Can dogs provide an easy noninvasive way to detect cancer? Several methods have been used to test this. In a recent study,50 five dogs were trained over a three week period to smell cancer in breath samples. To collect the data, cancer patients who had just been diagnosed and had not yet started treatment were asked to breathe into a tube. Breath samples were also collected from healthy control adults. Dogs were trained to sit if a breath sample came from a cancer patient. After training, the dogs were presented with breath samples from new subjects, with the samples randomly presented in a double-blind environment. The study was done for patients who were in different stages of cancer and for lung and breast cancer patients. The results for all groups were similar. The data for early-stage breast cancer are presented inTable B.1.

(a) Discuss the data collection for this study. Why is it important that the samples are from new subjects whose samples the dogs have not encountered before? That they are randomly presented? That the study is double-blind? That patients have not yet started treatment? Do you think this experiment was well designed?
(b) In the study for lung cancer, the experimenters had to account for the effect of smoking. Why?

(c) The question of interest is whether dogs are more likely to sit if the subject has cancer than if the subject does not have cancer. State the null and alternative hypotheses and give the relevant sample statistics.
(d) Without doing any computations, just looking at the data, do you expect the p-value to be relatively large or relatively small? Why? How strong is the evidence? (Sometimes, in extreme cases such as this one, we see results so obvious that a formal test may not be necessary. Unless results are exceptionally obvious, however, you should confirm your intuition with statistical inference.)

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Control Cancer Dog doesn't sit Dog sits 99 3 45