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. Let’s review some vocabulary

In Inferential Statistics we use the value of a sample statistic to estimate a parameter value.   POPULATION: ALL Montgomery College students and estimate their mean height

We want to estimate the mean height of MC students. Will x-bar be equal to mu? What if we had selected another sample? What is the variability of the x-bars about the mean mu? 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? WHY WORRIED ABOUT PROBABILITIES? In inferential statistics we test claims about population means by using probabilities

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 Meaning of FAIR –SHAPE, MEAN, ST.DEV = 1.7 Think now on the possible x-bars if n = 2, if n = 10

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)

The Central Limit Theorem in action 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