//  File MIT-Lab-P2-00-02.txt. Edition 5/15/2012.


//  Title
      Consistent_Estimation_Procedures
//  List of Population Proportions
      .1 .9 .1 .5
//  List of Sample Sizes
      1_2_3_4_10_16_25_50_100_200_400
//    List of From Bounds - Decimals
        0.000  1.000  .025  -1.000
//    List of To Bounds - Decimals
        0.000  1.000  .025  -1.000
//    List of From Bounds - Integers
        0 -1 1 -1
//    List of To Bounds - Integers
        0 -1 1 -1


//  Problem Specs
//    ActFrac
//    SampleSize
//    PauseCheckbox(-1 checked 0 cleared)
//    NonRandomSampleCheckbox(-1 visible unchecked, 0 not visible, 1 visible checked)
//    To-FromValues(0 hide, -1 reset values to none, 1 leave current values intact)


` .5 16 0 -1 0
Objective: Illustrate the difference between unbiased and consistent estimation
 procedures.
_
Random Polling Procedure: Place the names of the entire population in a bowl
 and mix the names thoroughly. Draw one name at random from the bowl.
 Record whether or not that individual supports Clint. Replace
 the name in the bowl and remix the names thoroughly. Repeat the process
 until the number of individuals queried equals the sample size.

` .5 16 0 -1 0
1. By default the actual fraction supporting Clint, ActFrac, equals .5. 
 Click the Start button and then after many, many, repetitions click Stop.
_
1a. What is the mean (average) of the estimated fractions?
_
1b. Is the random polling procedure biased or unbiased? Explain.


` .5 16 0 1 0
Next, consider a different polling procedure: 
_
Nonrandom Polling Procedure: Suppose that the pollster
 begins in Clint's dorm room. Then, he leaves Clint's room and polls the
 first 16 students he/she bumps into. Students who are friends tend to
 live near each other; consequently, those who live near Clint will be
 more inclined to vote for him. This is example of a nonrandom polling
 procedure. 
_
To investigate this nonrandom polling procedure the Non-Ran Samp checkbox
 is now checked.

` .5 16 0 1 0
2. Note that the actual fraction supporting Clint, ActFrac, equals .5. 
 Click the Start button and then after many, many, repetitions click Stop.
_
2a. What is the mean (average) of the estimated fractions? Is the nonrandom polling
 procedure biased or unbiased? Explain.
_
2b. If biased:
__________1) Is the estimation procedure biased upwards of downwards?
__________2) What is the magnitude of the bias?
__________3) What is the variance of the estimated fractions?


` .5 25 0 1 0
3. Now, note that the sample size was increased from 16 to 25. Click Start and then after many, many
 repetitions click Stop.
_
3a. What is the mean (average) of the estimated fractions? Is the nonrandom polling
 procedure biased or unbiased? Explain.
_
3b. If biased:
__________1) Is the estimation procedure biased upwards of downwards?
__________2) What is the magnitude of the bias?
__________3) What is the variance of the estimated fractions?


` .5 100 0 1 0
4. Next, note that the sample size was increased from 25 to 100. Click Start and then after many, many
 repetitions click Stop.
_
4a. What is the mean (average) of the estimated fractions? Is the nonrandom polling
 procedure biased or unbiased? Explain.
_
4b. If biased:
__________1) Is the estimation procedure biased upwards of downwards?
__________2) What is the magnitude of the bias?
__________3) What is the variance of the estimated fractions?

`
5. As the sample size increases:
_______5a. What happens to the magnitude of the bias?
_______5b. What happens to the variance of the estimated fractions?