Exploring Sampling Distributions: Properties and Relationships to Populations

What is a Distribution?

The purpose of this lab is to explore sampling distributions, their properties and their relationship to the populations they come from
1. Prior to doing any sampling, explain what a distribution is and what it tells you about data.
2. Explain what a sampling distribution is.
3. If the population is approximately Normal, or there is a large enough sample, what is the standard deviation of the sampling distribution (approximately)?
4. Under the Select Population Distribution, select the Real population data option and then under the Select Example, select College earnings.
a. What is the shape of the distribution of college earnings? Include a sketch or graph of it here. What are the mean and standard deviation of this population?
b. Based on the population mean and standard deviation, what would you expect the mean and standard deviation of the sampling distribution to be for a sample of size 20?
c. Select the option to draw 1000 samples and then select the Draw Samples button.
Describe the shape of the sampling distribution. How do the mean and standard deviation compare to the ones you just computed?
d. Adjust the sample size to n = 5. What would you estimate the mean and standard deviation of these samples should be?
e. Draw 1000 samples again, what is the shape of this sampling distribution? Repeat this three times. How do the means and standard deviations compare to the ones you just computed in part d?
5. For this example, you will be using a different example population of real data. Select either Age of soccer players, New York Airbnb prices, Distances of NYC taxi rides, or either of the flight options.
a. Once you have selected the new population distribution describe the shape of the population distribution. What are it’s mean and standard deviation? Include a sketch or image of the population and describe its shape.
b. For samples of size 5, compute what you would estimate the standard deviation of the sampling distribution to be.
c. Draw 1000 samples of size 5. Describe the shape of the sampling distribution. Include a picture of it. How does the standard deviation compare to what you
estimated in the previous part? How does the mean of the sampling distribution compare to the mean of the population?
d. Draw 1000 samples of size 40. Describe the shape of the sampling distribution and include an image of it.
6. For this example, instead of using Real Population Data as your population, select Bimodal.
a. Once you have selected the new population distribution describe the shape of the population distribution. What are it’s mean and standard deviation? Include a sketch or image of the population and describe its shape.
b. For samples of size 5, compute what you would estimate the standard deviation of the sampling distribution to be.
c. Draw 1000 samples of size 5. Describe the shape of the sampling distribution. Include a picture of it. How does the standard deviation compare to what you estimated in the previous part? How does the mean of the sampling distribution compare to the mean of the population?
d. Draw 1000 samples of size 40. Describe the shape of the sampling distribution and include an image of it.
7. For this example, instead of using Real Population Data as your population, select Uniform.
a. Once you have selected the new population distribution describe the shape of the population distribution. What are it’s mean and standard deviation? Include a sketch or image of the population and describe its shape.
b. For samples of size 5, compute what you would estimate the standard deviation of the sampling distribution to be.
c. Draw 1000 samples of size 5. Describe the shape of the sampling distribution. Include a picture of it. How does the standard deviation compare to what you
estimated in the previous part? How does the mean of the sampling distribution compare to the mean of the population?
d. For samples of size 40, compute what you would estimate the standard deviation of the sampling distribution to be.
e. Draw 1000 samples of size 40. Describe the shape of the sampling distribution and include an image of it. How do the mean and standard deviation compare to those you computed?
8. With a group of 2-3 people compare your answers to the previous questions.
a. Describe the effects of increasing the sample size on a sampling distribution.
b. In which examples above were your estimates of the standard deviation of the sampling distribution furthest from the actual values?
c. When dealing with small sample sizes, which population distributions produced sampling distributions that were not close to Normal?
d. What are the names of the 2-3 other people in your group?