SOCR EduMaterials Activities BallAndRunExperiment - Revision history

IvoDinov: posted new figures to reflect the addition of Proportion as a RV

2008-10-04T17:29:11Z

posted new figures to reflect the addition of Proportion as a RV

IvoDinov: revised to include the addition of Proportion (M) to this applet

2008-10-04T17:11:39Z

revised to include the addition of Proportion (M) to this applet

IvoDinov: /* Experiment */

2008-09-12T22:13:43Z

‎Experiment

IvoDinov at 17:16, 29 January 2008

2008-01-29T17:16:51Z

PriscillaChui: /* Applications */

2007-05-16T00:32:42Z

‎Applications

PriscillaChui: /* Goals */

2007-05-13T03:56:04Z

‎Goals

PriscillaChui at 05:56, 6 May 2007

2007-05-06T05:56:21Z

PriscillaChui: /* Ball and Urn Experiment */

2007-05-05T05:31:47Z

‎Ball and Urn Experiment

PriscillaChui: /* Ball and Urn Experiment */

2007-05-04T03:24:53Z

‎Ball and Urn Experiment

PriscillaChui: /* Ball and Urn Experiment */

2007-05-04T03:14:59Z

‎Ball and Urn Experiment

@@ Line 12: / Line 12: @@
 Go to the [http://socr.ucla.edu/htmls/exp/Ball_and_Urn_Experiment.html SOCR Experiments] and select the '''Ball and Urn Experiment''' from the drop-down list of experiments on the top left. The image below shows the initial view of this experiment:
-<center>[[Image:SOCR_Activities_BallAndUrnExperiment_SubTopic_Chui_050307_Fig1.JPG|300px]]</center>
+<center>[[Image:SOCR_Activities_BallAndUrnExperiment_Dinov_100408_Fig1.jpg|400px]]</center>
 When pressing the play button, one trial will be executed and recorded in the distribution table below. The fast forward button symbolizes the nth number of trials to be executed each time. The stop button ceases any activity and is helpful when the experimenter chooses “continuous,” indicating an infinite number of events. The fourth button will reset the entire experiment, deleting all previous information and data collected.
@@ Line 21: / Line 21: @@
 Every trial is recorded with ''Y'' = the number of red balls in the sample, ''M'' = the proportion of red balls in the sample, ''U'' = estimate of ''R'', and ''V'' = estimate of ''N''. In the distribution table, the values of ''Y'' range from 0 to ''n'' and it indicates the mean value for ''Y'' as well as the standard deviation.
-<center>[[Image:SOCR_Activities_BallAndUrnExperiment_SubTopic_Chui_050307_Fig2.JPG|300px]]</center>
+<center>[[Image:SOCR_Activities_BallAndUrnExperiment_Dinov_100408_Fig2.jpg|400px]]</center>
 Because the ball and urn experiment is a general example of replacement in statistics, it is best to discuss the differences between experimenting with replacement and without replacement.

