Transcript From Simulations to the Central Limit Theorem

Parameter: A number
describing a characteristic of
the population
(usually unknown)
Statistic: A number describing
a characteristic of a sample.
In Inferential Statistics we use
the value of a sample statistic
to estimate a parameter value.
We want to estimate the mean
height of MC students.
What if we get another sample, will x-bar
be the same?
What does the x-bar distribution look like?
How do we investigate the behavior of x-bar?
Graph the x-bar distribution and find its
mean and standard deviation
Simulation
Rolling a fair die
and recording
the outcome
randInt(1,6)
Press MATH
Go to PRB
Select 5: randInt(1,6)
Rolling a die n times and finding the
mean of the outcomes.
Mean(randInt(1,6,10)
Press 2nd STAT
Right to MATH
Select 3:mean
Press MATH
Right to PRB
5:randInt(
Rolling a die n times and finding the mean of the outcomes.
The Central Limit Theorem in action
Simulation
Roll a die 5 times and
record the number of
ONES obtained:
randInt(1,6,5)
Press MATH
Go to PRB
Select 5: randInt(1,6,5)
Roll a die 5 times, record the number of ONES obtained.
Do the process n times and find the mean number of ONES obtained.
The Central Limit Theorem in action
The Central Limit Theorem in action
Use website APPLETS to
simulate proportion
problems