Education Technology

# Activities

• ##### Subject Area

• Math: Statistics: Inferential Statistics

9-12

60 Minutes

• ##### Device
• TI-83
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition

TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
This is Activity 9 from the EXPLORATIONS Book:
Statistics Handbook for the TI-83

## Testing Goodness-of-Fit and Two-Way Table Chi-Square

#### Activity Overview

Students perform chi-square tests to see if data follows a hypothesized distribution. They also study the two-way table analysis.

#### Before the Activity

• See the attached PDF file for detailed instructions for this activity
• Print pages 101 - 105 from the attached PDF file for your class
• #### During the Activity

Distribute the pages to the class.

Follow the Activity procedures:

Chi-Square Test:

• Generate 100 random values between numbers 0 and 10
• Enter the expected and observed values of each class as lists
• Calculate the degrees of freedom
• Perform a chi-square test and determine the p-value
• Evaluate the hypothesis based on the p-value

• Simulate a binomial experiment using the randBin program
• Plot the observed frequencies
• Enter as lists number of successes, observed frequency of each number of successes, and the theoretical probabilities
• Calculate the chi-square statistic after condensing
• Calculate the p value and determine if they match the hypothesis of expected binomial distribution

• Two Way Table Chi-Square Test:
• Obtain a random sample of grades of students taking a test to test the hypothesis that the grade on the exam is independent of the sex of the test-taker
• Store the data in a matrix
• Perform a chi-square test and determine the p-value
• Evaluate the hypothesis
• #### After the Activity

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary