Example: Students in a high school mathematics class decided that their term pro
ID: 3248808 • Letter: E
Question
Example: 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. a) Describe the parameter of interest and a statistic the students could use to estimate the parameter. b) Is the best design for this study a sample survey, an experiment, or an observational study? Explain your reasoning. c) 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. d) Describe an appropriate method for obtaining a sample of 100 students, based on your answer in part (a) above.Explanation / Answer
Solution:
a) The parameter of interest is the proportion of all 1000 students at 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.
b) The best design would be a sample survey, because we are interested in estimating a population parameter, namely, the proportion of all parents at the school who are "strict". It is less time consuming and costly to take a random sample of students than to interview all students at the school.
c) Answers will vary. "Do your parents require you to do your homework before you can meet with your friends?" "Do your parents require that you be home before 11pm on a weekend night?" "Do your parents limit your mobile phone time?"
d) 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, the students could read triplets of digits 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.
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