IvoDinov at 04:23, 1 April 2008

2008-04-01T04:23:44Z

Jenny: New page: == Stats 13.1 - Laboratory Activity 5== ===Confidence Interval Activity=== ==== This is an activity to explore the confidence intervals for the popu...

2007-11-06T18:50:12Z

New page: == Stats 13.1 - Laboratory Activity 5== ===Confidence Interval Activity=== ==== This is an activity to explore the confidence intervals for the popu...

New page

== [[SOCR_Courses_2007_2008_Stat13_1 | Stats 13.1]] - Laboratory Activity 5==

===Confidence Interval Activity===

==== 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 "Confidence Interval Experiment".

The confidence interval for the population mean <math>\mu</math> when <math> \sigma </math> is known is given by:
<math>
\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_{\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:'''
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?
**'''2.''' What do the blue lines represent?
**'''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.

*'''Exercise 2:'''
**'''1.''' Reset and repeat (a) with <math>\alpha=0.01</math>. Take a snapshot and describe 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.

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_ConfIntervals}}

← Older revision		Revision as of 04:23, 1 April 2008
Line 36:		Line 36:
	* 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_ConfIntervals~~}}	+	{{translate\|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_Courses_2007_2008_Stat13_1_Lab5}}

SOCR Courses 2007 2008 Stat13 1 Lab5 - Revision history

IvoDinov at 04:23, 1 April 2008

Jenny: New page: == Stats 13.1 - Laboratory Activity 5== ===Confidence Interval Activity=== ==== This is an activity to explore the confidence intervals for the popu...