Print preview
Handout Preview Activity: Sampling Distributions drawing from a Normal Population
Before we start formally learning about sampling distributions, I’d like you to explore to see what happens when we take random samples from a population and calculate sample means.
Use the applet below to draw samples from a normal distribution and explore how sample means behave.
To change the sample size, enter “\(n=\#\)” for the number you want to be the sample size.
(This applet was made in GeoGebra by Steve Phelps.)
Link to GeoGebra:
https://www.geogebra.org/m/kUmJeEwx
-
The Population:
-
Population shape: \(\underline{\hspace{5cm}}\)
-
-
The Sample Means: Choose a sample size, use the applet to generate many samples, and record what you observe.
Sample Size (\(n\)) Approximate Mean of Sample Means (\(\mu_{\bar{x}}\)) Approximate Standard Deviation of Sample Means (\(\sigma_{\bar{x}}\)) \(n=4\) \(n=20\) \(n=35\) -
Compare:
-
How does the average of the sample means compare to the population mean?
-
How does the spread of the sample means change as \(n\) increases?
-
How does the shape of the distribution of sample means change as \(n\) increases?
-
-
Your Rule:Based on your observations:
-
The mean of the sampling distribution of the sample mean is about:
-
The standard deviation of the sampling distribution of the sample mean is about:
(We’ll check your “rules” together as a class and compare them with the exact formulas.) -
