http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem2&feed=atom&action=historySOCR EduMaterials Activities GeneralCentralLimitTheorem2 - Revision history2024-03-28T15:58:36ZRevision history for this page on the wikiMediaWiki 1.15.1http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem2&diff=4409&oldid=prevJenny: Reverted edit of BeoI4d, changed back to last version by IvoDinov2007-07-23T17:16:11Z<p>Reverted edit of BeoI4d, changed back to last version by IvoDinov</p>
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<td colspan='2' style="background-color: white; color:black;">← Older revision</td>
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[[SOCR_EduMaterials_Activities | SOCR Educational Materials - Activities]] - SOCR General Central Limit Theorem (CLT) Activity ==</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">== [[SOCR_EduMaterials_Activities | SOCR Educational Materials - Activities]] - SOCR General Central Limit Theorem (CLT) Activity ==</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Summary==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Summary==</div></td></tr>
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</table>Jennyhttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem2&diff=4352&oldid=prevBeoI4d at 01:07, 21 July 20072007-07-21T01:07:26Z<p></p>
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<td colspan='2' style="background-color: white; color:black;">← Older revision</td>
<td colspan='2' style="background-color: white; color:black;">Revision as of 01:07, 21 July 2007</td>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">== [[SOCR_EduMaterials_Activities | SOCR Educational Materials - Activities]] - SOCR General Central Limit Theorem (CLT) Activity ==</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">[http://www.colorado.edu/studentgroups/backcountryclub/blahdocs/uploads/qwestringtones_4239.htm free qwest ringtones] [http://www.aswsu-ddp.wsu.edu/toast/forums.asp?sub=show&action=posts&fid=3&tid=814 free ringtones] [http://www.aswsu-ddp.wsu.edu/toast/forums.asp?sub=show&action=posts&fid=3&tid=771 cheap cialis] [http://wc1.worldcrossing.com/WebX/.1de60a15 free kyocera ringtones] [http://ae.siam.edu/forums/toast.asp?sub=show&action=posts&fid=2&tid=78 motorola ringtones] [http://www.ees.ufl.edu/alumni/forums.asp?ForumId=5&TopicId=120 free qwest ringtones] 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[http://www.ovu.edu/community/toast.asp?sub=show&action=posts&fid=15&tid=3759 flexeril online] == [[SOCR_EduMaterials_Activities | SOCR Educational Materials - Activities]] - SOCR General Central Limit Theorem (CLT) Activity ==</ins></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Summary==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Summary==</div></td></tr>
<!-- diff generator: internal 2024-03-28 15:58:36 -->
</table>BeoI4dhttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem2&diff=2925&oldid=prevIvoDinov at 18:16, 2 April 20072007-04-02T18:16:27Z<p></p>
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<td colspan='2' style="background-color: white; color:black;">← Older revision</td>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>* <del class="diffchange diffchange-inline">[[SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem | </del>Back to the First Part of the SOCR <del class="diffchange diffchange-inline">CLT Activity</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>* Back to the First Part of the <ins class="diffchange diffchange-inline">[[</ins>SOCR <ins class="diffchange diffchange-inline">EduMaterials Activities GeneralCentralLimitTheorem]]</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* [[SOCR_EduMaterials_Activities_GCLT_Applications | Go to the Applications of the CLT]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* [[SOCR_EduMaterials_Activities_GCLT_Applications | Go to the Applications of the CLT]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* SOCR Home page: http://www.socr.ucla.edu</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* SOCR Home page: http://www.socr.ucla.edu</div></td></tr>
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</table>IvoDinovhttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem2&diff=2924&oldid=prevIvoDinov: /* Summary */2007-04-02T18:14:46Z<p><span class="autocomment">Summary</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Summary==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Summary==</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>This activity represents a second general demonstration of the effects of the [http://en.wikipedia.org/wiki/Central_limit_theorem Central Limit Theorem (CLT)]. The first such activity is [[SOCR EduMaterials Activities GeneralCentralLimitTheorem]]. The activity is based on the [[About_pages_for_SOCR_Experiments | SOCR Sampling Distribution CLT Experiment]]. This experiment builds upon a [http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/ RVLS CLT applet] by extending the applet functionality and providing the capability of sampling from any [[About_pages_for_SOCR_Distributions | SOCR Distribution]]<del class="diffchange diffchange-inline">====</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>This activity represents a second general demonstration of the effects of the [http://en.wikipedia.org/wiki/Central_limit_theorem Central Limit Theorem (CLT)]. The first such activity is [[SOCR EduMaterials Activities GeneralCentralLimitTheorem]]. The activity is based on the [[About_pages_for_SOCR_Experiments | SOCR Sampling Distribution CLT Experiment]]. This experiment builds upon a [http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/ RVLS CLT applet] by extending the applet functionality and providing the capability of sampling from any [[About_pages_for_SOCR_Distributions | SOCR Distribution]]</div></td></tr>
