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.
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).
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 Response Three sections essentially correct 2 Developing Response Two sections essentially correct 1 Minimal Response One section essentially correct
©2008 The College Board. All rights reserved.Visit the College Board on the Web: www.collegeboard.com.
©2008 The College Board. All rights reserved.Visit the College Board on the Web: www.collegeboard.com.
©2008 The College Board. All rights reserved.Visit the College Board on the Web: www.collegeboard.com.
