Applying statistics in real life

by | Mar 11, 2023 | Statistics

 

 

 

 

 

 

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.

In your initial discussion post, specifically, address the following:

Introduce yourself and describe a time when you used data in a personal or professional decision. This could be anything from analyzing sales data on the job to making an informed purchasing decision about a home or car.
Describe to Susan how to take a sample of the student population that would not represent the population well.
Describe to Susan how to take a sample of the student population that would represent the population well.
Finally, describe the relationship of a sample to a population and classify your two samples as random, systematic, cluster, stratified, or convenience.

Sample Solution

Hello, my name is [Name], and I’m a high school principal. Recently, I used data when deciding which college to send my daughter to. After researching the different colleges she was interested in, I looked at their admissions statistics and how many students get accepted each year out of the total applicants. This helped me narrow down her choices and decide which college would be best for her based on those numbers.

Sample Solution

Hello, my name is [Name], and I’m a high school principal. Recently, I used data when deciding which college to send my daughter to. After researching the different colleges she was interested in, I looked at their admissions statistics and how many students get accepted each year out of the total applicants. This helped me narrow down her choices and decide which college would be best for her based on those numbers.

To Susan: Taking a sample from the student population that would not represent the population well could include selecting only certain grade levels or genders (e.g., only seniors or females). Another way could be having one person from each classroom select a movie instead of giving all students in the school an equal opportunity to vote for what they want; this could lead to bias because some classes may have an overwhelming majority of one opinion over another depending on who got chosen as representatives for that particular class/grade level.

On the other hand, taking a sample that represents the population well would involve randomly selecting around 10-15 classrooms with varying grade levels and making sure there are at least two representatives from each grade level so that their opinions can be accurately represented without any gender or grade-level bias being included in the selection process. The number chosen should also reflect enough students so that it gives an accurate representation of what most people want while also avoiding over-sampling where too few classrooms are selected leading to skewed results due to small size of sample taken.

The relationship between samples and populations is important as samples are meant to provide us with information about overall trends among larger groups; thus allowing us make more informed decisions than if we relied solely on intuition alone without doing any sort of analysis beforehand. In this case both samples described above can be classified as random since neither method involves purposely choosing certain individuals (or classes) but rather relies upon chance by utilizing methods such as lottery systems etc., which allows for unbiased selections every time new sets need to made up regardless whether it’s same group again or completely different subset altogether .

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