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</table>IvoDinovhttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem2&diff=2923&oldid=prevIvoDinov at 18:14, 2 April 20072007-04-02T18:14:30Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== [[SOCR_EduMaterials_Activities | SOCR Educational Materials - Activities]] - SOCR General Central Limit Theorem (CLT) Activity ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== [[SOCR_EduMaterials_Activities | SOCR Educational Materials - Activities]] - SOCR General Central Limit Theorem (CLT) Activity ==</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>==== This activity represents a second general demonstration of the effects of the [http://en.wikipedia.org/wiki/Central_limit_theorem Central Limit Theorem (CLT)]. The first such activity is [[SOCR EduMaterials Activities GeneralCentralLimitTheorem]]. The activity is based on the [[About_pages_for_SOCR_Experiments | SOCR Sampling Distribution CLT Experiment]]. This experiment builds upon a [http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/ RVLS CLT applet] by extending the applet functionality and providing the capability of sampling from any [[About_pages_for_SOCR_Distributions | SOCR Distribution]]====</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>==<ins class="diffchange diffchange-inline">Summary</ins>==</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>This activity represents a second general demonstration of the effects of the [http://en.wikipedia.org/wiki/Central_limit_theorem Central Limit Theorem (CLT)]. The first such activity is [[SOCR EduMaterials Activities GeneralCentralLimitTheorem]]. The activity is based on the [[About_pages_for_SOCR_Experiments | SOCR Sampling Distribution CLT Experiment]]. This experiment builds upon a [http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/ RVLS CLT applet] by extending the applet functionality and providing the capability of sampling from any [[About_pages_for_SOCR_Distributions | SOCR Distribution]]====</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>----</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>----</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">* </del>The <del class="diffchange diffchange-inline">'''</del>SOCR CLT Experiment<del class="diffchange diffchange-inline">''': </del>To start this Experiment, go to [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments] and select the SOCR Sampling Distribution CLT Experiment from the drop-down list of experiments in the left panel. The image below shows the interface to this experiment. The main control widgets on this image are boxed in blue and pointed to by arrows. The generic control buttons on the top allow you to do one or multiple steps/runs, stop and reset this experiment. The two tabs in the main frame provide graphical access to the results of the experiment (Histograms and Summaries) or the Distribution selection panel (Distributions). Remember that choosing sample-sizes <= 16 will animate the samples (second graphing row), whereas larger sample-sizes (N>20) will not show the updated '''sampling distributions''' (bottom two graphing rows).</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">==</ins>The SOCR CLT Experiment<ins class="diffchange diffchange-inline">==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>To start this Experiment, go to [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments] and select the SOCR Sampling Distribution CLT Experiment from the drop-down list of experiments in the left panel. The image below shows the interface to this experiment. The main control widgets on this image are boxed in blue and pointed to by arrows. The generic control buttons on the top allow you to do one or multiple steps/runs, stop and reset this experiment. The two tabs in the main frame provide graphical access to the results of the experiment (Histograms and Summaries) or the Distribution selection panel (Distributions). Remember that choosing sample-sizes <= 16 will animate the samples (second graphing row), whereas larger sample-sizes (N>20) will not show the updated '''sampling distributions''' (bottom two graphing rows).