
	Item 32 Anchor Papers

HSA 2007 Algebra/Data Analysis Item 32

CID: CID35ed1745d43902fbe29e3fa4c02ba576
itemNum: 32
initialLetter
itemType: BCR
itemAnswerKey: N/A
itemMaxScorePoints: 3
origNum: x

The principal will survey 100 students to determine which elective courses to offer next year. The principal will use one of the methods below.

Method A: Survey the first 100 students who enter the cafeteria on a randomly selected day.

Method B: Have 25 teachers each randomly select 4 eleventh-grade students to be surveyed.

Method C: Assign each student a number. Use a random number generator to generate 100 numbers. Survey those students whose numbers are generated.

Complete the following in the Answer Book:

Which method will provide the principal with a simple random sample of the student population? Use principles of simple random sampling to justify your answer.
Use principles of simple random sampling to justify why each of the other two methods does not provide a simple random sample.

Score Level 1 Anchor Paper
This response indicates little attempt to apply a reasonable strategy. The student incorrectly chooses Method A as providing a simple random sample and gives no correct justification for this answer. The justification for why Method B will not provide a simple random sample is correct (you'd only have 11^th graders). The justification for why Method C will not provide a simple random sample is incorrect and shows a flaw in reasoning. The student states that (Method C wouldn't work because you would have to make sure that every student got a number) which is actually a reason why Method C would provide a simple random sample. The response demonstrates a minimal understanding and analysis of the problem.
Score Level 1 Anchor Paper
This response indicates little attempt to apply a reasonable strategy. The student correctly chooses Method C as providing a simple random sample but gives no valid justification. The justification for why Method A does not provide a simple random sample is incorrect. Method A does not give a simple random sample because only the first 100 students to enter the cafeteria are included, not because (many students enter the cafeteria with friends who like or would want to take the same elective). The justification for why Method B will not provide a simple random sample is correct (you are only surveying eleventh graders). The response demonstrates a minimal understanding and analysis of the problem.
Score Level 1 Anchor Paper
This response indicates little attempt to apply a reasonable strategy. The student correctly chooses Method C as providing a simple random sample and gives a partial justification (that gives every person a chance not just some people). No justification is given for why Methods A and B will not give simple random samples. The 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 correctly chooses Method C as providing a simple random sample but a justification addressing equal chance and independence is missing. The justification for why Method A will not provide a simple random sample is correct (that will limit the principal to one group of student in one cafeteria period). A correct justification is also given for why Method B will not give a simple random sample (the principal will be limited to only eleventh graders with certain teachers). The 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 correctly chooses Method C as providing a simple random sample and gives a complete justification (each student is equaly likely to be picked and it will be chosen independently). No justification is given for why Methods A and B will not provide simple random samples. The 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 correctly chooses Method C as providing a simple random sample and gives a complete justification (every student of the population will have an equal opportunity to be chosen; the population will be chosen independently of one another). The justification for why Method A will not provide a simple random sample is plausible but not well developed (not every student of the population will have an equal opportunity to be chosen; the students will be chosen dependently on one another). The justification needs to specifically address what about Method A keeps it from giving every student an equal chance. Similarly, the justification for why Method B will not provide a simple random sample (not every student of the population will have an equal opportunity to be chosen) is not well developed and needs to specifically address why Method B does not provide every student an equal chance. The 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 correctly chooses Method C as providing a simple random sample and gives a partial justification (this will randomly choose everybody). Independence is not addressed. The justification for why Method A will not provide a simple random sample is correct (some kids get to school early every day). This indicates that early students go to the cafeteria to wait for school to start and they would always be the first 100 to enter the cafeteria, excluding those students who do not arrive at school early. Correct justification is also given for why Method B will not give a simple random sample (it's only for eleventh graders). The 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 a correct solution in the context of the problem. The student correctly chooses Method C as providing a simple random sample and gives a fully developed justification (each member of the population is equally likely to be chosen, and they are picked independently). The justification for why Method A will not provide a simple random sample is correct (not everyone eats in the cafeteria and some people may be absent). A correct justification is also given for why Method B will not provide a simple random sample (students of other teachers that weren't chosen, won't have a chance to be surveyed). The response demonstrates a complete understanding and analysis of the problem.
Score Level 3 Anchor Paper
This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The student correctly chooses Method C as providing a simple random sample and gives a fully developed justification (everyone will have an equally likely chance to be chosen to survey and each student will be chosen independently). The justification for why Method A will not provide a simple random sample is correct (a student may not be able to get to the cafeteria that day or may be absent. So the students do not have an equally likely chance to be chosen). A correct justification is also given for why Method B will not provide a simple random sample (only the eleventh grade students get to be offered to be surveyed and 9^th and 10^th graders won't get a chance to say their oppinion). The response demonstrates a complete understanding and analysis of the problem.

