Score Level 1 Anchor Paper

This response indicates little application of a reasonable strategy. The student's attempted justification for more confidence in Survey B does not mention either equal chance or independent selection. Instead, the term "random" ("they were randomly picked"), which is given in the question, is used, and, therefore, this justification needs further clarification. The student's attempted justification for less confidence in Survey A does not address equal chance or independent selection. However, an understanding of the relevant concept of bias is indicated. ("Students that use a certain method of transportation could have all arrived to school at a certain time which could have varied the results of the survey.") No answer is given to the third part of the question. This response demonstrates a minimal understanding and analysis of the problem.

Score Level 1 Anchor Paper

This response indicates little application of a reasonable strategy. The student's attempted justification for more confidence in Survey B does not address either equal chance or independent selection. Instead, the student uses the word "random" ("those students were chosen more randomly"), which is given in the question; therefore, this justification needs further clarification. The justification for less confidence in Survey A is a restatement of information given in the question. ("In survey A those are the first 80 people to school") The correct number of expected bike-riding students is provided. The explanation supports the solution; the student sets up a proportion and solves for x. This response demonstrates a minimal understanding and analysis of the problem.

Score Level 2 Anchor Paper

This response indicates an incomplete application of a reasonable strategy. The student's justification for more confidence in Survey B supports the solution, but is incomplete. This justification references only equal chance ("Everyone was given an equal chance of being selected.") and fails to address independent selection. The justification for less confidence in Survey A supports the solution ("not everyone wasn't given an equal chance to be sampled, the sample only represents early birds, sample was biased {pointed at one group of people}"). This response demonstrates a conceptual understanding and analysis of the problem.

Score Level 2 Anchor Paper

This response indicates an incomplete application of a reasonable strategy. The student's attempted justification for more confidence in Survey B does not address equal chance or independent selection. The student, instead, uses the term "random" ("Survey B is random because Juan used a number generator"), which is given in the question; therefore, the justification needs further clarification. The justification for less confidence in Survey A addresses equal chance. ("Some students may arrive late or use a different entrance. This gives some less of a chance of being surveyed, so the survey isn't random.") The correct number of expected bike-riding students is provided. The explanation supports the solution; the student sets up a proportion and solves it. This response demonstrates a conceptual understanding and analysis of the problem.

Score Level 3 Anchor Paper

This response indicates application of a reasonable strategy that leads to some correct solutions. The student's justification for more confidence in Survey B is generally well developed. ("It was chosen in a lottery style format {which means it was at random & everybody has a chance to be picked}.") The justification addresses equal chance but does not address independent selection. The justification for less confidence in Survey A supports the solution ("It also eliminates people who don't come to school and arrivals after the initial 80") and indicates that those students would not have a chance to be selected. The correct number of expected bike-riding students is provided, and the explanation supports the solution. ("10 people bike out of 80 in Survey B. 400 is 80(5). Therefore, 10(5)=50.") This response demonstrates a clear understanding and analysis of the problem.

Score Level 3 Anchor Paper

This response indicates application of a reasonable strategy that leads to some correct solutions. The student's justification for more confidence in Survey B is generally well developed. ("Sample B's method gave everyone an equal chance of being sampled.") This justification addresses equal chance but does not address independent selection. The justification for less confidence in Survey A supports the solution and is implied in the following quote. ("Some people might come to school late that day, didn't come to school that day, or went in the school at a different entrance. Not everyone had an equal chance of being sampled.") The correct number of expected bike-riding students is provided, and the symbolic explanation supports the solution. The student finds the percentage of students expected to ride bikes, then multiplies that by the total student population. This response demonstrates a clear understanding and analysis of the problem.

Score Level 4 Anchor Paper

This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The student not only provides a fully developed justification for more confidence in Survey B, but also recognizes that Survey B meets the requirements of a simple random sample (all students are equally likely to be chosen, and they are chosen independently of each other). The student further clarifies ("a random number generator is one of the best methods…everyone/everything has an equal chance to be sampled, and each sample is independent of the others") and then observes that Survey A is not a simple random sample. The justification is fully developed and clearly presented ("not everyone has an equal chance to be surveyed. Some buses might be late, some students might be absent that day, etc."). The correct number of expected bike-riding students is provided. By setting up a proportion and solving for x, the explanation is fully developed. This response demonstrates a complete understanding and analysis of the problem.

Score Level 4 Anchor Paper

This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The student provides a fully developed justification for more confidence in Survey B. ("For example, Survey B is a simple random sample, as all students stand an equal chance of being selected, and all the selections are made independently of one another…not basing selection on any particular order that would reduce chances of selection forsome…the numbers are generated independently of each other, not being based on previous ones.") The justification for less confidence in Survey A is fully developed and clearly presented. ("Students do not stand an equal chance of selection, and they may not be selected independently of one another…there may be a constant order to which students enter the school, meaning that all students will not have an equal chance for selection, as some arrive earlier/later than others…students may arrive with friends or in groups, meaning that if they are all chosen they are not chosen independently of each other.) This response demonstrates a complete understanding and analysis of the problem.