Question

3) In 2011, an article published by the medical journal Gut-An International Journal of Gastroenterology and Hepatology (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 eight-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 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 different colorectal cancer patient; the others contained breath from noncancer patients. The dog was then trained to sit next to the bag which she thought contained breath from al 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 experimental procedure, with a different set of five patients each time: four noncancer patients and one cancer patient. And, each time, whether or not she correctly identified the bag with the breath of the cancer patient was recorded. (a) Why is it important to use new patients each time? [Hint: How does this help us meet the binomial model?] (b) Identify the observational units and variable of interest. Indicate which outcome you will consider "success." (c) Define the parameter of interest (in context). (d) Using symbols, state appropriate null and alternative hypotheses for deciding whether Marine is able to identify the correct bag more than we would expect by chance alone. (e) How many of the 33 attempts would Marine need to get correct in order for the p-value for the test in (d) to be less than 0.05? Explain how you arrive at your answer

Answer 1

a) Here we have a bernaulu random variable with having variable of interest is " Probability that Labrador Marine successfully identify the correct air bag means air bag by cancer patient. Therefore by repeating experiment 33 times bernouli random variable follows Binomial Distribution.

x- successfully identified the bag by cancer patient.

It is important to use new patient every time because to test patient at every stage or patient with every type. Also we have to test that Marine could identify patient with different bio-diversity.

b)

Observational Unit : Observe the successfully Marine identify the cancer bag in 33 trials.

c) Here parameter of interest is how many timy times dicission made by Marine is correct.

d) Here H₀: Marine is unable to find correct bag. (p=0)

H₁: Marine successfuly identify correct bag. (p!=0)

Here you can use value of "p" of your interest.

Therefore by using below formulae you can calculate "n"

Thus, the p-value is given by

• for right tail event,
• for left tail event,
• for double tail event.