Authentic Learning Task (ALT) #6: Colors in the Bag

Printer-Friendly Version

Overview

This Authentic Learning Task (ALT) introduces an additional distribution that can be used to test hypotheses about population means. Test statistics calculated from sample data can be used to make statements about population means and proportions if they are significant. To be significant, a test statistic of a parameter must be at least a specified distance from the standardized hypothesized value.

In this ALT, you are introduced to hypothesis testing for differences in means when the data is not continuous or interval in nature (non-parametric). You use a chi-square test to determine whether or not observed results compare favorably to the expected values. This ALT builds upon what you have already learned about sample data, distributions, and levels of significance.

After completing this ALT, you should be able to demonstrate the following competency:

• Analyze variability in a process using hypothesis testing
  (Comp. 5).

Materials and Equipment
No materials or equipment are needed for this ALT.

Safety and Disposal
No special safety or disposal procedures are required.

Pre-Activity

In this activity we address the question: Does the bag of M&M’s meet the manufacturers claim on the distribution of colors? This problem question is of the general form: “Is there a significant difference between (among) the sample means?" However this case is different because the data is non-parametric in nature.

Click here to access the Decision Tree to aid in the selection of the proper test.

In this case, you will sample from outgoing bags of materials to determine if the distribution of colors (attribute) meets our expected values. This requires the use of a Chi-Square test

Hypothesis testing - Chi-Squared Contingency Tables
Visit the NIST website and the Participant Journal for detailed examples on how to perform a test.

Self-Assessment

Rework the example for NIST using an Excel Spreadsheet.

Click here for the worked answers to the NIST problem.

Activity

In your team, perform the following steps to complete the activity:

1. Complete Instruction Sheet: Colors in the Bag.

Post-Activity

Your team should now post all of its results from the activity to the Discussion Board.

Assignment
There are no instructions to prepare for ALT #7: Hard Candy.

Assessment
Your facilitator may use Assessment Sheet: Colors in the Bag to evaluate your results from the activity and your posting to the Discussion Board.

Go to next ALT

Probability, Sampling, and Hypothesis Testing Home Page