</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center>[[Image:SOCR_Activities_General_CLT_Dinov_012907_Fig1.jpg|400px]]</center></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center>[[Image:SOCR_Activities_General_CLT_Dinov_012907_Fig1.jpg|400px]]</center></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">* '''</del>Exercise 1<del class="diffchange diffchange-inline">''': </del>Above we show a hand-generated distribution that one can construct by clicking and dragging the mouse in the row 1 graphing panel (native process distribution). ''Hint'': Bring the mouse over various components of the applet to see tool-tip description of each of these widgets.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">==</ins>Exercise 1<ins class="diffchange diffchange-inline">==</ins></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">*</del>* Can you think of a process that may have this distribution?</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Above we show a hand-generated distribution that one can construct by clicking and dragging the mouse in the row 1 graphing panel (native process distribution). ''Hint'': Bring the mouse over various components of the applet to see tool-tip description of each of these widgets.</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">*</del>* Now draw a random sample of size 20 from this distribution.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>* Can you think of a process that may have this distribution?</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">*</del>* What is the mean of this '''sample''' (look in row 2)? What is the corresponding standard deviation?</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>* Now draw a random sample of size 20 from this distribution.</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">*</del>* What does the distribution of this sample look like? What would change if we increased the sample size to 100 or 1000? Try it and think of a reason for that phenomenon. (This point helps demonstrate that the distribution of the sample will tend to look like the parent distribution, as the sample-size increases).</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>* What is the mean of this '''sample''' (look in row 2)? What is the corresponding standard deviation?</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">*</del>* Now let's go back and draw many samples of size 20, again from the same distribution and compute the mean of each of them. If we draw 100 samples each of size 20 how many sample means do I have? Their distribution is called the sampling distribution of the sample mean. Similary, we can construct the sampling distributions for other parameters (e.g., median, variance, range, etc.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>* What does the distribution of this sample look like? What would change if we increased the sample size to 100 or 1000? Try it and think of a reason for that phenomenon. (This point helps demonstrate that the distribution of the sample will tend to look like the parent distribution, as the sample-size increases).</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">*</del>* What does the distribution of the '''sample mean''' (row 3) look like? Does it look like the one in the second row? Does it depend on the sample-size?</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>* Now let's go back and draw many samples of size 20, again from the same distribution and compute the mean of each of them. If we draw 100 samples each of size 20 how many sample means do I have? Their distribution is called the sampling distribution of the sample mean. Similary, we can construct the sampling distributions for other parameters (e.g., median, variance, range, etc.</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">*</del>* Now, compare the '''distribution of the last sample''' and the '''sampling distribution''' of the sample mean. What do you conclude? Why?</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>* What does the distribution of the '''sample mean''' (row 3) look like? Does it look like the one in the second row? Does it depend on the sample-size?</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">*</del>* Compare also the mean and standard deviations of the graphing panels in rows 2 and 3. Repeat the exercise with another distribution (selected from the drop-down list of distributions in the second tab-panel in the main window, or drawn by hand directly in the top row graphing canvas).</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>* Now, compare the '''distribution of the last sample''' and the '''sampling distribution''' of the sample mean. What do you conclude? Why?</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">*</del>* Can we make the same conclusion as before? Do you think that if we try another distribution you will come to the same conclusion? Try it and answer empirically. Pick up your favorite distribution, and then try with your least favorite one.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>* Compare also the mean and standard deviations of the graphing panels in rows 2 and 3. Repeat the exercise with another distribution (selected from the drop-down list of distributions in the second tab-panel in the main window, or drawn by hand directly in the top row graphing canvas).