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1. (20 pt) Go to http://www.stat.tamu.edu/~west/ph/sampledist.html. Use a skewed distribution. Take 1000 samples of sizes 2, 10 and 100. Construct a mean for each sample and look at the distribution of the sample means (third row). Record the mean and SD in the population for the original random variable. Make a table and record the mean of the means, and the standard deviation of the mean for each sample size (2, 10 and 100). For a bell-shaped distribution we showed that the mean of the sample means is very similar to the mean in the population for all population sizes. This is the property of unbiasedness. From your results, does the mean appear to be unbiased when the original distribution of the data is skewed? For a bell-shaped distribution we showed that the standard deviation of the mean, or the standard error of the mean, decreases with sample size. Is this true for skewed distributions? Calculate the standard error of the mean that is expected for each sample size and record in the table. How did the observed result compared to your calculation? * * Mean of the Population: 15.5297 * Median of the Population: 12.2861 * Standard Deviation of the Population: 12.5078 * * Sample Size | * Mean of the means | * Standard Deviation | * Standard Error of the Mean | * 2 | * 15.7741 | * 8.8115 | * 6.23067 | * 10 | * 15.4568 | * 3.847 | * 1.21653 | * 100 | * 15.5223 | * 1.2636 | * 0.12636 | * * Taking the mean of the population as the true value, we can find the percent errors for the means of the different sample sizes. * * Percent error of mean of sample size 2 = 15.7741-15.529715.5297*100%= 1.57% error * Percent error of mean of sample size 10 = 15.4568-15.529715.5297*100%= 0.47% error * Percent error of mean of sample size 100 = 15.5223-15.529715.5297*100%=

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