Question

Which sample fairly represents the population? Check all that apply. measuring the heights of every fiftieth person on the school roster to determine the average heights of the boys in the school calling every third person on the soccer team’s roster to determine how many of the team members have completed their fundraising assignment observing every person walking down Main Street at 5 p.m. one evening to determine the percentage of people who wear glasses sending a confidential e-mail survey to every one-hundredth parent in the school district to determine the overall satisfaction of the residents of the town taking a poll in the lunch room (where all students currently have to eat lunch) to determine the number of students who want to be able to leave campus during lunch

Answer 1

A sample is a small subset of a population, on which startistical analysis is carried out to obtain the characteristics of the population.

Sampling is the process of selecting units (e.g., people, organizations) from a population of interest to obtain the characteristics of the population.

When drawing a sample, it is important that all the components of the population of interest is adequately represented.

Thefollowing samples are categorised based on whether they fairly represent the population of interest or not.

1.) Measuring the heights of every fiftieth person on the school roster to determine the average heights of the boys in the school.

Here, the population of interest is the boys in the school. Drawing a sample of every fiftieth person on the school roster will contain both boys and girls whereas girls are not needed for the purpose of the survey.

Threfore, the sample does not represent fairly the population of interest.

2.) Calling every third person on the soccer team’s roster to determine how many of the team members have completed their fundraising assignment.

Here, the population of interest is the team members, so drawing a sample of every third person on the soccer team's roster represents fairly the population of interest.

3.) Observing every person walking down Main Street at 5 p.m. one evening to determine the percentage of people who wear glasses.

Here the population of interest is people who wear glasses, though observing people walking down the road might be a good way to drawing this sample, but the sample will be biased because by 5 pm, the sum will be down and the people who wear glasses because of the sun might not have their glasses on again.

So this sample does not fairly represent the population of interest.

4.) Sending a confidential e-mail survey to every one-hundredth parent in the school district to determine the overall satisfaction of the residents of the town.

Here, the population of interest is the residents of the town and not all residents of the town might be a parent.

So, the sample of one-hundredth parent in the school district does not fairly represent the population of interest.

5.) Taking a poll in the lunch room (where all students currently have to eat lunch) to determine the number of students who want to be able to leave campus during lunch.

Here, the population of interest is the students and taking a poll in the lunch room (where all students currently have to eat lunch) fairly represent the population of interest.


Therefore, the samples that fairly represent the population are:

Calling every third person on the soccer team’s roster to determine how many of the team members have completed their fundraising assignment.
and
Taking a poll in the lunch room (where all students currently have to eat lunch) to determine the number of students who want to be able to leave campus during lunch.