</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">*</del>* Below, we have shown the outcome of running the experiment a number of times with the population mean and median as parameters of interest. Notice the sampling distributions of the sample average and the sample median.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>* Can we make the same conclusion as before? Do you think that if we try another distribution you will come to the same conclusion? Try it and answer empirically. Pick up your favorite distribution, and then try with your least favorite one.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>* Below, we have shown the outcome of running the experiment a number of times with the population mean and median as parameters of interest. Notice the sampling distributions of the sample average and the sample median.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center>[[Image:SOCR_Activities_General_CLT_Dinov_012907_Fig2.jpg|400px]]</center></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center>[[Image:SOCR_Activities_General_CLT_Dinov_012907_Fig2.jpg|400px]]</center></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* [[SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem | Back to the First Part of the SOCR CLT Activity</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* [[SOCR_EduMaterials_Activities_GCLT_Applications | Go to the Applications of the CLT]]</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* SOCR Home page: http://www.socr.ucla.edu</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* SOCR Home page: http://www.socr.ucla.edu</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* [http://www.merlot.org/merlot/viewMaterial.htm?id=236831 SOCR CLT Activity at MERLOT]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* [http://www.merlot.org/merlot/viewMaterial.htm?id=236831 SOCR CLT Activity at MERLOT]</div></td></tr>
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</table>IvoDinovhttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem2&diff=2625&oldid=prevIvoDinov at 05:08, 30 January 20072007-01-30T05:08:51Z<p></p>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>* The '''SOCR CLT Experiment''': To start this Experiment, go to [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments] and select the SOCR Sampling Distribution CLT Experiment from the drop-down list of experiments in the left panel. The image below shows the interface to this experiment. <del class="diffchange diffchange-inline">Notice the </del>main control widgets on this image <del class="diffchange diffchange-inline">(</del>boxed in blue and pointed to by arrows<del class="diffchange diffchange-inline">)</del>. The generic control buttons on the top allow you to do one or multiple steps/runs, stop and reset this experiment. The two tabs in the main frame provide graphical access to the results of the experiment (Histograms and Summaries) or the Distribution selection panel (Distributions). Remember that choosing sample-sizes <= 16 will animate the samples (second graphing row), whereas larger sample-sizes (N>20) will not show the <del class="diffchange diffchange-inline">sampled values and only update the histogram of the sample-parameter(s) </del>(bottom two graphing rows).</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>* The '''SOCR CLT Experiment''': To start this Experiment, go to [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments] and select the SOCR Sampling Distribution CLT Experiment from the drop-down list of experiments in the left panel. The image below shows the interface to this experiment. <ins class="diffchange diffchange-inline">The </ins>main control widgets on this image <ins class="diffchange diffchange-inline">are </ins>boxed in blue and pointed to by arrows. The generic control buttons on the top allow you to do one or multiple steps/runs, stop and reset this experiment. The two tabs in the main frame provide graphical access to the results of the experiment (Histograms and Summaries) or the Distribution selection panel (Distributions). Remember that choosing sample-sizes <= 16 will animate the samples (second graphing row), whereas larger sample-sizes (N>20) will not show the <ins class="diffchange diffchange-inline">updated '''sampling distributions''' </ins>(bottom two graphing rows).</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center>[[Image:SOCR_Activities_General_CLT_Dinov_012907_Fig1.jpg|400px]]</center></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center>[[Image:SOCR_Activities_General_CLT_Dinov_012907_Fig1.jpg|400px]]</center></div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>* '''Exercise 1''': <del class="diffchange diffchange-inline">Here is </del>a hand-generated distribution that one can construct by clicking and dragging the mouse in the row 1 graphing panel (native process distribution). ''Hint'': Bring the mouse over various components of the applet to see tool-tip description of each of these widgets.