//  File New-Lec1-03-03-00-02.txt. Edition 12/29/2012.


//  Lab Specs
//    Title
        Opinion_Poll_Simulation
//    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  .450
//    List of To Bounds - Decimals
        0.000  1.000  .025  .550
//    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 25 0 0 -1
Objective: Show that the reliability of Clint's unbiased estimation procedure
 depends on the variance of the estimated fraction's, EstFrac's, probability
 distribution.
_
Note that .5 has been selected as the actual population fraction. Once again, the election
 is a toss up: half the population supports Clint and half does not. 

`
Focus on the From and To lists in the lower left hand corner of the screen.
 When you specify a From and To value, the simulation calculates the
 percent of repetitions in which the numerical value of the estimated
 fraction falls between the From and To values.
_
By default, .450 is selected in the From list and .550 in the To list. 
 The simulation will now calculate the percent of repetitions in which the numerical value
 of the estimated fraction falls between .450 and .550.
 
` .5 25 0 0 -1
1. We begin with a sample size of 25. 
_
1a. Using the appropriate equations, calculate the mean and variance of EstFrac's
 probability distribution. Is the estimation procedure unbiased? Explain.
_
1b. Be certain that the Pause checkbox is cleared. Click Start and then, after many,
 many repetitions, click Stop. What are the mean and variance of the numerical values
 of the estimated fractions?
`
1c. How do the mean and variance of EstFrac's probability distribution
 compare to the mean and variance of the numerical values after many,
 many repetitions? 
_
1d. What percent of the repetitions fell between .450 and .550; that is,
 what percent of the repetitions fell within .05 of the actual population fraction,
 .50?


` .5 100 0 0 1
2. Next, note that the sample size has been changed to 100.
_
2a. Using the appropriate equations, calculate the mean and variance EstFrac's
 probability distribution. Is the estimation procedure unbiased? Explain.
_
2b. Be certain that the Pause checkbox is cleared. Click Start and then, after many,
 many repetitions, click Stop. What are the mean and variance of the numerical values
 of the estimated fractions?
`
2c. How do the mean and variance of EstFrac's probability distribution
 compare to the mean and variance of the numerical values after many,
 many repetitions? 
_
2d. What percent of the repetitions fell between .450 and .550; that is,
 what percent of the repetitions fell within .05 of the actual population fraction,
 .50?


` .5 400 0 0 1
3. Now, the sample size is set to 400.
_
3a. Using the appropriate equations, calculate the mean and variance EstFrac's
 probability distribution. Is the estimation procedure unbiased? Explain.
_
3b. Be certain that the Pause checkbox is cleared. Click Start and then, after many,
 many repetitions, click Stop. What are the mean and variance of the numerical values of the
 estimated fractions?
`
3c. How do the mean and variance of EstFrac's probability distribution
 compare to the mean and variance of the numerical values after many,
 many repetitions? 
_
3d. What percent of the repetitions fell between .450 and .550; that is,
 what percent of the repetitions fell within .05 of the actual population fraction,
 .50?

`
4a. What happens to the variance of the numerical 
 values of the stimated fractions as the sample size increases?
_
4b. What happens to the percent of repetitions that fall close to the actual
 population fraction as the sample size increases and the variance decreases?
_
4c. That is, what happens to the reliability of an estimate as the sample size 
 increases and the variance decreases? Explain this intuitively.