Here's an example of how chi square can be used. Consider a security manager at a local Nordstrom's store. S/he takes over the job and finds that 25% of losses are due to shoplifting, 25% due to breakage/loss, and 50% due to employee theft. But nationally the percentages are different, they are 35% of losses are due to shoplifting, 35% due to breakage/loss, and 30% due to employee theft. The question is, is it just sampling error that accounts for the difference, or is the local store different than the national numbers? This is a typical chi-square problem. The categories are mutually exclusive (don't overlap) and mutually exhaustive (cover all categories).