SOCR EduMaterials Activities ConfIntervals - Revision history

Nchristo: /* This is an activity to explore the confidence intervals for the populatuon mean when the standard deviation is known. */

2009-03-02T04:40:35Z

‎This is an activity to explore the confidence intervals for the populatuon mean when the standard deviation is known.

Nchristo: /* This is an activity to explore the confidence intervals for the populatuon mean when the standard deviation is known. */

2009-03-02T04:37:55Z

‎This is an activity to explore the confidence intervals for the populatuon mean when the standard deviation is known.

Nchristo: /* This is an activity to explore the confidence intervals for the populatuon mean when the standard deviation is known. */

2009-03-02T04:21:12Z

‎This is an activity to explore the confidence intervals for the populatuon mean when the standard deviation is known.

Nchristo: /* This is an activity to explore the confidence intervals for the populatuon mean when the standard deviation is known. */

2007-05-25T00:14:30Z

‎This is an activity to explore the confidence intervals for the populatuon mean when the standard deviation is known.

Nchristo: /* This is an activity to explore the confidence intervals for the populatuon mean when the standard deviation is known. */

2007-05-25T00:13:25Z

‎This is an activity to explore the confidence intervals for the populatuon mean when the standard deviation is known.

IvoDinov at 03:05, 29 December 2006

2006-12-29T03:05:07Z

Nchristo: /* This is an activity to explore the confidence intervals for the populatuon mean when the standard deviation is known. */

2006-11-25T06:08:24Z

‎This is an activity to explore the confidence intervals for the populatuon mean when the standard deviation is known.

Nchristo: /* This is an activity to explore the confidence intervals for the populatuon mean when the standard deviation is known. */

2006-11-25T06:07:08Z

‎This is an activity to explore the confidence intervals for the populatuon mean when the standard deviation is known.

Nchristo: /* This is an activity to explore the confidence intervals for the populatuon mean when the standard deviation is known. */

2006-11-25T06:03:09Z

‎This is an activity to explore the confidence intervals for the populatuon mean when the standard deviation is known.

Nchristo at 05:59, 25 November 2006

2006-11-25T05:59:49Z

@@ Line 15: / Line 15: @@
 **'''3.'''  How is the confidence interval represented?
 **'''4.'''  What does the green dot represent?
-**'''5.'''  Write down the formula on which the confidence intervals are based.
+**'''5.'''  Write down the formula on which the confidence intervals are based and explain why they have different width.
 *'''Exercise 2:'''

@@ Line 11: / Line 11: @@
 *'''Exercise 1:'''
 Using the scroll down button select "Number of Experiments = 100".  Select sample size <math>n=20</math>, and choose number of intervals 200.  It means:  You will select 200 samples and with each sample you will obtain a confidence interval.  You will do this 100 times.  How many intervals (out of the 200) do you expect to miss the population mean <math>\mu=0</math>?  Take a snapshot and describe what you observe.
 **'''1.'''  What do the numbers -3, -2, -1, 0, 1, 2, 3 represent?
 **'''2.'''  What do the blue lines represent?

@@ Line 12: / Line 12: @@
 Using the scroll down button select "Number of Experiments = 100".  Select sample size <math>n=20</math>, and choose number of intervals 200.  It means:  You will select 200 samples and with each sample you will obtain a confidence interval.  You will do this 100 times.  How many intervals (out of the 200) do you expect to miss the population mean <math>\mu=0</math>?  Take a snapshot and describe what you observe.
-**'''1.'''  What do the number -3, -2, -1, 0, 1, 2, 3 represent?
+**'''1.'''  What do the numbers -3, -2, -1, 0, 1, 2, 3 represent?
 **'''2.'''  What do the blue lines represent?
 **'''3.'''  How is the confidence interval represented?

