http://www.ltcconline.net/greenl/java/Statistics/clt/cltsimulation.html #4) Go t

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http://www.ltcconline.net/greenl/java/Statistics/clt/cltsimulation.html

#4) Go to the following website: http://w w.ltcconline .net/greenViava/Statistics/clt/cltsimulation. html Run simulations by first clicking on a population distribution (Uniform, Left-Skewed, Right-skewed, or Normal), then click on each sample size (n=2, n-9, n=25, n-36, and n-100). Click "New Dist" to switch to a different distribution For each population distribution, how large of sample is needed to obtain an approximate normal sampling distribution of X? Compare the population mean and standard deviation (on the top graph) to the mean and standard deviation of the simulated X distribution (on the bottom graph). How do the means compare? How do the standard deviations compare? a) b)

Explanation / Answer

a. A normal distribution or sampling is where thegraph is symmetric on both sides and takes on an approximately smooth appeareance without being skewed.

After having tried n=2, n=9, n=25, n=36 and n=100 for each kind of population distribution (uniform, left skewed, right skewed and normal. we can see that the curve or the graph being generated fits the above definition roughly around the point when n=30.

Hence we see that we have to obtain a sample size of n=30 to obtain an approximate normal distribution of Xbar

b. The mean and standard deviation of the bottom graph, change with respect to the top graph.

This change is reflected in a way that the standard devation tends to decrease with increase in the sample size as compared to the top graph while the mean which is initially lower or higher than the mean on the top graph tends towards the mean of the top graph with increasing sample size and finally becomes almost equal at n=100.

Hence with this lends credence to the fact that with increasing sample sizes the std. deviation decreases and mean tends towards the mean of the population and is a more accurate representation of the population

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