Chapter 12: Inference on Categories of Data
Source: M&M's
Did you know that M&M's® Milk Chocolate Candies are supposed to come in the following percentages: 24% blue, 20% orange, 16% green, 14% yellow, 13% red, 13% brown? (Note: These values are different from those that used to be available on the M&M's website, but have been confirmed by ScientificAmeriken.) Do they really? Could a quality control engineer test that? How far from those expected percentages is acceptable?
These are all questions we're going to answer in Section 12.1, using something called a GoodnessofFit Test.
In Chapter 4, we studied relationships between two variables. We learned that we could quantify the strength of the linear relationship between two quantitative variables with the correlation.
What about qualitative (categorical) variables, though? For example, suppose we consider a survey given to 82 students in a Basic Algebra course at ECC, with the following responses to the statement "I enjoy math."
Strongly Agree 
Agree  Neutral  Disagree  Strongly Disagree 

Men  9  13  5  2  1 
Women  12  18  11  6  5 
How do we study this relationship? Is there a way to tell if gender and whether the student enjoys math are related? In Section 4.4, we discussed construction conditional distributions and analyzing them, but can we be more precise? In fact, there is a way, and we'll study it in Sections 12.2.
If you're ready to begin, just click on the "start" link below, or one of the section links on the left.