Test for single proportion.

A study published in the British Medical Journal described how dogs were used in an attempt to identify patients having bladder cancer.  A trial involved six different samples of urine from healthy people plus another sample of urine from a person known to have bladder cancer.  The trail was repeated 54 times with 22 right identifications and 32 wrong identification.

a. Given that each trial involved six healthy samples and one sample from a patient with bladder cancer, what is the possibility that a dog would select the cancer sample if it made a random guess?

b. Among 54 trails, there were 22 correct identifications.  Test hypothesis that the dogs did significantly better than what would be expected with random guessing.  Does it appear that the dogs were guessing?  Does it appear that the dogs were guessing, or do they appear to have some ability to identify the cancer sample?

c. assume that the dogs did better than what would be expected with random guessing, did they do well enough to be used for actual medical diagnoses? Why or why not?