1. In a study of children with osteosarcoma (a type of bone cancer), the patients' tumors were checked for the presence of the HER2 receptor, and those that had HER2+ tumors had the drug trastuzumab added to their chemotherapy regimens. There were concerns that this extra drug might make the therapy less tolerable and therefore fewer patients would successfully complete protocol therapy. The data from the trial are below.

		Completed protocol therapy
		Yes	No	Total
HER2 status	Positive	27	12	39
Negative	22	29	51
	Total	49	41	90

a)Write your hypotheses, perform an appropriate statistical test, and write your conclusion.

b)What is the observed odds ratio?

c) Take this result as a pilot study and calculate the sample size needed to have a 90% chance of detecting a similar difference at a two-sided = 0.05, assuming you can enroll equal numbers of children with HER2 positive and negative tumors.

2. A group of 180 students were interviewed to see how many follow a prudent diet. They were then given a 90-day series of in-depth lectures, including clinical evaluations on nutrition and its association with heart disease and cancer. One year later, the students were re-interviewed and assessed for the type of diet they followed, yielding the following data:

		Diet at follow-up prudent
		Yes	No	Total
Initial diet prudent	Yes	21	17	38
No	37	105	142
	Total	58	122	180

a) Explain why McNemar's test is appropriate here.

b) Define the population parameters of interest and state the null and alternative hypotheses in terms of these parameters.

c) Perform the test and write out your conclusion.