Question

DUE FRIDAY PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!! 20 POINTS

Students in a high school mathematics class decided that their term project would be a study 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.
1. Describe the parameter of interest and a statistic the students could use to estimate the parameter.



2. Is the best design for this study a sample survey, an experiment, or an observational study? Explain your reasoning.



3. The students quickly realized that, as there is no definition of “strict”, they could not simply ask a student, “Are your parents or guardians strict?” Write three questions that could provide objective data related to strictness.



4. Describe an appropriate method for obtaining a sample of 100 students, based on your answer in question 1.

Answer 1

1. The parameter of interest is the proportion of students in the school who think of their parents or guardians as “strict”. A statistic that the students could use to estimate the parameter is the proportion of students in their sample who think of their parents or guardians as “strict”.

2. The best design for this study is a sample survey. An experiment would involve manipulating the parents' behavior and observing the effect on the students, which is not ethical. An observational study would only observe the behavior without manipulation, but it is not clear what behavior to observe in this case.

3. Here are three questions that could provide objective data related to strictness:

1. How often are your parents or guardians late to pick you up from school or activities?
2. How often do your parents or guardians check your homework or schoolwork?
3. How often do your parents or guardians allow you to go out with friends on school nights?

4. An appropriate method for obtaining a sample of 100 students is random sampling. The students could assign each student in the school a number, and then use a random number generator to select 100 numbers. They could then survey the students corresponding to those numbers. Another method could be stratified sampling, where the students divide the school into groups based on grade level, and then randomly sample a proportionate number of students from each group.