@@ Line 7: / Line 7: @@
 \bar x - z_{\frac{\alpha}{2}} \frac{\sigma}{\sqrt{n}} \le \mu \le \bar x + z_{\frac{\alpha}{2}} \frac{\sigma}{\sqrt{n}}
 </math>
-where <math>z_{\frac{\alpha}{2}}</math> is the value of <math>z</math> such that the area to its left (or right) is <math>\frac{\alpha}{2}</math>.  For example if we choose a <math>95 \% </math> confidence level then <math>1-\alpha=0.95</math> or <math>\alpha=0.05</math> and therefore <math>\frac{\alpha}{2}=0.025</math> which gives <math>z^*=1.96</math>.  The sample mean <math>\bar x</math> is the mean of the sample of size <math>n</math>, and <math>\sigma </math> is the standard deviaton.  In this lab we will generate many confidence intervals based on different sample sizes.  The samples in this lab are always selected from the standard normal distribution <math>N(0,1)</math>.  Therefore we know that the mean is $\mu=0$, and the standard deviation <math>\sigma=1</math>.  Let's pretend that <math>\mu</math> is unknown and that only <math>\sigma</math> is known.  We will select many samples each one of size <math>n</math> and use it to construct a confidence interval for the population mean.
+where <math>z_{\frac{\alpha}{2}}</math> is the value of <math>z</math> such that the area to its left (or right) is <math>\frac{\alpha}{2}</math>.  For example if we choose a <math>95 \% </math> confidence level then <math>1-\alpha=0.95</math> or <math>\alpha=0.05</math> and therefore <math>\frac{\alpha}{2}=0.025</math> which gives <math>z_{\frac{\alpha}{2}}=1.96</math>.  The sample mean <math>\bar x</math> is the mean of the sample of size <math>n</math>, and <math>\sigma </math> is the standard deviaton.  In this lab we will generate many confidence intervals based on different sample sizes.  The samples in this lab are always selected from the standard normal distribution <math>N(0,1)</math>.  Therefore we know that the mean is <math>\mu=0</math>, and the standard deviation <math>\sigma=1</math>.  Let's pretend that <math>\mu</math> is unknown and that only <math>\sigma</math> is known.  We will select many samples each one of size <math>n</math> and use it to construct a confidence interval for the population mean.
 *'''Exercise 1:'''

@@ Line 5: / Line 5: @@
 The confidence interval for the population mean <math>\mu</math> when <math> \sigma </math> is known is given by:
 <math>
-\bar x - z^* \frac{\sigma}{\sqrt{n}} \le \mu \le \bar x + z^* \frac{\sigma}{\sqrt{n}}
+\bar x - z_{\frac{\alpha}{2}} \frac{\sigma}{\sqrt{n}} \le \mu \le \bar x + z_{\frac{\alpha}{2}} \frac{\sigma}{\sqrt{n}}
 </math>
-where <math>z^*</math> is the value of <math>z</math> such that the area to its left (or right) is <math>\frac{\alpha}{2}</math>.  For example if we choose a <math>95 \% </math> confidence level then <math>1-\alpha=0.95</math> or <math>\alpha=0.05</math> and therefore <math>\frac{\alpha}{2}=0.025</math> which gives <math>z^*=1.96</math>.  The sample mean <math>\bar x</math> is the mean of the sample of size <math>n</math>, and <math>\sigma </math> is the standard deviaton.  In this lab we will generate many confidence intervals based on different sample sizes.  The samples in this lab are always selected from the standard normal distribution <math>N(0,1)</math>.  Therefore we know that the mean is $\mu=0$, and the standard deviation <math>\sigma=1</math>.  Let's pretend that <math>\mu</math> is unknown and that only <math>\sigma</math> is known.  We will select many samples each one of size <math>n</math> and use it to construct a confidence interval for the population mean.
+where <math>z_{\frac{\alpha}{2}}</math> is the value of <math>z</math> such that the area to its left (or right) is <math>\frac{\alpha}{2}</math>.  For example if we choose a <math>95 \% </math> confidence level then <math>1-\alpha=0.95</math> or <math>\alpha=0.05</math> and therefore <math>\frac{\alpha}{2}=0.025</math> which gives <math>z^*=1.96</math>.  The sample mean <math>\bar x</math> is the mean of the sample of size <math>n</math>, and <math>\sigma </math> is the standard deviaton.  In this lab we will generate many confidence intervals based on different sample sizes.  The samples in this lab are always selected from the standard normal distribution <math>N(0,1)</math>.  Therefore we know that the mean is $\mu=0$, and the standard deviation <math>\sigma=1</math>.  Let's pretend that <math>\mu</math> is unknown and that only <math>\sigma</math> is known.  We will select many samples each one of size <math>n</math> and use it to construct a confidence interval for the population mean.
 *'''Exercise 1:'''

