• What is the difference between distribution of a population, a distribution of a sample, and a sampling distribution?
• How is sample size related to the normal distribution?

http://onlinestatbook.com/stat_sim/sampling_dist/(Links to an external site.)

- The instructions can be found on the website Sampling Distributions p:onlinestatbookcomxstat simisamplgnks to an external site.1 c2 l and below: - This simulation lets you explore various aspects of sampling distributions with four histograms. - A histogram of a normal distribution is displayed at the top of the screen. The distribution portrayed at the top of the screen is the population from which samples are taken. The mean of the distribution is indicated by a small blue line and the median is indicated by a small purple line. Since the mean and median are the same, the two lines overlap. The red line extends from the mean one standard deviation in each direction. Note the correspondence between the colors used on the histogram and the statistics displayed to the left of the histogram. - The second histogram displays the sample data. This histogram is initially blank. The third and fourth histograms show the distribution of statistics computed from the sample data. The number of samples {replications} on which the third and fourth histograms are based is indicated by the label "Reps=." - The simulation is set to initially sample ve numbers from the population, compute the mean of the ve numbers, and plot the mean. Click the "Animated sample\" button and you will see the five numbers appear in the histogram. The mean of the five numbers will be computed and the mean will be plotted in the third histogram. Do this several times to see the distribution of means begin to be formed. Once you see how this works, you can speed things up by taking 5,000, or 10,000 samples at a time. - The following statistics can be computed from the samples by choosing from the pop-up menu: 0 Mean 0 Standard deviation of the sample {N is used in the denominator] o The variance of the sample {N is used in the denominator] o Unbiased estimate of variance {N-l is used in the denominator} 0 Mean absolute value of the deviation from the mean 0 Range - Selecting a sample size: The exercises can be found at the following website: h_tl:p:onlinestatbookcomgstat simzsampljglinks to an external site.]_ a o The size of each sample can be set to 2.5.10, 16. 2D, or 25 from the pop-up menu. Be sure not to confuse sample size with number of samples. 0 Experiment with skewed and uniform populations and vary the sample size from 2 to 25 {click on the N= downward arrow on the panel where the sample mean appears.) Be sure to use the "Animated" button to see how a sample of size n is drawn from the population and a single value for the sample mean is obtained. 0 Then use the larger numbers to perform many replications of the sampling. Note the difference between sample size and number of replications. - Comparison to a normal distribution: By clicking the "Fit normal" button you can see a normal distribution superimposed over the simulated sampling distribution. - Changing the population distribution: You can change the population by clicking on the top histogram with the mouse and dragging