Scientists are working to train dogs to smell cancer, including early stage cancer that might not be detected with other means. In previous studies, dogs have been able to distinguish the smell of bladder cancer, lung cancer, and breast cancer. Now, it appears that a dog in Japan has been trained to smell bowel cancer. Researchers collected breath and stool samples from patients with bowel cancer as well as from healthy people. The dog was given five samples in each test, one from a patient with cancer and four from healthy volunteers. The dog correctly selected the cancer sample in 33 out of 36 breath tests and in 37 out of 38 stool tests.

(a) The cases in this study are the individual tests. What are the variables?

(b) Make a two-way table displaying the results of the study. Include the totals.

(c) What proportion of the breath samples did the dog get correct? What proportion of the stool samples did the dog get correct?

(d) Of all the tests the dog got correct, what proportion were stool tests?