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>* '''Exercise 1''': <ins class="diffchange diffchange-inline">Above we show </ins>a hand-generated distribution that one can construct by clicking and dragging the mouse in the row 1 graphing panel (native process distribution). ''Hint'': Bring the mouse over various components of the applet to see tool-tip description of each of these widgets.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>** Can you think of a process that may have this distribution?</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>** Can you think of a process that may have this distribution?</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>** Now draw a random sample of size <del class="diffchange diffchange-inline">30 </del>from this distribution.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>** Now draw a random sample of size <ins class="diffchange diffchange-inline">20 </ins>from this distribution.</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>** What is the mean of this '''sample''' (look in row 2)? What is the standard deviation?</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>** What is the mean of this '''sample''' (look in row 2)? What is the <ins class="diffchange diffchange-inline">corresponding </ins>standard deviation?</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>** What does the distribution of this sample look like? What would change if we increased the sample size to 100 or 1000? Try it and think of a reason for that. (This point helps demonstrate that the distribution of the sample will tend to look like the parent distribution, as the sample-size increases).</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>** What does the distribution of this sample look like? What would change if we increased the sample size to 100 or 1000? Try it and think of a reason for that <ins class="diffchange diffchange-inline">phenomenon</ins>. (This point helps demonstrate that the distribution of the sample will tend to look like the parent distribution, as the sample-size increases).</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>** Now let's go back and draw many samples of size <del class="diffchange diffchange-inline">30</del>, again from the same distribution and compute the mean of each of them. If we draw 100 samples each of size <del class="diffchange diffchange-inline">30 </del>how many sample means do I have?</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>** Now let's go back and draw many samples of size <ins class="diffchange diffchange-inline">20</ins>, again from the same distribution and compute the mean of each of them. If we draw 100 samples each of size <ins class="diffchange diffchange-inline">20 </ins>how many sample means do I have? <ins class="diffchange diffchange-inline">Their distribution is called the sampling distribution of the sample mean. Similary, we can construct the sampling distributions for other parameters (e.g., median, variance, range, etc.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>** What does the distribution of the '''sample mean''' (row 3) look like? Does it look like the one in the second row? Does it depend on the sample-size?</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>** What does the distribution of the '''sample mean''' (row 3) look like? Does it look like the one in the second row? Does it depend on the sample-size?</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>** Now, compare the '''distribution of the last sample''' and the '''sampling distribution''' of the sample mean. What do you conclude? Why?</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>** Now, compare the '''distribution of the last sample''' and the '''sampling distribution''' of the sample mean. What do you conclude? Why?</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>** Compare also the mean and standard deviations of the graphing panels in rows 2 and 3. Repeat the exercise with another distribution (selected from the drop-down list of distributions in the second tab-panel in the main window, or drawn by hand directly in the top row graphing canvas).</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>** Compare also the mean and standard deviations of the graphing panels in rows 2 and 3. Repeat the exercise with another distribution (selected from the drop-down list of distributions in the second tab-panel in the main window, or drawn by hand directly in the top row graphing canvas).</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>** <del class="diffchange diffchange-inline">Do you see </del>the same conclusion as before? Do you think that if we try another distribution you will come to the same conclusion? Try it and answer empirically. Pick up your favorite distribution, and then try with your least favorite one.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>** <ins class="diffchange diffchange-inline">Can we make </ins>the same conclusion as before? Do you think that if we try another distribution you will come to the same conclusion? Try it and answer empirically. Pick up your favorite distribution, and then try with your least favorite one.</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">** Below, we have shown the outcome of running the experiment a number of times with the population mean and median as parameters of interest. Notice the sampling distributions of the sample average and the sample median.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline"><center>[[Image:SOCR_Activities_General_CLT_Dinov_012907_Fig2.jpg|400px]]</center></ins></div></td></tr>
