1. First refresh your memory about the meaning of the sampling distribution of the mean by clicking the "animate" button. You will see five scores sampled from the population at the top and float down to the sample data graph. The mean of these five scores is shown in blue and drops down to the graph below which is where the distribution of means is shown. Do this a few more times and then click the 10,000 button several times to see the distribution of means for a large number of samples. Various statistics are shown to the left of the distribution. Compare the mean of the distribution of means to the population mean of 16. It should be very close, but may not match exactly because the simulated distribution of means is just an approximation of the sampling distribution.
  2. Test to see if the mean the distribution of means for N=10 is equal to the population mean (keep in mind, since this is an approximation, it may not be exactly equal). If it is equal then the mean is an unbiased estimate.
  3. Change the parent population to the "skewed distribution" and see if the mean of the distribution of means is equal to the population mean of 8.08. If so, the mean is unbiased for this skewed distribution.
  4. Choose the median as the statistic. Try some simulations with the normal distribution. If the sample median is an unbiased estimate of the population median, then the mean of the distribution of the median will equal the median of the population.
  5. Try some simulations with the skewed distribution and check with the median is a biased estimate.
  6. Choose the variance as the statistic. Estimate the distribution of the variance and not its shape.
  7. Set the sample size to 5 and use the normal population. Estimate the sampling distribution of the variance with the simulation. Note whether the mean is equal to the population variance of 25.
  8. Choose the mean for one graph and the median for the other. Make the sample size the same for both graphs and estimate the sampling distributions. Compare the spreads of the distributions. The standard deviation of the distributions are the standard errors of the mean and median respectively. Which statistic has the smaller standard error? Try this with different sample sizes. For sample size 25, note the ratio of the standard error of the median to the standard error of the mean.
  9. Compare the standard errors for the mean and the median with the skewed distribution. Try several sample sizes.
  10. Try different shapes of distributions and not the relative sizes of the standard errors of the mean and median.