A 7th grade student wants to find our which subject is the most popular subject among the 120 students in her grade. She decides to use an alphabetical list of student names from which to choose her sample.
Which of the following is an example of a sample that would NOT be random?
A.Going through the list and choosing the first 25 names on the list.***
B. Writing each student’s name on a card and then drawing out 25 names without looking.
C. Choosing one student at random from the list and going through the list and choosing every fifth student until she has 25 names.
D. Separating the students on the list into boys and girls and choosing a sample from each group that is proportional to the size of the group.
The example of a sample that would NOT be random is A. Going through the list and choosing the first 25 names on the list. This method does not involve any random selection process, but rather takes the first 25 names in the order they appear on the list.
The example that would NOT be random is A. Going through the list and choosing the first 25 names on the list.
To have a random sample, every student in the population (the 120 students) should have an equal chance of being selected. The first 25 names on the list could be bias towards alphabetical order, and it may not represent the true distribution of subjects among the 7th-grade students.
To get a random sample, options B, C, and D are better choices:
- Option B involves writing each student's name on a card and then drawing out 25 names without looking. This ensures randomness in the selection process as each card has an equal chance of being picked.
- Option C involves choosing one student at random from the list and then selecting every fifth student until she has 25 names. This method ensures randomness as the starting point is chosen randomly, and then every fifth student is selected.
- Option D involves separating the students on the list into boys and girls and choosing a sample from each group that is proportional to the size of the group. This method ensures representation from both genders and proportional representation within each group.