Mini Practice Set Responses ~ Algebra/Data Analysis ~ Item 21


	Item 21 Mini Practice Set Responses

Juan conducted two different surveys about student transportation to school. For Survey A, he stood at the entrance of the school at 7:30 a.m. and surveyed the first 80 students. For Survey B, he used a random number generator to select 80 students in the school to survey. His results are shown in the tables below.

Complete the following in the Answer Book:

Use principles of simple random sampling to justify why Juan should have more confidence in the results of Survey B.
Use principles of simple random sampling to justify why Juan should have less confidence in the results of Survey A.
According to the data collected from Survey B, of the 400 total students in the school, how many students should Juan expect to ride a bike? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

Score Level 4 Paper
This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The student provides a fully developed justification for more confidence in Survey B. ("Everyone has a fair chance, and every person is chosen independently.") The justification for less confidence in Survey A is fully developed and clearly presented. ("Some students could get to school late and that means it is not a fair chance for everyone to get picked.") The student provides the correct number of expected bike-riding students, and the explanation is fully developed. ("I multiplied 400 {# of students} times 10 {# of students}, then I divided 4,000 by 80 {people surveyed}.) This response demonstrates a complete understanding and analysis of the problem.
Score Level 1 Paper
This response indicates little application of a reasonable strategy. The student's attempted justification for more confidence in Survey B, and less in Survey A, does not incorporate equal chance or independent selection. Used repeatedly, the term "random" is given in the question and, therefore, needs further clarification. The correct number of expected bike-riding students is provided. By setting up a proportion and solving for x, a symbolic explanation is given which supports the solution. This response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.)
Score Level 3 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 ("gives an equal chance of all the students to be represented") and addresses equal chance, but not independent selection. The justification for less confidence in Survey A supports the solution ("looking at the first 80 people takes away the chance for all the people who come to school later"). The number of expected bike-riding students is correct, and the symbolic explanation supports the solution. This response demonstrates a clear understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)
Score Level 2 Paper
This response indicates an incomplete application of a reasonable strategy. The student's justification for more confidence in Survey B supports the solution. ("It gives every person an equal chance and randomly selected the 80 people that were chosen for the survey.") This justification does not address independent selection. The justification for less confidence in Survey A supports the solution ("…it is very exclusionary. Any students who arrive later had no chance of being selected to be surveyed"). The answer to the third part of the question is incomplete. This response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.)

Mini Practice Set Papers ~ Algebra/Data Analysis ~ Item 21

Complete the following in the Answer Book:

Use principles of simple random sampling to justify why Juan should have more confidence in the results of Survey B.
Use principles of simple random sampling to justify why Juan should have less confidence in the results of Survey A.
According to the data collected from Survey B, of the 400 total students in the school, how many students should Juan expect to ride a bike? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

Score Level 4 Paper

This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The student provides a fully developed justification for more confidence in Survey B. ("Everyone has a fair chance, and every person is chosen independently.") The justification for less confidence in Survey A is fully developed and clearly presented. ("Some students could get to school late and that means it is not a fair chance for everyone to get picked.") The student provides the correct number of expected bike-riding students, and the explanation is fully developed. ("I multiplied 400 {# of students} times 10 {# of students}, then I divided 4,000 by 80 {people surveyed}.) This response demonstrates a complete understanding and analysis of the problem.

Score Level 1 Paper

This response indicates little application of a reasonable strategy. The student's attempted justification for more confidence in Survey B, and less in Survey A, does not incorporate equal chance or independent selection. Used repeatedly, the term "random" is given in the question and, therefore, needs further clarification. The correct number of expected bike-riding students is provided. By setting up a proportion and solving for x, a symbolic explanation is given which supports the solution. This response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.)

Score Level 3 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 ("gives an equal chance of all the students to be represented") and addresses equal chance, but not independent selection. The justification for less confidence in Survey A supports the solution ("looking at the first 80 people takes away the chance for all the people who come to school later"). The number of expected bike-riding students is correct, and the symbolic explanation supports the solution. This response demonstrates a clear understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)

Score Level 2 Paper

This response indicates an incomplete application of a reasonable strategy. The student's justification for more confidence in Survey B supports the solution. ("It gives every person an equal chance and randomly selected the 80 people that were chosen for the survey.") This justification does not address independent selection. The justification for less confidence in Survey A supports the solution ("…it is very exclusionary. Any students who arrive later had no chance of being selected to be surveyed"). The answer to the third part of the question is incomplete. This response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.)