Question: A 2004 study published in the BMJ attracted quite a bit of worldwide media interest. The objective of the study was to determine whether dogs can be trained to identify people with bladder cancer on the basis of urine odor more successfully than would be expected by chance alone. Six dogs of varying breeds and ages completed a seven month period of training. The training objective was to enable the dogs to discriminate between urine from patients with bladder cancer and urine from control patients without bladder cancer. The dogs were taught to indicate which among several urine samples was from a bladder cancer patient by lying beside the sample.

In the experiment each of six dogs was tested in nine trials. In each trial, one urine sample from a bladder cancer patient was randomly placed among six control samples. In the total of 54 trials with the six dogs, the dogs made the correct selection 22 times. Does this study support the conclusion that dogs can be trained to distinguish patients with bladder cancer on the basis of urine odor more successfully than would be expected by chance alone?

(a) State the null hypothesis and the alternative hypothesis.

(b) What statistical test procedure can be used to test the null hypothesis? Specify the test statistic and its distribution under the null hypothesis.

(c) Implement the test and report your findings.