//  File MIT-Lab-02-03-00-02.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  -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 -1 0 0
Three Objectives:
_
First, show that the fraction of those supporting Clint in a single poll
 typically does not equal the fraction of the actual
 population that supports Clint. That is, the estimated population fraction,
 EstFrac, typically does not equal the actual population fraction, ActFrac.
`
Second, show that the estimated fraction, EstFrac, is a random variable.
 Even if we knew the actual population fraction, we are not able to
 predict the estimated fraction before a poll is conducted.
_
Third, recall that 12 of the 16 students Clint polled supported him. We shall
 show it possible that 12 or even more of the students sampled in one
 poll could support Clint even though the election is actually a toss up.


` .5 16 -1 0 0
The list in the upper left hand corner indicates the actual population fraction, the
 actual fraction of the population supporting Clint. For purposes of
 illustrate, we assume that the actual population fraction, ActFrac, equals .5.
 That is, we assume that the election is a toss up: half the
 population supports Clint and half does not. 
_
The list to the right indicates the sample size, the number of individuals polled.
 By default, the sample size is specifed as 16, the same as Clint's poll.


`
1. To conduct one poll, click the Start button. The simulation reports now
 reports the number of individuals polled who support Clint. How many of
 the 16 individuals polled support Clint?
_
2. To conduct a second poll, click the Continue button. How many of the 16
 individuals support Clint in the second poll?


`
3. Click the Continue button several more times, each time noting the number
 of individuals who support Clint. Even though the actual population fraction,
 ActFrac, equals .5, do half of the individuals sampled in a single poll
 typically support Clint? 
_
4. Even though we know that the actual fraction, ActFrac, equals one half, is it possible
 to predict the value of the estimated fraction, EstFrac, before a poll is
 conducted. That is, is the estimated fraction, EstFrac, a random variable? 
 Explain why or why not.

` .5 16 0 0 0
5. Note that the Pause checkbox is cleared. The simulation will no longer
 stop after each poll. Click Continue and then after many, many repetitions,
 click Stop. Is it possible that 12 or more of the individuals sampled in one
 poll of 16 could support Clint even though the election is actually a toss up
 (even though the actual population fraction, ActFrac, is one half).