High School Common Core Mathematics

Front 1

Students in a high school mathematics class decided that their term project would be astudy of the strictness of the parents or guardians of students in the school. Their goal was to estimate the proportion of students in the school who thought of their parents or guardians as "strict." They do not have time to interview all 1000 students in the school, so they plan to obtain data from a sample of students. A. Describe the parameter of interest and a statistic the students could use to estimate the parameter.

Back 1

The parameter of interest is the proportion of all 1000 students in the school who have strict parents or guardians. A possible statistic to estimate this parameter is the proportion of students in the collected sample who have strict parents or guardians.

Front 2

Students in a high school mathematics class decided that their term project would be astudy of the strictness of the parents or guardians of students in the school. Their goal was to estimate the proportion of students in the school who thought of their parents or guardians as "strict." They do not have time to interview all 1000 students in the school, so they plan to obtain data from a sample of students. B. Is the best design for this study a sample survey, an experiment, or an observational study? Explain.

Back 2

The best design would be a sample survey, because we are interested in etimating a population parameter, namely, the proportion of all parents at the school who are "strict." The is less time consuming and costly to take a random sample of students than to interview all students at the school.

Front 3

Students in a high school mathematics class decided that their term project would be astudy of the strictness of the parents or guardians of students in the school. Their goal was to estimate the proportion of students in the school who thought of their parents or guardians as "strict." They do not have time to interview all 1000 students in the school, so they plan to obtain data from a sample of students. C. The students quickly realized that, as there is no one definition of "strict," they could not simply as a student, "Are your parents or guardians strict?" Write three questions that could provide objective data related to strictness.

Back 3

Answers will vary. Some examples:
"Do your parents require that you complete your homework before you can go out/ meet with friends?"
"Do your parents have a specific curfew on weeknights or weekends?"
"Do your parents limit your time with television, video games, cell phone, or other electronics?"
"Do your parents require that you are home for dinner every night?"
"Do your parents call to check in on you when you are out with friends?"

Front 4

Students in a high school mathematics class decided that their term project would be astudy of the strictness of the parents or guardians of students in the school. Their goal was to estimate the proportion of students in the school who thought of their parents or guardians as "strict." They do not have time to interview all 1000 students in the school, so they plan to obtain data from a sample of students. D. describe an appropriate method for obtaining a sample of 100 students.

Back 4

Answers will vary. A list of all students should be obtained from the principal's office and a subset of student names should be taken from the list by randomly sampling without replacement. For example, students could read triplets of didgits from a random number table so that 000 represents the first student on the principal's list and 999 the last. The students would begin at an arbitrary point in the table and then write down consecutive triplets until they had obtained the desired sample size. If a three-digit number is repeated, then they should skip that triplet and write down the next. Alternatively, a computer could be asked to take a random sample without replacement from the digits 1 through 1000.

Front 5

Which question is unbiased?
A. Does the government have a right to enforce voting age for citizens?
B. Do you think the weather in the month of June is always 25 degrees Celcuis or greater?
C. Do you prefer the University's full time degree program or part time degree program?
D. Do you think the government should be allowed to cut down trees to construct a metro railway line in the city?

Back 5

C. Do you prefer the University's full time degree program or part time degree program? This question is unbiased because it is open and does not provide any condition.

Front 6

Which question is biased?
A. Do you have a full time degree program at the university?
B. Should there be a dress code in the office?
C. Do you prefer newspapers or news on television?
D. Do you think a new underground metro railway line should be built for local city transport?

Back 6

C. Do you prefer newspapers or news on television? This question is biased because the use of different mediums can influence a person's thought process based on their experience.

Front 7

From a class containing 12 girls and 10 boys, three students are to be selected to serve on a school advisory panel. here are four different methods of making the selection:
1. Select the first three names on the class roll.
2. Select the first three students who volunteer.
3. Place the names of all the students in a hat, mix them up, and then select 3 names.
4. Select the first three students who show up for class tomorrow.
Which of these is the best sampling method if you want the school panel to represent a fair and representative view of the opinions of the class? Explain.

Back 7

Choice 3 is the best solution in terms of fairness because each of the other methods does not give equal chance of selection to all the students in the class. Any one student should have the same chance of being selected as any other student.

Front 8

From a class containing 12 girls and 10 boys, three students are to be selected to serve on a school advisory panel. here are four different methods of making the selection:
1. Select the first three names on the class roll.
2. Select the first three students who volunteer.
3. Place the names of all the students in a hat, mix them up, and then select 3 names.
4. Select the first three students who show up for class tomorrow.
Explain the weaknesses of the methods that are not the best.

Back 8

Choice 1 is not fair because only students whose name starts with letters at the beginning of the alphabet have a chance of being selected, therefore all students in the class do not have an equal chance of being selected. Choice 2 is not fair because volunteers may have a special interest in a particular issue which the class does not share in. This also does not give all students in the class an equal chance of selection. Choice 4 is not fair because there are many factors determining who are the first three students to show up for class, which may vary from day to day, therefore there is not an equal chance of being selected for all students.

Front 9

Each number on a six-sided die has a probability of being rolled of 0.166. A. Mary rolls the dice 3 times in a row and each time it lands on the same number. Does this make you question the model of probability for die?

Back 9

This does not make me question the model of probability for die because Mary has only rolled the die 3 times. This is not a large enough sample to make it stand out that she rolled the same number all three times.

Front 10

Each number on a six-sided die has a probability of being rolled of 0.166. B. Mary found that she was able to roll a 1, 25% of the time by rolling the die 1000 times. Does this make you question the model of probability for die?

Back 10

This would make me question the model of probability for a die because the outcome is three times greater than what is expected for a sample that is large, as was Mary's. It would be difficult to consider Mary's experiment invalid, but it would prompt questions and repeats of the experiment to determine validity.

Front 11

When flipping a coin, there is a 50% chance that it will land on heads and a 50% chance that it will land on tails. Fred flips a coin 5 times and it lands on tails 4 times. Does this make you question the model of probability for flipping a coin?

Back 11

This would not make me question the probability model for flipping a coin. The sample is too small, and there are no factors in a coin that make one or the other side more likely, such as a weight difference.