//  File MIT-Lab-18-05-00-02.txt.  Edition 1/21/2013.


//  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 an estimation procedure that is unbiased and then
 illustrate and estimation procedure that is biased but consistent.
_
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 note that the Non-Ran
 Samp checkbox is now checked.

` .5 16 0 1 0
2. As before 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. The sample size has been 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. The sample size has been increased again 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, what happens to the
5a. magnitude of the bias?
5b. variance of the estimated fractions?
_
6. Is the nonrandom estimation procedure consistent?