Anchor Papers ~ Algebra/Data Analysis ~ Item 32

HSA 2007 Algebra/Data Analysis Item 32

CID: CID35ed1745d43902fbe29e3fa4c02ba576
itemNum: 32
initialLetter
itemType: BCR
itemAnswerKey: N/A
itemMaxScorePoints: 3
origNum: x

The principal will survey 100 students to determine which elective courses to offer next year. The principal will use one of the methods below.

Method A: Survey the first 100 students who enter the cafeteria on a randomly selected day.

Method B: Have 25 teachers each randomly select 4 eleventh-grade students to be surveyed.

Method C: Assign each student a number. Use a random number generator to generate 100 numbers. Survey those students whose numbers are generated.

Complete the following in the Answer Book:

Which method will provide the principal with a simple random sample of the student population? Use principles of simple random sampling to justify your answer.
Use principles of simple random sampling to justify why each of the other two methods does not provide a simple random sample.

Score Level 1 Anchor Paper

This response indicates little attempt to apply a reasonable strategy. The student incorrectly chooses Method A as providing a simple random sample and gives no correct justification for this answer. The justification for why Method B will not provide a simple random sample is correct (you'd only have 11^th graders). The justification for why Method C will not provide a simple random sample is incorrect and shows a flaw in reasoning. The student states that (Method C wouldn't work because you would have to make sure that every student got a number) which is actually a reason why Method C would provide a simple random sample. The response demonstrates a minimal understanding and analysis of the problem.

Score Level 1 Anchor Paper

This response indicates little attempt to apply a reasonable strategy. The student correctly chooses Method C as providing a simple random sample but gives no valid justification. The justification for why Method A does not provide a simple random sample is incorrect. Method A does not give a simple random sample because only the first 100 students to enter the cafeteria are included, not because (many students enter the cafeteria with friends who like or would want to take the same elective). The justification for why Method B will not provide a simple random sample is correct (you are only surveying eleventh graders). The response demonstrates a minimal understanding and analysis of the problem.

Score Level 1 Anchor Paper

This response indicates little attempt to apply a reasonable strategy. The student correctly chooses Method C as providing a simple random sample and gives a partial justification (that gives every person a chance not just some people). No justification is given for why Methods A and B will not give simple random samples. The 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 correctly chooses Method C as providing a simple random sample but a justification addressing equal chance and independence is missing. The justification for why Method A will not provide a simple random sample is correct (that will limit the principal to one group of student in one cafeteria period). A correct justification is also given for why Method B will not give a simple random sample (the principal will be limited to only eleventh graders with certain teachers). The 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 correctly chooses Method C as providing a simple random sample and gives a complete justification (each student is equaly likely to be picked and it will be chosen independently). No justification is given for why Methods A and B will not provide simple random samples. The 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 correctly chooses Method C as providing a simple random sample and gives a complete justification (every student of the population will have an equal opportunity to be chosen; the population will be chosen independently of one another). The justification for why Method A will not provide a simple random sample is plausible but not well developed (not every student of the population will have an equal opportunity to be chosen; the students will be chosen dependently on one another). The justification needs to specifically address what about Method A keeps it from giving every student an equal chance. Similarly, the justification for why Method B will not provide a simple random sample (not every student of the population will have an equal opportunity to be chosen) is not well developed and needs to specifically address why Method B does not provide every student an equal chance. The 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 correctly chooses Method C as providing a simple random sample and gives a partial justification (this will randomly choose everybody). Independence is not addressed. The justification for why Method A will not provide a simple random sample is correct (some kids get to school early every day). This indicates that early students go to the cafeteria to wait for school to start and they would always be the first 100 to enter the cafeteria, excluding those students who do not arrive at school early. Correct justification is also given for why Method B will not give a simple random sample (it's only for eleventh graders). The 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 a correct solution in the context of the problem. The student correctly chooses Method C as providing a simple random sample and gives a fully developed justification (each member of the population is equally likely to be chosen, and they are picked independently). The justification for why Method A will not provide a simple random sample is correct (not everyone eats in the cafeteria and some people may be absent). A correct justification is also given for why Method B will not provide a simple random sample (students of other teachers that weren't chosen, won't have a chance to be surveyed). The response demonstrates a complete understanding and analysis of the problem.

Score Level 3 Anchor Paper

This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The student correctly chooses Method C as providing a simple random sample and gives a fully developed justification (everyone will have an equally likely chance to be chosen to survey and each student will be chosen independently). The justification for why Method A will not provide a simple random sample is correct (a student may not be able to get to the cafeteria that day or may be absent. So the students do not have an equally likely chance to be chosen). A correct justification is also given for why Method B will not provide a simple random sample (only the eleventh grade students get to be offered to be surveyed and 9^th and 10^th graders won't get a chance to say their oppinion). The response demonstrates a complete understanding and analysis of the problem.