Support for the
Java 2 runtime environment (version 1.4 or later). Click on the icon to download the appropriate
plug-in.Object Library > Applets > Mean Estimate Experiment
The experiment is to select a random sample of size n from a specified distribution, and then to construct an approximate confidence interval for the mean at a specified confidence level.
The distribution can be chosen with a list box; the options are normal, gamma, and uniform. In each case, the appropriate parameters and the sample size can be varied with scroll bars. The density and mean of the selected distribution are shown in blue in the first graph.
The confidence level can be selected from a list box, as can the type of interval--two sided, upper bound, or lower bound. The interval can be constructed assuming either that the distribution standard deviation is known or unknown. In the first case the pivot variable has the standard normal distribution; in the second case the pivot variable has the student t distribution with n - 1 degrees of freedom. The density of the pivot variable and the critical values are shown in blue in the second graph.
Variables L and R denote the left and right endpoints of the confidence interval and I indicates the event that the confidence interval contains the distribution mean. The theoretical density of I is shown in blue in the third graph.
On each update, the sample density and the confidence interval are shown in red in the first graph, and the value of the pivot variable is shown in red in the second graph. Note that the confidence interval contains the mean in the first graph if and only if the pivot variable falls between the critical values in the second graph. The third graph shows the proportion of successes and failures in red. The first table gives the sample values; the second table records L, R, the pivot variable (Z or T) and I. Finally, the third table gives the theoretical and empirical densities of I.
This applet illustrates the following topics and concepts. Click on the links to learn more about the mathematical theory.
Click on the link below to download the Java archive file:
To add the applet to your web page, insert the following in the html file, at the point where you want the applet to appear:
<applet code="edu.uah.math.experiments.MeanEstimateExperiment.class"
archive="MeanEstimateExperiment.jar" width="650" height="400"></applet>
The jar file and the html file must be in the same folder.
This width and height dimensions are simply suggestions and can be varied. Generally, components such as graphs and tables expand and contract proportionally, while components such as buttons, scrollbars, dice, and coins are fixed in size.
Support for the
Java 2 runtime environment (version 1.4 or later). Click on the icon to download the appropriate
plug-in.Copyright © 2001-2003 Kyle Siegrist, Dawn Duehring
This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but without any warranty; without even the implied warranty of merchantability or fitness for a particular purpose. See the GNU General Public License for more details.
If you are interested in the Java source code or the Java documentation and object model for this applet, please visit MeanEstimateExperiment in the Object section of the Library.