Education Technology

# Activities

• ##### Subject Area

• Math: Statistics: Inferential Statistics

9-12

60 Minutes

• ##### Device
• TI-89 / TI-89 Titanium

TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
This is Activity 9 from the EXPLORATIONS Book:
Advanced Placement Statistics with the TI-89

## Sampling Distributions

#### 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.

• 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