Final answer:
The chi-square analysis can help determine if observations differ from expectations and if a given hypothesis is correct. It is used to assess data sets, populations, events, and variability. The chi-square test can be used to determine if data fits a particular distribution, if two factors are independent, and if two data sets come from the same distribution.
Step-by-step explanation:
The chi-square analysis can help us to decide whether our observations of an event differ from our expectations. It is used to assess whether a data set fits a specific distribution, whether the distributions of two populations are the same, whether two events might be independent, and whether there is a different variability than expected within a population.
For example, the goodness-of-fit test uses the chi-square distribution to determine if data fits a particular distribution. The test of independence compares observed values to expected values to determine whether two factors are independent. The test for homogeneity compares observed values against expected values to determine whether two data sets come from the same distribution.