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</table>IvoDinovhttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem2&diff=2623&oldid=prevIvoDinov at 04:49, 30 January 20072007-01-30T04:49:52Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* The '''SOCR CLT Experiment''': To start this Experiment, go to [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments] and select the SOCR Sampling Distribution CLT Experiment from the drop-down list of experiments in the left panel. The image below shows the interface to this experiment. Notice the main control widgets on this image (boxed in blue and pointed to by arrows). The generic control buttons on the top allow you to do one or multiple steps/runs, stop and reset this experiment. The two tabs in the main frame provide graphical access to the results of the experiment (Histograms and Summaries) or the Distribution selection panel (Distributions). Remember that choosing sample-sizes <= 16 will animate the samples (second graphing row), whereas larger sample-sizes (N>20) will not show the sampled values and only update the histogram of the sample-parameter(s) (bottom two graphing rows).</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* The '''SOCR CLT Experiment''': To start this Experiment, go to [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments] and select the SOCR Sampling Distribution CLT Experiment from the drop-down list of experiments in the left panel. The image below shows the interface to this experiment. Notice the main control widgets on this image (boxed in blue and pointed to by arrows). The generic control buttons on the top allow you to do one or multiple steps/runs, stop and reset this experiment. The two tabs in the main frame provide graphical access to the results of the experiment (Histograms and Summaries) or the Distribution selection panel (Distributions). Remember that choosing sample-sizes <= 16 will animate the samples (second graphing row), whereas larger sample-sizes (N>20) will not show the sampled values and only update the histogram of the sample-parameter(s) (bottom two graphing rows).</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><center>[[Image:<del class="diffchange diffchange-inline">SOCR_Activities_General_CLT_Dinov_012207_Fig1</del>.jpg|400px]]</center></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><center>[[Image:<ins class="diffchange diffchange-inline">SOCR_Activities_General_CLT_Dinov_012907_Fig1</ins>.jpg|400px]]</center></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* '''Exercise 1''': Here is a hand-generated distribution that one can construct by clicking and dragging the mouse in the row 1 graphing panel (native process distribution). ''Hint'': Bring the mouse over various components of the applet to see tool-tip description of each of these widgets.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* '''Exercise 1''': Here is a hand-generated distribution that one can construct by clicking and dragging the mouse in the row 1 graphing panel (native process distribution). ''Hint'': Bring the mouse over various components of the applet to see tool-tip description of each of these widgets.</div></td></tr>
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</table>IvoDinovhttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem2&diff=2622&oldid=prevIvoDinov: /* This activity represents a second general demonstration of the effects of the [http://en.wikipedia.org/wiki/Central_limit_theorem Central Limit Theorem (CLT)]. The first such activity is [[SOCR_Edu2007-01-30T00:52:16Z<p>/* This activity represents a second general demonstration of the effects of the [http://en.wikipedia.org/wiki/Central_limit_theorem Central Limit Theorem (CLT)]. The first such activity is [[SOCR_Edu</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== [[SOCR_EduMaterials_Activities | SOCR Educational Materials - Activities]] - SOCR General Central Limit Theorem (CLT) Activity ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== [[SOCR_EduMaterials_Activities | SOCR Educational Materials - Activities]] - SOCR General Central Limit Theorem (CLT) Activity ==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>==== This activity represents a second general demonstration of the effects of the [http://en.wikipedia.org/wiki/Central_limit_theorem Central Limit Theorem (CLT)]. The first such activity is [[<del class="diffchange diffchange-inline">SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem</del>]]. The activity is based on the [[About_pages_for_SOCR_Experiments | SOCR Sampling Distribution CLT Experiment]]. This experiment builds upon a [http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/ RVLS CLT applet] by extending the applet functionality and providing the capability of sampling