Activity Overview
Students studies the distribution of sample proportions with a simulation. They find small sample size leads to skewed distribution and as the sample size increases, the distribution becomes more normal.
Before the Activity
Install the Statistics with List Editor application on the calculator using one of these two methods:
TI Connect™, a TI Connectivity Cable, and the Unit-to-Unit Link Cable
TI-Navigator™ "send to class" feature
See the attached PDF file for detailed instructions for this activity
Print pages 117 - 128 from the attached PDF file for your class
During the Activity
Distribute the pages to the class.
Follow the Activity procedures:
Enter data for a large sample population with 33% Caucasians
Use the simulation and find the number of Caucasians in a random sample of 10
Observe the number of Caucasians in the sample does not reflect the actual distribution in the population
Repeat the steps for an increased sample size of 50
Compare the two histograms
Observe that as the sample size increases, the distribution is more symmetric and normal
Set up Normal Probability scatter plots and observe that the data points of the second set lie on a straight line
Observe that linearity is an indication of the data being Normally Distributed
Use the normal distribution to approximate a binomial distribution
Take different sample sizes from the population, and use the Central Limit Theorem to show that as sample size increases, the distribution of the means of the samples becomes more Normal
After the Activity
Review student results:
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary