Question

Use the following information to answer questions 25-34 We all know that dogs have an amazing sense of smell. They are used to help hunters find their prey, determine the location of missing people, and screen luggage for drugs. But can a dog's keen sense of smell also be used to determine whether a patient has cancer? This is a question that has been asked recently and studies have been conducted to try to answer it. In 2011, an article published by the medical journal Gut - An International Journal of Gastroenterology and Hepatolgy (Sonoda, et al.) reported the results of a study conducted in Japan in which a dog was tested to see whether she could detect colorectal cancer. The dog used was an 8-year-old black Labrador named Marine. (As her name might suggest, she was originally trained for water rescues.) The study was designed so that the dog first smelled from a bag that had been breathed into by a patient with colorectal cancer. This was the standard that the dog would use to judge the other bags. Marine then smelled the breath in five different bags from five different patients, only one of which contained breath from a colorectal cancer patient (not the same as the original patient); the others contained breath from non-cancer patients. The dog was then trained to sit next to the bag which she thought contained breath from a cancer patient (i.e., had the cancer "scent"). If she sat down next to the correct bag, she was rewarded with a tennis ball. Marine completed 33 attempts of this procedure, with a different set of four non-cancer patients and one cancer patient each time. The ch she sniffed the bags was randomly determined each time. It turned out that in 30 of the 33 attempts Marine correctly identified the bag containing the breath from the cancer patient. Is this evidence that Marine is doing better than just guessing? 25. (5 points) State the null and alternative hypothesis 26. (5 points) Identify the observational units 27. (5 points) Identify the variable(s)
Use the paragraph to answer 25-34 (all parts of one question)

Answer 1

25. Ho : Marine is able to indentify patients with cancer

H1 : Marine is not able to identify patients with cancer or is just guessing

26. Here, for a sample of 33 units, she was correct 30 times. Here we can compute the probability of identifying a cancer patient correctly , p = 30/33 = 0.91 and in ideal scenario we can assume population P = 1.

27. The variable is p = 0.91 and q = 0.09 , n = 33 which will follow bernaulli dist with mean p and variance pq/n.

28. The statistic will be $z = \frac{p-P}{\sqrt{PQ/n}}$ = -1.8065 and can be compared with critical value or p-value with level of significance.