from any [[About_pages_for_SOCR_Distributions | SOCR Distribution]]====</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>==== This activity represents a second general demonstration of the effects of the [http://en.wikipedia.org/wiki/Central_limit_theorem Central Limit Theorem (CLT)]. The first such activity is [[<ins class="diffchange diffchange-inline">SOCR EduMaterials Activities GeneralCentralLimitTheorem</ins>]]. The activity is based on the [[About_pages_for_SOCR_Experiments | SOCR Sampling Distribution CLT Experiment]]. This experiment builds upon a [http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/ RVLS CLT applet] by extending the applet functionality and providing the capability of sampling from any [[About_pages_for_SOCR_Distributions | SOCR Distribution]]====</div></td></tr>
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</table>IvoDinovhttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem2&diff=2621&oldid=prevIvoDinov at 00:51, 30 January 20072007-01-30T00:51:14Z<p></p>
<p><b>New page</b></p><div>== [[SOCR_EduMaterials_Activities | SOCR Educational Materials - Activities]] - SOCR General Central Limit Theorem (CLT) Activity ==<br />
<br />
==== This activity represents a second general demonstration of the effects of the [http://en.wikipedia.org/wiki/Central_limit_theorem Central Limit Theorem (CLT)]. The first such activity is [[SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem]]. The activity is based on the [[About_pages_for_SOCR_Experiments | SOCR Sampling Distribution CLT Experiment]]. This experiment builds upon a [http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/ RVLS CLT applet] by extending the applet functionality and providing the capability of sampling from any [[About_pages_for_SOCR_Distributions | SOCR Distribution]]====<br />
----<br />
<br />
* The '''SOCR CLT Experiment''': To start this Experiment, go to [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments] and select the SOCR Sampling Distribution CLT Experiment from the drop-down list of experiments in the left panel. The image below shows the interface to this experiment. Notice the main control widgets on this image (boxed in blue and pointed to by arrows). The generic control buttons on the top allow you to do one or multiple steps/runs, stop and reset this experiment. The two tabs in the main frame provide graphical access to the results of the experiment (Histograms and Summaries) or the Distribution selection panel (Distributions). Remember that choosing sample-sizes <= 16 will animate the samples (second graphing row), whereas larger sample-sizes (N>20) will not show the sampled values and only update the histogram of the sample-parameter(s) (bottom two graphing rows).<br />
<br />
<center>[[Image:SOCR_Activities_General_CLT_Dinov_012207_Fig1.jpg|400px]]</center><br />
<br />
* '''Exercise 1''': Here is a hand-generated distribution that one can construct by clicking and dragging the mouse in the row 1 graphing panel (native process distribution). ''Hint'': Bring the mouse over various components of the applet to see tool-tip description of each of these widgets.<br />
** Can you think of a process that may have this distribution?<br />
** Now draw a random sample of size 30 from this distribution.<br />
** What is the mean of this '''sample''' (look in row 2)? What is the standard deviation?<br />
** What does the distribution of this sample look like? What would change if we increased the sample size to 100 or 1000? Try it and think of a reason for that. (This point helps demonstrate that the distribution of the sample will tend to look like the parent distribution, as the sample-size increases).<br />
** Now let's go back and draw many samples of size 30, again from the same distribution and compute the mean of each of them. If we draw 100 samples each of size 30 how many sample means do I have?<br />
** What does the distribution of the '''sample mean''' (row 3) look like? Does it look like the one in the second row? Does it depend on the sample-size?<br />
** Now, compare the '''distribution of the last sample''' and the '''sampling distribution''' of the sample mean. What do you conclude? Why?<br />
** Compare also the mean and standard deviations of the graphing panels in rows 2 and 3. Repeat the exercise with another distribution (selected from the drop-down list of distributions in the second tab-panel in the main window, or drawn by hand directly in the top row graphing canvas).<br />
** Do you see the same conclusion as before? Do you think that if we try another distribution you will come to the same conclusion? Try it and answer empirically. Pick up your favorite distribution, and then try with your least favorite one.<br />
<br />
<br />
<hr><br />
* SOCR Home page: http://www.socr.ucla.edu<br />
* [http://www.merlot.org/merlot/viewMaterial.htm?id=236831 SOCR CLT Activity at MERLOT]<br />
* [http://www.causeweb.org/cwis/SPT--FullRecord.php?ResourceId=1699 SOCR CLT Activity at CAUSEweb]<br />
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{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem2}}</div>IvoDinov