Question

suppose you are interested in whether or not the students at your high school would favor a grading system in which students may receive final grades of a+, a, a-, b+, b, b-, c+, c, c-, and so on. describe how you might obtain a random sample of 100 students from the entire student population
choose the correct answer below.
a. sort the students by their overall average grades. then, select the 50 students with the best grades and the 50 students with the worst grades.
b. post an advertisement requesting the assistance of 100 students. among the first 100 students to arrive, select them in a random order.
c. assign each student at the school a number, write each number on a card, and place all of the cards in a box. then, randomly select 100 cards.
d. determine the ten streets on which the most students at the school live. then, select ten students from each street. if fewer than ten students live on a street, fill in the spot with a randomly selected student.

Explanation:

• Option A: Sorting by grades and selecting only the best and worst 50 students is a biased sampling method as it doesn't give equal chance to all students in the population.
• Option B: Selecting the first 100 students who respond to an advertisement is a convenience sampling method. The students who respond first may not be representative of the entire student population (e.g., they may be more interested in the topic or have more free time).
• Option C: Assigning each student a number, writing the numbers on cards, and randomly selecting 100 cards is a simple random sampling method. In simple random sampling, every individual in the population has an equal chance of being selected.
• Option D: Determining streets based on where most students live and then selecting students from those streets is a form of cluster sampling. But it is not a simple random sample as it is based on a non - random (location - based) criterion for initial selection (unless the streets are randomly selected first, which is not the case here).

Answer:

C. Assign each student at the school a number, write each number on a card, and place all of the cards in a box. Then, randomly select 100 cards.