Question Video: Determining Which Sample Is Not a Simple Random Sample | Nagwa Question Video: Determining Which Sample Is Not a Simple Random Sample | Nagwa

Question Video: Determining Which Sample Is Not a Simple Random Sample Mathematics • First Year of Preparatory School

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A teacher wants to know the favorite subject of the students in his school. Since the school has 300 students, he decides to only ask a sample of the population. For which of the following sampling methods does each student not have an equal probability of being chosen for the sample? [A] A sample of 30 students who are chosen by selecting 30 national IDs randomly [B] A sample o f 30 students selected by writing names of students in small papers, folding the papers, placing the papers in a bowl, and drawing 30 pieces of paper [C] A sample of 30 students selected by putting students’ names in a list, giving each name a random number from 1 to 300, and choosing the names that have numbers divisible by 10 [D] A sample of 100 children who have blue eyes

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Video Transcript

A teacher wants to know the favorite subject of the students in his school. Since the school has 300 students, he decides to only ask a sample of the population. For which of the following sampling methods does each student not have an equal probability of being chosen for the sample? Option (A) a sample of 30 students who are chosen by selecting 30 national IDs randomly. Option (B) a sample o f 30 students selected by writing names of students in small papers, folding the papers, placing the papers in a bowl, and drawing 30 pieces of paper. Option (C) a sample of 30 students selected by putting students’ names in a list, giving each name a random number from one to 300, and choosing the names that have numbers divisible by 10. Or option (D) a sample of 100 children who have blue eyes.

We begin by recalling that a simple random sample is a sample of the population such that every member of the population has an equal chance of being selected for the sample. This means that we need to determine in which of the four given options does every student have the same probability of being chosen for the sample and which options do not have an equal probability for every student.

Let’s start with option (A). Here, students are chosen randomly by their national ID. We may worry that national IDs may not be random, which could well be true. For example, twins would likely have sequential ID numbers. However, we choose 30 students by randomly selecting 30 IDs from the list of 300. And in this way, every ID on the list has an equal chance of selection. Option (A) then represents a simple random sample. And we can eliminate this since we’re looking for sampling methods where each student does not have an equal chance of selection.

In option (B), we have a similar story. Every student’s name is written on a piece of paper, the papers are shuffled in a bowl, and 30 are drawn at random. Of course, with 300 students, we might need quite a big bowl. Nevertheless, since the 30 pieces of paper are drawn randomly, every student has an equal chance of selection. We can therefore eliminate option (B), since this is a simple random sample and every student does have an equal chance of selection.

Option (C) is quite similar in that this time each of the 300 students’ names are listed and then randomly allocated a number from one to 300. The sample then consists of the names that are allocated a number divisible by 10. And there will be 30 of these. Since the allocation of numbers to names is random, each student has an equal chance of being allocated a number divisible by 10. Hence, this is a simple random sample, and we can eliminate option (C).

Finally, in option (D), the sample consists of 100 children who have blue eyes. This means that any student who does not have blue eyes has zero chance of being selected for the sample. So this is not a simple random sample, and this is our answer. Option (D) is the only sampling method where each student does not have an equal probability of being chosen for the sample.

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