Chapter 12.2, Problem 12E

Beryllium disease: Beryllium is an extremely lightweight metal that is used in many industries, such as aerospace and electronics- Long-term exposure to beryllium can cause people to become sensitized. Once an individual is sensitized: continued exposure can result in chronic beryllium disease, which involves scarring of the lungs. In a study of the effects of exposure to beryllium, workers were categorized by their duration of exposure (in years) and by their disease status (diseased, sensitized, or normal). The results were as follows:

1. Compute the expected frequencies under the null hypothesis.
2. Compute the value of the chi-square statistic.
3. How many degrees of freedom are there?
4. Test the hypothesis of independence. Using the $\alpha =0.01$ level of significance. What do you conclude?