In this question, you will construct a randomisation distribution using the data in the following table.

These data are based on a study in which dogs were trained to smell cancer in breath and stool samples. To train the dogs, cancer patients who had just been diagnosed and healthy control adults were asked to breathe into a tube and provide a stool sample. Dogs were then trained to sit if a sample came from a cancer patient. After training, the dogs were presented with samples from new subjects, with the samples randomly presented in a double-blind experiment.

Breath test Stool test

Dog identifies cancer 23 37

Dog does not identify caner 13 11

total 36 48

Is a breath sample inferior for cancer identification compared to a stool sample?

Determine at a 5% significance level (= 0.05).

1. (i)What are the null and alternative hypotheses for the research questionhighlightedabove?
2. (ii)Whatarethesampleproportionsofcorrectcanceridentificationforthetwomethodsand what is the sample statistic? Include appropriate notation in your answer.
3. (iii)What is the main assumption we make when creating a randomisation distribution?
4. (iv)Use StatKey to generate a randomisation distribution of10,000differences in sample proportions. Please include your randomisation distribution in your assignment solutions.
5. (v)Describetheshapeandcentreofyourrandomisationdistributioninoneortwosentences.
6. (vi)Use your randomisation distribution to calculate a p-value for the test.
7. (vii)Use your p-value to make a decision and conclusion for your hypothesesin context.