Chi-Square Goodness-of-Fit Test

In Chapter 8 we worked with the Pipeline Safety data table to learn about estimating a population proportion. In that chapter, we looked at the IGNITE column—a dichotomous variable indicating whether natural gas ignited in connection with a reported disruption. At this point, let's consider a different variable in the data table that indicates the type of disruption. The LRTYPE_TEXT column shows four different values: LEAK, RUPTURE, OTHER, and N/A (not available) corresponding to the reported type of disruption involved in the pipeline incident. Suppose we naively wondered whether all disruption types are equally likely to occur.

Here's how we'll approach the question. First we'll specify a hypothesis reflecting our question and express the hypothesis as a model describing the causes. There are four categories, and we're provisionally asserting that all four categories happen with equal probability in the United States. In short, our hypothesis becomes this: