Question

Categorize these samples as representative or not representative of the given populations.

1.Tina interviewed the school’s soccer team members to learn the exercise habits of the students at her school.

2.Alana talked to three of five teachers from each department in her school to find out which school subject teachers enjoyed most when they were young.

3.Joe talked to fathers of high school students to understand the responsibilities of working parents.

4.Alisha spoke to her contacts on a social media website to find out how much time social media users spend online.

Answer 1

Samples must accurately reflect the characteristics of the larger population to be representative. The soccer team sample and fathers-only sample are not representative of their respective populations. Stratified, cluster, and random samples can be used to ensure diverse and representative sample selection.

Step-by-step explanation:

To categorize samples as representative or not representative of their respective populations, one must evaluate whether the sample selected is likely to accurately reflect the characteristics of the larger group. Let's examine the scenarios provided:

1. Tina interviewing the school's soccer team to learn about the exercise habits of all students is not a representative sample. The soccer team likely exercises more than the average student.
2. Alana talking to three of five teachers from each department uses a stratified sampling method that could be representative if all departments are similarly composed concerning the preferences of teachers.
3. Joe talking to fathers of high school students is not necessarily representative for understanding responsibilities of all working parents, as it excludes mothers and parents of younger children.
4. Alisha speaking to her contacts on social media provides a convenience sample and might not represent all social media users' habits, as Alisha's contacts might not be diverse.

Next, let's identify the type of sampling used in other instances:

• A soccer coach uses stratified sampling by selecting players from distinct age groups.
• A pollster interviewing human resource personnel practices a form of cluster sampling, as they sample everyone within several clusters (companies).
• An educational researcher interviewing an equal number of male and female teachers uses stratified sampling to ensure representation of both genders.

For the sampling of students' GPAs in our hypothetical experiment, to calculate the average GPA at the school, a random sample of about 200 students would best reflect the student body while managing practical constraints.