Vikey Lin
Professor Reifsteck
April 21, 2023
Sampling Distribution Report
I.
Theoretical Background
A sampling distribution is a probability distribution that is obtained through the
sampling of a specific population (CFI Team, 2022). The population is the entire pool
where a sample is drawn from and it is normally distributed. Therefore, samples are
representative of the population, but there can be extreme samples that over-represent
the population and deviate from the population mean (worksheet, p.1). However, most
samples are normally distributed, so they should be close to the population mean.
Larger samples and sample of samples would give us a better outlook of the data.
II.
Population
We tested this theory with a practical sample, which was the distribution of green
M&Ms in a bag. The M&Ms we had, around 30 per person, was the sample of the
population, the entire pool of M&Ms. According to Mars, Inc. the distribution of green
M&Ms in a bag of plain ones was 16 percent and that was the claim we put to the test.
III.
Your Sample
My sample had a total of 30 M&Ms and 1 green M&M. The proportion of green
M&Ms to the total of M&Ms in my sample was 3.33%. The population mean was
12.67%, so my sample is not close to the population mean and is off by 9.34%.
All Samples or — Sample of Samples
The smallest proportion of the sample was 0% and the largest was 33.33%. The
average of all samples was 12.67%. This is close to the initial population claim which
was 16%. However, it does not support the initial claim that 16% of the M&Ms in a bag
are green because if you calculate the percent error, it would be 20.81%, which is far
off. Furthermore, if we had tested more bags and had a bigger sample, our results
would be more accurate and give us a better perspective.
IV.
Citations:
CFI Team. (2022, December). Sampling Distribution. CFI.
https://corporatefinanceinstitute.com/resources/data-science/sampling-distribution/