Education Technology

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.

    Follow the Activity procedures:
    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