@@ Line 4: / Line 4: @@
 == Description ==
 The ball and urn experiment is a general java applet that displays the effects of replacement in an event.
-With a total of ''n'' balls chosen at random from an urn, ''R'' are red and ''(N-R)'' are green. For every trial, the number of red balls ''Y'' that have been selected are recorded numerically in the distribution table (on the right) and graphically in the distribution graph (blue). On each update, the empirical density and moments of ''Y'' are displayed in the distribution graph as red and are recorded in the distribution table. The experimenter has the abilities to manipulate trials by choosing with replacement or without replacement in the list box and varying parameters ''N'', ''R'', and ''n'' with scroll bars.
+With a total of ''n'' balls chosen at random from an urn, ''R'' are red and ''(N-R)'' are green. For every trial, the number (''Y'') or the proportion (''M'') of red balls ''Y'' that have been selected are recorded numerically in the distribution table (on the right) and graphically in the distribution graph (blue). On each update, the empirical density and moments of ''Y'' or ''M'' are displayed in the distribution graph as red, and are recorded in the distribution table. The experimenter has the abilities to manipulate trials by choosing with replacement or without replacement in the list box and varying parameters ''N'', ''R'', and ''n'' with scroll bars.
 == Goals ==
@@ Line 19: / Line 19: @@
 When parameter ''N'' is increased, the distribution graph remains normal but is shifted left—the distribution table numerically shows this as well—and when is shifted right when parameter ''N'' is decreased. When ''R'' is increased, the distribution graph remains normal and is shifted to the right; when ''R'' is decreased, the distribution graph is shifted to the left. But when ''R'' is set to the extreme boundaries, the distribution graph will eventually take shape of a rectangle. The normality of the distribution graph is dependent upon ''n'' as it takes upon a normal shape when ''n'' is large and an inaccurate normal shape when ''n'' is small.
-Every trial is recorded with ''Y'' = the number of red balls in the sample, ''U'' = estimate of ''R'', and ''V'' = estimate of ''N''. In the distribution table, the values of ''Y'' range from 0 to ''n'' and it indicates the mean value for ''Y'' as well as the standard deviation.
+Every trial is recorded with ''Y'' = the number of red balls in the sample, ''M'' = the proportion of red balls in the sample, ''U'' = estimate of ''R'', and ''V'' = estimate of ''N''. In the distribution table, the values of ''Y'' range from 0 to ''n'' and it indicates the mean value for ''Y'' as well as the standard deviation.
 <center>[[Image:SOCR_Activities_BallAndUrnExperiment_SubTopic_Chui_050307_Fig2.JPG|300px]]</center>

@@ Line 10: / Line 10: @@
 == Experiment ==
-Go to the [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments] and select the '''Ball and Urn Experiment''' from the drop-down list of experiments on the top left. The image below shows the initial view of this experiment:
+Go to the [http://socr.ucla.edu/htmls/exp/Ball_and_Urn_Experiment.html SOCR Experiments] and select the '''Ball and Urn Experiment''' from the drop-down list of experiments on the top left. The image below shows the initial view of this experiment:
 <center>[[Image:SOCR_Activities_BallAndUrnExperiment_SubTopic_Chui_050307_Fig1.JPG|300px]]</center>

@@ Line 10: / Line 10: @@
 == Experiment ==
-Go to the SOCR Experiments ([[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html]]) and select the Ball and Urn Experiment from the drop-down list of experiments on the top left. The image below shows the initial view of this experiment:
+Go to the [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments] and select the '''Ball and Urn Experiment''' from the drop-down list of experiments on the top left. The image below shows the initial view of this experiment:
 <center>[[Image:SOCR_Activities_BallAndUrnExperiment_SubTopic_Chui_050307_Fig1.JPG|300px]]</center>

@@ Line 28: / Line 28: @@
 == Applications ==
-The ball and urn experiment is applicable in daily lives. For instance, at a supermarket, the manager may determine if removing damaged oranges from the produce section will create a better image of the market as customers will randomly select oranges in good condition, or if removing damaged oranges will waste time and effort as customers will continue to randomly select oranges that may either be in good condition or damaged.
+The ball and urn experiment is applicable in daily lives.
 The ball and urn java applet may also be applied to situations when one is looking for a penny in the coin bag. Will the probability of randomly selecting a penny be higher when removing coins that are not pennies from the bag, or replacing them back into the bag after every try?
 {{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_BallAndRunExperiment}}

@@ Line 9: / Line 9: @@
 To provide a method for events being randomly chosen without bias and develop a common sense about the behaviors of the variables.
-'''*Experiment:'''
+== Experiment ==
 Go to the SOCR Experiments ([[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html]]) and select the Ball and Urn Experiment from the drop-down list of experiments on the top left. The image below shows the initial view of this experiment:
@@ Line 25: / Line 25: @@
 Because the ball and urn experiment is a general example of replacement in statistics, it is best to discuss the differences between experimenting with replacement and without replacement.
 Sampling without replacement will require more time and trials for the distribution graph to take shape of a normal curve and sampling with replacement does not require as much time and trials because it eventually takes shape of a normal curve.
 == Applications ==

