# Activities

• • • ##### Subject Area

• Math: Statistics: Inferential Statistics

• ##### Author 9-12

60 Minutes

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

TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
This is Activity 12 from the EXPLORATIONS Book:
Advanced Placement Statistics with the TI-89

## Tests of Significance

#### Activity Overview

Students understand how tests of significance can be performed with confidence intervals. They use a simulation to clarify the meaning of a hypothesis. Students examine large sample tests for a proportion, mean, difference between two proportions, and difference between two means. They also study tests for fit, homogeneity of proportions, and independence.

#### 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 149 - 161 from the attached PDF file for your class
• #### During the Activity

Distribute the pages to the class.

Large Sample Test for a Proportion:

• Identify the null and the alternate hypothesis
• Use a normal distribution to approximate the binomial
• Determine the p-value and the z-value
• Use the p-value to accept or reject the hypothesis
• Use the formula to calculate the z value, and verify if it corresponds to the p-value
• Test the hypothesis with an appropriate confidence interval such that the null hypothesis value is within the interval
• Test the hypothesis using a two-tailed test
• Simulate appropriate confidence intervals of certain size to clarify the meaning of Test of Significance

• Large Sample Test for a Mean:
• If the sample means are normally distributed use the z-test to evaluate the hypothesis
• Determine the p- and z-values
• Based on the p-value, accept or reject the hypothesis

• Perform Large Sample Tests for difference between two proportions and difference between two means

• Chi-Square Tests:
• Make a frequency table for a series of trials
• Enter the data as a list
• Create a list for the proportion of the number of successes
• Perform a Chi-square test using the calculator
• Determine the p-value and check the reasonableness for a binomial distribution
• Perform a Chi-square test for a two-way table
• #### After the Activity

Review student results:

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