A Guide to Business Statistics

Chapter 9Hypothesis Tests of Categorical Data

In this chapter, we focus on hypothesis tests when data are categorical. Many survey questions and polls result in data that fall into this category. Each week in the United States, for example, samples of adult Americans are asked whether they approve of the way the current president is handling his responsibilities. This question is used to form the “presidential approval rating” by dividing the number that approve by the total number of respondents. Another example of categorical data is whether or not people who file their taxes get audited. A tax filing service may be very interested in publishing an estimate of the proportion of tax returns that get audited each year. Although categorical variables are not numeric, we can easily convert them into binary data. Recall, with binary data each observation (or response) can be coded as 0 or 1, where 1 is the category of specific interest. In these cases, the statistic of interest is often the proportion which is simply the number of 1s divided by the total number of observations.

There are two goals for this chapter. The first is to learn how to use a single sample of data to test a hypothesis concerning an unknown population proportion. To introduce the process and intuition of conducting a hypothesis test of a proportion, we will use M&M's as an example. The company Mars makes many claims about their original M&M's candies. One is captured by their famous slogan “M&M's melt in ...