Question

Question 1 (4 points)Paolo wants to know how many of the 500 students at his school have at least one per. He wants to survey a random sample of 20 students.He is considering two sampling methods.Method A: Paolo assigns a number to each student at school. He writes the numbers on slips of paper, randomly chooses 20 numbers,and surveys those students.Method B: Paolo puts up a sign that asks students to voluntarily record the number of pers they have. He takes the first 20 students.Part 1: Which method would give Paolo a random sample? What about this sampling method makes it random? (2 points)Part 2: Describe why the other sampling method would NOT give him a random sample. (2 points)BRecord Arne

Answer 1

Part 1:

The sampling method that gives Paolo a random sample is the Method A.

This is because the Method A allows for no bias on the part of Paolo in the selection of the entries that make up the sample. Paolo just randomly picks any slip, without any prior knowledge of what number was written on it by the student.

Therefore, the entire process of selection is indeed random, and therefore the method A produces a truly random sample.

Part 2:

The method B would not give Paolo a random sample for the following reasons:

1) The students may self-select themselves in the process. What this means is that, some students may choose not to volunteer to participate just because they feel uncomfortable being asked about the number of pers they have. This could result in a situation where only students with a high or low number of pers show up to participate, and the data that Paolo would have will not be random or even representative enough.

2) Also, because Paolo will be selecting the records of only the first twenty students, the selection is already defined, and can no longer be said to be random. it will only be random if Paolo selects 20 recorded numbers from a total of about 40 students' record. But as this is not the case, the method B will not yield Paola a random sample.