Question

A survey was administered to parents of high school students in a certain state to see if the parents thought the students’ academic needs were being met. To select the sample, the parents were divided into two groups— one group of parents who live in cities with populations of more than 100,000 and the other group of parents who live in cities with populations less than or equal to 100,000. A random sample of 100 parents from each group was taken. Which of the following statements about the sample of 200 parents is true? (A) It is a convenience sample because the sample of parents was easily obtained. (B) It is a stratified random sample because parents were randomly selected from each group. (C) It is a random cluster sample because parents were randomly selected from each group. (D) It is a random cluster sample because groups of high schools were randomly selected. (E) It is a systematic sample because the parents were systematically divided into two groups.

Answer 1

Option C is correct

It is a stratified random sample because parents were randomly selected from each group.

Explanation:

I'll talk about the different types of sampling.

1) Random Sampling

In random sampling, each parent would have an equal chance of being surveyed. If this particular scenario wanted to use random sampling, they would have used computer generated random numbers for the parents and surveyed them, not just pick random parents equally from two cities.

2) Systematic sampling is easier than random sampling. In systematic sampling, a particular number, n, is counted repeatedly and each of the nth parent is picked to be sampled.

3) Convenience Sampling

This is the worst sampling technique. It is also the easiest. In Convenience sampling, they just survey the first set of parents that they find.

4) Stratified Sampling

Stratified sampling divides the population into groups called strata. A sample is taken from each of these strata using either random, systematic, or convenience sampling.

So, for this question, random sampling is used to pick a sample from the two strata (from the 2 cities). This is why the sampling used in this question is a stratified random sampling technique.

5) Cluster sampling

Cluster Sampling divides the population into groups which are called clusters or blocks (the different cities). The clusters are selected randomly, and every element in the selected clusters is surveyed (each parent in the selected cities, is surveyed!).

Hope this Helps!!!