Probability Question

Background

Population distributions take various shapes and represent the spread of the data showing all possible values and how they occur. Most of us are familiar with “Bell Shaped” or normal distributions. In addition to this distribution, we are going to explore “Skewed” and “Uniform” (rectangular) distributions. Through sufficient repetitive sampling from the population, we can calculate summary statistics to estimate true parameters. In this exercise, you will adjust for the sample size and number of times we sample. From these simulations, you can compare your resulting histograms and summary statistics with the original population distribution and parameters.

Instructions

Part I:

CONDUCT THIS ACTIVITY IN MYLAB BY PEARSON

Please log into my course and follow the directions below to create the distributions and answer the questions.

1. Select “Content” from the Brightspace Navigation bar.
2. Select “MyLab Statistics” from the Content menu.
3. Click on the “MTH 210 StatCrunch” tab
4. Click on “Open Link”
5. Go to the second arrow and Click on “Visit the StatCrunch Website”
6. Click on the Orange > Open StatCrunch
7. Click on Applets > Sampling Distributions
8. The top plot shows the True Population Distribution which you are sampling from.

Uniform and Right Skewed Distributions (Do steps 1-5 below for both distributions):

1. Select the correct distribution and click on “Compute!”

1. For sample size (2nd graph down), keep n=2

1. Click on “5 times” at the top.  Click on Options > copy > right click and click copy image, then paste it into a Word Document. You can shrink the size of your image by dragging the corners in to take up less space and use a portrait layout.
2. Change n=10 and n=50 and keep 5 times at the top for each.  Copy and paste the output for both into a Word Document just as you did in #4 above.
   1. Now repeat the process with n=2, n=10 and n=50 but change the number of times to 1000. Copy and paste your results for each into a Word Document.

When you are finished, you will have 6 images copied and pasted for each distribution (12 total)

Part II: Analysis

ANSWER THE FOLLOWING QUESTIONS IN THE SUBMISSION BOX.

1. Compare the sampling distributions of the mean and the median in terms of shape, center, and spread (standard deviation) for uniform and Right skewed distributions. For each distribution type, what happens to these characteristics as the sample size increases?  What happens when the number of samples increases? Use your histograms and summary statistics to support your conclusions.