Statistics Help?

Question

In real-life applications, statistics helps us analyze data to extract information about a population. In this module discussion, you will take on the role of Susan, a high school principal. She is planning on having a large movie night for the high school. She has received a lot of feedback on which movie to show and sees differences in movie preferences by gender and also by grade level.

She knows if the wrong movie is shown, it could reduce event turnout by 50%. She would like to maximize the number of students who attend and would like to select a PG-rated movie based on the overall student population's movie preferences. Each student is assigned a classroom with other students in their grade. She has a spreadsheet that lists the names of each student, their classroom, and their grade. Susan knows a simple random sample would provide a good representation of the population of students at their high school, but wonders if a different method would be better.



1. Describe to Susan how to take a sample of the student population that would not represent the population well.
2. Describe to Susan how to take a sample of the student population that would represent the population well.
3. Finally, describe the relationship of a sample to a population and classify your two samples as random, cluster, stratified, or convenience.

Answer 1

Any sampling method that did not involve random selection would likely not be representative of the population of students. For example, if the principal simply surveyed the first 50 students to enter the school on a particular day, she would likely not have a representative sample. Students who get to school early are likely to be students who like school a lot and they probably have different movie preferences than students who do not like school.

The best sampling method would be stratified sampling since she knows that gender and grade level affect movie preferences. She needs to determine the proportion of male and female students in each grade level. Each grade level/gender combination will be a strata. She should take an SRS of each strata with a sample size that guarantees the proportions of the sample match the proportions of the population.

A sample is a subset of individuals in a population. The "bad" sample in my example is a convenience sample. The "representative" sample is a stratified sample.