← Older revision		Revision as of 03:24, 4 May 2007
Line 22:		Line 22:
	Every trial is recorded with ''Y'' = the number of red balls in the sample, ''U'' = estimate of ''R'', and ''V'' = estimate of ''N''. In the distribution table, the values of ''Y'' range from 0 to ''n'' and it indicates the mean value for ''Y'' as well as the standard deviation.		Every trial is recorded with ''Y'' = the number of red balls in the sample, ''U'' = estimate of ''R'', and ''V'' = estimate of ''N''. In the distribution table, the values of ''Y'' range from 0 to ''n'' and it indicates the mean value for ''Y'' as well as the standard deviation.

−	[[~~Image:~~http://wiki.stat.ucla.edu/socr/uploads/6/6e/SOCR_Activities_BallAndUrnExperiment_SubTopic_Chui_050307_Fig2.JPG]]	+	[[http://wiki.stat.ucla.edu/socr/uploads/6/6e/SOCR_Activities_BallAndUrnExperiment_SubTopic_Chui_050307_Fig2.JPG]]

@@ Line 3: / Line 3: @@
-*'''Description:'''The ball and urn experiment is a general java applet that displays the effects of replacement in an event.
+*'''Description:'''
 With a total of ''n'' balls chosen at random from an urn, ''R'' are red and ''(N-R)'' are green. For every trial, the number of red balls ''Y'' that have been selected are recorded numerically in the distribution table (on the right) and graphically in the distribution graph (blue). On each update, the empirical density and moments of ''Y'' are displayed in the distribution graph as red and are recorded in the distribution table. The experimenter has the abilities to manipulate trials by choosing with replacement or without replacement in the list box and varying parameters ''N'', ''R'', and ''n'' with scroll bars.
@@ Line 12: / Line 13: @@
 Go to the SOCR Experiments ([[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html]]) and select the Ball and Urn Experiment from the drop-down list of experiments on the top left. The image below shows the initial view of this experiment:
+[[http://wiki.stat.ucla.edu/socr/uploads/6/60/SOCR_Activities_BallAndUrnExperiment_SubTopic_Chui_050307_Fig1.JPG]]
 When pressing the play button, one trial will be executed and recorded in the distribution table below. The fast forward button symbolizes the nth number of trials to be executed each time. The stop button ceases any activity and is helpful when the experimenter chooses “continuous,” indicating an infinite number of events. The fourth button will reset the entire experiment, deleting all previous information and data collected.
@@ Line 22: / Line 22: @@
 Every trial is recorded with ''Y'' = the number of red balls in the sample, ''U'' = estimate of ''R'', and ''V'' = estimate of ''N''. In the distribution table, the values of ''Y'' range from 0 to ''n'' and it indicates the mean value for ''Y'' as well as the standard deviation.
+[[Image:http://wiki.stat.ucla.edu/socr/uploads/6/6e/SOCR_Activities_BallAndUrnExperiment_SubTopic_Chui_050307_Fig2.JPG]]
@@ Line 29: / Line 29: @@
 Sampling without replacement will require more time and trials for the distribution graph to take shape of a normal curve and sampling with replacement does not require as much time and trials because it eventually takes shape of a normal curve.
-Applications:
+*'''Applications:'''
 The ball and urn experiment is applicable in daily lives. For instance, at a supermarket, the manager may determine if removing damaged oranges from the produce section will create a better image of the market as customers will randomly select oranges in good condition, or if removing damaged oranges will waste time and effort as customers will continue to randomly select oranges that may either be in good condition or damaged.
 The ball and urn java applet may also be applied to situations when one is looking for a penny in the coin bag. Will the probability of randomly selecting a penny be higher when removing coins that are not pennies from the bag, or replacing them back into the bag after every try?