORING GUIDELINES (Form B) © 2008 The College Board. All rights reserved. Visit the College Board on the Web: www.collegeboard.com. Question 1 Intent of QuestionThe primary goals of this question were to assess a student’s ability to (1) construct a dotplot that can used to compare two distributions and to make appropriate comparisons of the center and spread of the two distributions and (2) understand and explain why in some situations inferential procedures that generalize from samples to larger populations are not appropriate. SolutionPart (a): A similarity is that the two distributions are centered in approximately the same place. A difference is that the distribution for the schools with the lowest proportions of students meeting the standards is less variable. Part (b): The two groups of schools are not random samples from two populations of interest. One group is the population of all 10 schools with the highest proportion of students meeting the standards, and the other group is the population of all 10 schools with the lowest proportion of students meeting the standards. Therefore, inferential procedures that generalize from samples to larger populations are not appropriate. ScoringPart (a) is divided into three sections. Section 1 is related to the dotplots, section 2 is related to the centers of the distributions, and section 3 is related to the spreads. Each is scored as either essentially correct (E) or incorrect (I). Section 1 is scored as follows: Essentially correct (E) if the dotplots are given with appropriate labels and scales (minor errors in the placement of the dots are okay). Incorrect (I) if the labels or scales are missing OR if a histogram with dots or a scatterplot is given. www.mymathscloud.com
AP® STATISTICS 2008 SCORING GUIDELINES (Form B) © 2008 The College Board. All rights reserved. Visit the College Board on the Web: www.collegeboard.com. Question 1 (continued) Section 2 is scored as follows: Essentially correct (E) if the response states that the two distributions have approximately the same center (no numerical values are required) OR if the response states that the means are slightly different. Incorrect (I) if measures of center are not given OR if they are given, but there is no comparison of the center of the two distributions. Section 3 is scored as follows: Essentially correct (E) if the response states that the spread of the two distributions differs (no numerical values are required). Incorrect (I) if measures of spread are not given OR if they are given, but there is no comparison of the spread of the two distributions. Note: Usually distributions are described in terms of shape, center, and spread. However, with small data sets, shape is difficult to judge, so no comparison of shape is required. Part (b) is considered as section 4 and is scored as either essentially correct (E), partially correct (P), or incorrect (I). Section 4 is scored as follows: Essentially correct(E) if the responsestates that the data are not samples from some larger population OR that they are not random samples but instead are those with the highest and lowest proportions of students meeting a standard, and therefore inference is not appropriate. The response must not include any other reason (such as small sample sizes or the shape of the distribution). Partially correct (P) if the response states only that the schools are not randomly selected. The response must not include any other reason (such as small sample sizes or the shape of the distribution). Incorrect (I) if the responsestates that the sample sizes are too small OR if the response refers to the shape of the distribution or to some other criterion. Note: If there is information relating to part (a) in the explanation in part (b), it may be used in the scoring of part (a). www.mymathscloud.com
AP® STATISTICS 2008 SCORING GUIDELINES (Form B) © 2008 The College Board. All rights reserved. Visit the College Board on the Web: www.collegeboard.com. Question 1 (continued) 4 Complete Response All four sections essentially correct 3 Substantial ResponseThree sections essentially correct 2 Developing Response Two sections essentially correct 1 Minimal Response One section essentially correct www.mymathscloud.com
AP® STATISTICS 2008 SCORING GUIDELINES (Form B) © 2008 The College Board. All rights reserved. Visit the College Board on the Web: www.collegeboard.com. Question 2 Intent of QuestionThe primary goals of this question were to assess a student’s ability to (1) recognize an unbiased estimator and explain why the estimator is unbiased and (2) compare two estimators with respect to center and variability. SolutionPart (a): Statistics A, C, and D appear to be unbiased. This is indicated by the fact that the mean of the estimated sampling distribution for each of these statistics is about 75, the value of the true population parameter. Part (b): Statistic A would be a better choice because it appears to be unbiased. Although the variability of the two estimated sampling distributions is similar, statistic A would produce estimates that tend to be closer to the true population parameter value of 75 than would statistic B. Part (c): Statistic C would be a better choice because it has smaller variability. Although both statistic C and statistic D appear to be unbiased, statistic C would produce estimates that tend to be closer to the true population parameter value of 75 than would statistic D. ScoringParts (a), (b), and (c) are each scored as essentially correct (E), partially correct (P), or incorrect (I). Part (a) is scored as follows: Essentially correct (E) if the response contains the following two components. Component 1: Identifies statistics A, C, and D as the unbiased estimators. Component 2: Clearly demonstrates an understanding of the meaning of the term unbiased. That is, states that the mean (or center) of each distribution is about 75. No other characteristic (e.g., shape, spread) should be mentioned in the response unless it clearly is discounted as a criterion for being unbiased. Partially correct (P) if the response contains just one of these components. That is, the response either identifies statistics A, C, and D as the unbiased estimators but gives a weak or no explanation or includes some discussion of another characteristic (e.g., shape, spread) as of some importance in judging bias ORdemonstrates clear understanding of the meaning of the term unbiased but identifies only one or two of statistics A, C, and D as unbiased estimators. Incorrect (I) otherwise. www.mymathscloud.com
AP® STATISTICS 2008 SCORING GUIDELINES (Form B) © 2008 The College Board. All rights reserved. Visit the College Board on the Web: www.collegeboard.com. Question 2 (continued) Part (b) is scored as follows: Essentially correct (E) if the response gives a clear explanation that statistic A is the better choice because it is centered at 75. (It is not necessary that the term unbiased be used as long as the response clearly addresses the center. It is not necessary to mention that statistics A and B both have about the same variability.) Note: Students who were penalized in part (a) for mentioning other characteristics should not be repenalized in part (b). Partially correct (P) if the response shows an understanding that centering is an important issue in determining which statistic is better but either does not apply the concept correctly OR communicates the explanation poorly. Incorrect (I) otherwise. Part (c) is scored as follows: Essentially correct (E) if the response gives a clear explanation that statistic C is the better choice based on the fact that it has less variability. (It is not necessary to mention that statistics A and B are both centered at the parameter.) Partially correct (P) if the response shows an understanding that variability is an important issue in determining which statistic is better but either does not apply the concept correctly OR communicates the explanation poorly. Incorrect (I) otherwise.4 Complete ResponseAll three parts essentially correct 3 Substantial Response Two parts essentially correct and the other part partially correct OR Part (a) and one other part essentially correct and the remaining part incorrect 2 Developing Response Part (a) essentially correct and one of the other parts partially correct OR All three parts partially correct OR Part (a) partially correct and one of parts (b) and (c) essentially correct www.mymathscloud.com
