Education Technology

Special Cases of Normally Distributed Data

Activity Overview

Students perform single and two-sample t procedures to investigate special cases of normally distributed data. They explore inference for a least-square regression line, including the confidence interval.

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 163 - 181 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:
    Single-Sample t Procedure:

  • Create lists and enter functions to plot a normal distribution, and t distributions
  • Note that the peak of the Normal distribution is highest, and the tails of the t distribution are larger than the normal distribution
  • Enter sample data and analyze its distribution
  • Graph a normal probability plot and examine the linearity of the points
  • Decide on the type of distribution
  • Calculate the t value, Confidence Interval, and the Margin of Error
  • Find the p-value and evaluate the hypothesis

  • Two-Sample t Procedures:
  • Enter two sets of data as a list, the size of one sample 1 being less than the other
  • Find the 90% confidence interval for the difference in the means of the data sets
  • Observe that pooled and nonpooled results are similar because their degrees of freedom are close
  • Note that if degrees of freedom are not close, the nonpooled result should be considered
  • Determine the p-value and evaluate the hypothesis

  • Inference for Least-Square Regression Line:
  • Enter the weight of the car and its mileage per gallon data as lists and check for a linear relationship between them
  • Perform a Linear Regression T Test
  • Test the hypothesis by determining the p-value and determine the regression equation
  • Check the validity of the t-test by setting up a normal probability plot of residuals
  • Find the 90% confidence interval for the slope of the regression line
  • Estimate the mean for normal data and transformed data
  • Check residuals for transformed data
  • After the Activity

    Review student results:

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