Sampling Distributions

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Sampling Dist. Ans.

You can link to a sampling distributions applet to create from scratch the sampling distribution of the mean, and also observe how this distribution changes with shifts in population shape and sample size.

  • Read the Instructions (printing a hard copy, if possible, for easy reference.)
  • To simulate from scratch the sampling distribution of the mean, follow the directions in the "Basic operations" paragraph of the Instructions. Always click the "Fit normal" button to superimpose a normal distribution over the simulated sampling distribution.
  • Click on "Begin" to start this simulation, and when finished, return to this page.

Question: This simulation illustrates two of the three important properties of the sampling distribution of the mean discussed in Chapter 13. Which are they?  Answer

 
  • To simulate the effect of the central limit theorem, use the pop-up menus as follows: specify "Skewed" as the shape of the population; specify N = 5 for the one sampling distribution of means (third histogram); and specify the mean and N=25 for the second sampling distribution of means (fourth histogram); and click on both "Fit normal" buttons.  Then, click the "Animated sample" button to observe precisely how the process works. To speed things up, take 10,000 samples at a time.  Refer to the left margin and use measures of skew ("lopsided-ness") and kurtosis ("peaked-ness"), which each should equal zero when the distribution is normal, to decide whether the sampling distribution with N = 25 approaches a normal distribution more rapidly than the sampling distribution with N = 5, as predicted by the central limit theorem.  (If, just by chance, results seem to contradict the central limit theorem -- because measures of skewness or kurtosis for N=25 are slightly larger than for N=5 -- continue taking 10,000 samples, without clearing, and note any changes with very large numbers of samples.)
  • Repeat this process after changing the shape of the population to "Uniform" or, to create your own shape with the mouse, specify "Custom".