Statistics
Activity:
Candy Pieces
Posted on May 19, 2008
Topic: Hypothesis Testing
This activity introduces the statistics concept of hypothesis testing. Students will use a chi-square test for goodness-of-fit to determine if there is a significant difference between the proportions they find in the sample, and the proportions they would expect if the manufacturer produced equal proportions of each color.
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Activity Key Steps:
In this activity, students are introduced to chi-square. They use a scenario about a popular brand of candy pieces. This candy comes in five colors.
The scenario goes on to say that the candy might likely be made from a manufacturing process that was designed to produce equal proportions of each color; they use the chi-square test for goodness-of-fit.
Students use Spreadsheets & Lists to help them calculate test for goodness-of-fit. They enter the number of pieces of each color. Students use the 
formula to compute a relative size of each piece of candy and enter in Column D. Column E gives the sum of the of all the values found in Column D and gives students a value for chi-square.
Students now find whether the chi-square found is large or small. They will see that they do so by comparing the observed chi-square to the theoretical distribution of the probabilities.
At the end of this activity, students will be able to apply what they have learned to other scenarios and other real-world applications. They will also be able to use a X²goodness-of-fit test to test the hypothesis that an observed frequency distribution fits an expected frequency distribution.