Education Technology

# Special Cases of Normally Distributed Data

Math: Statistics: Inferential Statistics
9-12
60 Minutes
TI Connect™
TI-89 / TI-89 Titanium
This is Activity 13 from the EXPLORATIONS Book:
Advanced Placement Statistics with the TI-89

Lessons

# 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.

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