Difference between revisions of "SOCR EduMaterials Activities ConfidenceIntervals"

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=== Choose the Confidence Interval Experiment. In this [Help_pages_for_SOCR_Experiments experiment] you will investigate the emperical properties of the sample-size, confidence level, the size of the constructed confidence interval and the practical utilization of Confidence Intervals in statistical data analysis ===
 
=== Choose the Confidence Interval Experiment. In this [Help_pages_for_SOCR_Experiments experiment] you will investigate the emperical properties of the sample-size, confidence level, the size of the constructed confidence interval and the practical utilization of Confidence Intervals in statistical data analysis ===
  
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* Exercise 1: Consider a Poisson random variable X with parameter λ=1.5. Select the Poisson distribution in the applet, and r=1.5 (since r represents the parameter, λ).  Then set n=1 to indicate that you have only one random variable.    Do not touch anything else. You will see a blue distribution on the right and on the left. The distribution on the left is the theoretical distribution of the X that we specified and the distribution on the right is the theoretical distribution of the sample average  (which in the applet is denoted by M).  Let's denote the sample average by <b>X<sup>-</sup></b>!
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* Exercise 1:  
  
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* Question 1(a): Compare these two theoretical distributions.  Attach a snapshot of how they look and the theoretical distribution tables below them. They are exactly the same! Because when n=1, X<sup>-</sup>=X.
 
 
<center>[[Image:SOCR_Activities_CI_Dinov_092206_Fig1.jpg|300px]]</center>
 
<center>[[Image:SOCR_Activities_CI_Dinov_092206_Fig1.jpg|300px]]</center>
  
 
   
 
   
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* Question 1(b): Compare the Mean of the theoretical distribution of  the X variable and that of the Mean of the distribution of the  (the distribution of the M). These are theoretical means. What is their relation?  
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* Question 1: Compare the Mean of the theoretical distribution of  the X variable and that of the Mean of the distribution of the  (the distribution of the M). These are theoretical means. What is their relation?  
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The Mean of the theoretical distribution of the X is 1.5, while that of the Mean of the distribution of the  is 1.5, too. They are the same. Theoretically, E(X<sup>-</sup>) = E(X) is always true if X<sup>-</sup> is the mean of several independent and identical random variables (IID) no matter how large is n.
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* Exercise 2:
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<center>[[Image:SOCR_Activities_CI_Dinov_092206_Fig2.jpg|300px]]</center>
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* Question 2: Compare the Mean of the theoretical distribution of the X variable and that of the Mean of the distribution of the  (the distribution of the M). These are theoretical means. What is their relation?
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* Exercise 3:
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<center>[[Image:SOCR_Activities_CI_Dinov_092206_Fig3.jpg|300px]]</center>
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* Question 3: Compare the Mean of the theoretical distribution of  the X variable and that of the Mean of the distribution of the  (the distribution of the M). These are theoretical means. What is their relation?
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* Exercise 4:
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<center>[[Image:SOCR_Activities_CI_Dinov_092206_Fig4.jpg|300px]]</center>
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* Question 4: Compare the Mean of the theoretical distribution of the X variable and that of the Mean of the distribution of the  (the distribution of the M). These are theoretical means. What is their relation?
  
  

Revision as of 14:07, 22 September 2006

SOCR Educational Materials - Activities - SOCR COnfidence Intervals Activity

URL Go to: http://www.socr.ucla.edu/htmls/SOCR_Experiments.html

Choose the Confidence Interval Experiment. In this [Help_pages_for_SOCR_Experiments experiment] you will investigate the emperical properties of the sample-size, confidence level, the size of the constructed confidence interval and the practical utilization of Confidence Intervals in statistical data analysis

  • Exercise 1:
SOCR Activities CI Dinov 092206 Fig1.jpg


  • Question 1: Compare the Mean of the theoretical distribution of the X variable and that of the Mean of the distribution of the (the distribution of the M). These are theoretical means. What is their relation?
  • Exercise 2:
SOCR Activities CI Dinov 092206 Fig2.jpg
  • Question 2: Compare the Mean of the theoretical distribution of the X variable and that of the Mean of the distribution of the (the distribution of the M). These are theoretical means. What is their relation?


  • Exercise 3:
SOCR Activities CI Dinov 092206 Fig3.jpg


  • Question 3: Compare the Mean of the theoretical distribution of the X variable and that of the Mean of the distribution of the (the distribution of the M). These are theoretical means. What is their relation?


  • Exercise 4:
SOCR Activities CI Dinov 092206 Fig4.jpg


  • Question 4: Compare the Mean of the theoretical distribution of the X variable and that of the Mean of the distribution of the (the distribution of the M). These are theoretical means. What is their relation?



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