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Handout Preview Activity: Sampling Distributions drawing from a Population that is NOT Normal
Now go to the GeoGebra link below to draw samples from a distribution that is NOT normal and explore how the sample means behave.
Link to GeoGebra:
https://www.geogebra.org/m/dzfukxkt
Work through the same steps you did above to try to develop rules based on your observations.
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The Population:
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Population shape: \(\underline{\hspace{5cm}}\)
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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:
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How does the average of the sample means compare to the population mean?
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How does the spread of the sample means change as \(n\) increases?
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How does the shape of the distribution of sample means change as \(n\) increases?
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Your Rule:Based on your observations:
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The mean of the sampling distribution of the sample mean is about:
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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.) -
