Cancer of the colon and rectum is less common in the Mediterranian region than in other western countries. The Mediterrainian diet contains little animal fat and lots of olive oil. Italian researchers compared 1953 patients with colon or rectal cancer with a control gropup of 4154 patients admitted to the same hospitals for unrealted reasons. They estimared consumption of various foods from a details interview, then divided the patients into three groups according to their consumption of olive oil.

a) Is this an observational or experimental study. Justify answer.
b) Write down an Null and alternate hypothesis for analysing this data set.
c) Results:

Olive Oil
Low Medium High Total
Colon cancer 398 397 430 1225
Rectal cancer 250 241 237 728
Controls 1368 1377 1409 4154

Give an example calculation of one of the 6 cells in the table of the expected frequency under the null hypothesis. Explain how the null hypothesis is the basis of this calculation.
d) determine the value of the relevent test statistic and the corresponding p-value.
e) what is the result of your analysis? write an appropriate conclusion
f) what assumptions about the data have you made? Are these assumptions justified in this case?