MAT 240 1-1 Discussion
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Apr 3, 2024
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MAT 240: Applied Statistics
1-1 Discussion: Population, Samples, and Bias
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.
Hi everyone,
My name is Alyssa and I live just north of Boston in a small town called Danvers, with my fiancé, 9-year-old daughter, 3 month old son, 3 cats, and 1 French bulldog. Yes, we have a full house! I am studying marketing with a concentration in digital marketing at SNHU and am excited to learn alongside you this semester. A time when I have used data recently was a big yard sale my parents and I had this past weekend. Yard sales are a lot more
work than you think, and there was lots of data to be analyzed. Specifically, once the yard sale was over, we had to analyze what we sold, what we had left, and how much of a profit we made. My dad and fiancé are big on numbers, so of course we had to analyze the data to see what we made per hour and how lucrative the profits were.
Another time I have used data, in a professional setting, was when I was the assistant manager at a restaurant. I used to be
in charge of running reports, analyzing the data, and putting it
into an email format for my bosses to read. Specifically, inventory sticks out to me as a function I had to complete in my job, that included a lot of data. Inventory, as you may know, is taking count of all the liquor in a restaurant once a month. We would have to take count of everything in the restaurant, compare it to the previous month’s data, and analyze how much we needed to order and what was popular and selling the most at the time. Susan is looking to host a movie night that maximizes the number of students who attend. With the data that she collected; she should be able to select a movie title that is popular amongst the majority of her students. When selecting
the movie title, Susan must look at all the data she has collected. Susan should avoid looking at data that is specific to
the population, to select the movie title. An example of this would be if Susan picked the movie title based on only the data collected by one grade, such as the 9
th
grade only. Susan should also avoid looking at data that is specific to gender as well. Susan must look at all the data from the population and not limit it to only a specific type of student, in order to make her decision. Susan should avoid non-random sampling, sampling from only specific subgroups, and should avoid including or excluding any data from the population when making her decision. A sample of the population that would provide Susan with a movie title that would be liked by the majority of the students would be by using the quantitative data that resulted from Susan’s survey. By taking all of the data and counting up how many votes each movie title received, Susan will be able to determine what movie title is best appropriate for her to show at her movie event in order to get the most students to show. Another way that Susan could decide on the best movie title to show, would be by using random sampling. By using random sampling, Susan would randomly select individuals from the population to ensure that every member has an equal chance of being included in the sample. This would help Susan to minimize bias and increases the likelihood of obtaining a sample that reflects the population's diversity.
A sample is a subset of a population that is selected for the purpose of studying and drawing conclusions of the entire population. My first sample would be categorized as convenience sampling, as it is nonrandom and may provide bias data. My second sample is random sampling, as it involves selecting a sample that gives everyone included in the population an equal chance at being selected.
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Discussion Post Responses:
In your response posts to at least two peers, discuss the following:
Choose
two different
sampling methods from among your peers' responses. Then, identify bias in each peer's sample and explain how you think they could remove the bias from their sample.
Hi Kathryn,
I enjoyed reading your discussion post! It’s awesome that
Amazon is paying for your continued education. You offered some great detail and insight, in addition to thoroughly explaining why you chose the sampling method that you did. I agree with you, that a random sample of the population is one of the best ways for Susan to determine what movie title to show her students. Like you mentioned in your post, a sampling unit would not represent the data well. For this situation, Susan should avoid separating the students by gender, age, or grade level. Separating the students by these categories would result in a sampling method that would depict bias results, which Susan wants to avoid.
To avoid the selection bias described, Susan should avoid
non-random sampling, sampling from only specific subgroups, and should avoid including or excluding any data from the population when making her decision. She can use random sampling to make her decision, as it would be the best, most accurate, and non-bias method of determining a movie title. Systematic sampling is another option as well, which would entail Susan selecting students at a regular interval, as you mentioned in your discussion post. Either of these sampling methods would work for Susan to obtain her desired results.
Nice work this week! Best of luck this semester and with your continued studies. Enjoy your Labor Day! Hi Alex,
I enjoyed reading your discussion post! I definitely relate to you as a parent; I have two little ones of my own as well. Psychology is super interesting, it was actually my first major when I first enrolled in college, but I have since switched over to Marketing. I’m sure you will do great things with your degree!
Your recommendations for the Susan scenario are great, and I fully agree with you. The use of a sampling method that does not represent the student population well, will certainly introduce bias into the results. I enjoyed reading the examples
you gave as to what that would look like in a real-world scenario; it definitely provides further context and understanding behind the importance of Susan selecting a sampling method that best fits her desired results. As you mentioned, the wrong sampling method could result in overrepresentation and/or underrepresentation of many of the
students in the population. Because Susan is looking to pick a movie title that interests the majority of her students, it is important that she uses a sampling method that eliminates bias and reflects the overall population.
As you stated, a stratified sampling approach is one of the best methods for Susan to achieve her desired results. Your description of stratified sampling here was thorough, easy to understand, and fits the necessary elements for Susan’s situation. Another method, which I chose to use in my discussion post, is simple random sampling. Simple random sampling involves randomly selecting students from the population. This method allows each student an equal chance at being selected and is an excellent way to collect data for an
unbiased representation of a group.
Nice work this week! I thoroughly enjoyed your contribution to
the discussion board for this module. Best of luck this semester and with your continued studies. Enjoy your Labor Day with your family!
Thomas, L. (2023, June 22). Simple random sampling: Definition, steps & examples
. Scribbr. https://www.scribbr.com/methodology/simple-random-sampling/#:~:text=Simple
%20random%20sampling%20is%20a,possible%20of%20this%20random%20subset.
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