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Connexions module: m11204 1 Basic Simulation ∗ David Lane This work is produced by The Connexions Project and licensed under the Creative Commons Attribution License † 1 General Instructions This simulation illustrates the concept of a sampling distribution. Depicted on the top graph is the population from which we are going to sample. There are 33 different values in the population: the integers from 0 to 32 (inclusive). You can think of the population as consisting of having an extremely large number of balls with each 0's, an extremely large number with 1's, etc. on them. The height of the distribution shows the relative number of balls of each number. There is an equal number of balls for each number, so the distribution is a rectangle. The second graph shows the sampling processes as it might happen in the physical world. After you push the "animated sampling" button, five balls are selected and and are plotted on the second graph. The mean of this sample of five is then computed and plotted on the third graph. If you push the "animated sampling" button again, another sample of five will be taken, and again plotted on the second graph. The mean will be computed and plotted on the third graph. This third graph is labeled "Distribution of Sample Means, N = 5" because each value plotted is a sample mean based on a sample of five. At this point, you should have two means plotted in this graph. The mean is depicted graphically on the distributions themselves by a blue vertical bar below the X-axis. For Graphs 1 and 3, a red line starts from this mean value and extends one standard deviation in length in both directions. The values of both the mean and the standard deviation are given to the left of the graph. Notice that the numeric form of a property matches its graphical form. The sampling distribution of a statistic is the relative frequency distribution of that statistic that is approached as the number of samples (not the sample size!)

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