← Older revision		Revision as of 03:05, 29 December 2006
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	* SOCR Home page: http://www.socr.ucla.edu		* SOCR Home page: http://www.socr.ucla.edu

−	{{translate\|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=~~SOCR_EduMaterials_Activities_ConfidenceIntervals~~}}	+	{{translate\|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_ConfIntervals}}

← Older revision		Revision as of 06:08, 25 November 2006
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	Below you can see a snapshot of the run of 100 intervals with <math> n=36, \ \alpha=0.05 </math>.		Below you can see a snapshot of the run of 100 intervals with <math> n=36, \ \alpha=0.05 </math>.

−	<center>[[Image: ~~SOCR_Activities_Christou_christou_confint1~~.jpg\|600px]]</center>	+	<center>[[Image: SOCR_Activities_Christou_christou_confint.jpg\|600px]]</center>

← Older revision		Revision as of 06:07, 25 November 2006
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	Below you can see a snapshot of the run of 100 intervals with <math> n=36, \ \alpha=0.05 </math>.		Below you can see a snapshot of the run of 100 intervals with <math> n=36, \ \alpha=0.05 </math>.

−	<center>[[Image: ~~SOCR_Activities_Christou_christou_confint~~.jpg\|600px]]</center>	+	<center>[[Image: SOCR_Activities_Christou_christou_confint1.jpg\|600px]]</center>

@@ Line 1: / Line 1: @@
 == This is an activity to explore the confidence intervals for the populatuon mean when the standard deviation is known. ==
-* '''Description''':  You can access the applet for the confidence intervals experiment at [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments].  Use the scroll down button to find the "Sample Mean Experiment".
+* '''Description''':  You can access the applet for the confidence intervals experiment at [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments].  Use the scroll down button to find the "Confidence Interval Experiment".
 The confidence interval for the population mean <math>\mu</math> when <math> \sigma </math> is known is given by:

← Older revision		Revision as of 05:59, 25 November 2006
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	**'''2.''' Reset and repeat (a) with sample size now <math>n=80</math>. Take a snapshot and describe in detail what you see.		**'''2.''' Reset and repeat (a) with sample size now <math>n=80</math>. Take a snapshot and describe in detail what you see.
	**'''3.''' Reset and repeat (a) with sample size <math>n=80</math> and <math>\alpha=1.0E-4</math> (this is <math>10^{-4}</math>). Take a snapshot and describe in detail what you see.		**'''3.''' Reset and repeat (a) with sample size <math>n=80</math> and <math>\alpha=1.0E-4</math> (this is <math>10^{-4}</math>). Take a snapshot and describe in detail what you see.
		+
		+
		+	Below you can see a snapshot of the run of 100 intervals with <math> n=36, \ \alpha=0.05 </math>.
		+
		+	<center>[[Image: SOCR_Activities_Christou_christou_confint.jpg\|600px]]</center>
		+
		+
		+	<hr>
		+	* SOCR Home page: http://www.socr.ucla.edu
		+
		+	{{translate\|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_ConfidenceIntervals}}