Special Cases of Normally Distributed Data

Author

Texas Instruments

Alignment

Standards Alignment

Textbook Alignment

Subject Area

Math: Statistics: Inferential Statistics

Level

9-12

Activity Time

60 Minutes

Software

TI Connect™

TI Calculator

TI-89 / TI-89 Titanium

Applications

Statistics with List Editor for TI-89

Other Materials

This is Activity 13 from the EXPLORATIONS Book:
Advanced Placement Statistics with the TI-89

Resource Types

Lessons

Report an Issue

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

Download Files

Download All Files (ZIP)

Before the Activity Files

Teacher Notes Appendix A PDF Teacher Notes Appendix B PDF Teacher Notes PDF

Author

Texas Instruments

Alignment

Standards Alignment

Textbook Alignment

Subject Area

Math: Statistics: Inferential Statistics

Level

9-12

Activity Time

60 Minutes

Software

TI Connect™

TI Calculator

TI-89 / TI-89 Titanium

Applications

Statistics with List Editor for TI-89

Other Materials

This is Activity 13 from the EXPLORATIONS Book:
Advanced Placement Statistics with the TI-89

Resource Types

Lessons

Report an Issue

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Special Cases of Normally Distributed Data

Statistics with List Editor for TI-89

Special Cases of Normally Distributed Data

Before the Activity Files

Statistics with List Editor for TI-89

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