c
The Mediterranean diet contains little animal fat and lots of olive oil.
Italian researchers compared 1953 patients with colon or rectal cancer with a control group of 4154 patients admitted to the same hospitals for unrelated reasons.
They estimated consumption of various foods from a detailed interview, then divided the patients into three groups according to their consumption of olive oil.
The table presents some of the data.

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

The researchers conjectured that high olive oil consumption would be more common among patients without cancer than among patients with colon cancer or rectal cancer.
What do the data say?

1. State: What is the question we want to answer?
A. Is it possible to reduce colon and rectal cancer by consuming olive oil?
B. Does olive oil have qualities that prevent cancer?
C. Is high amount of oil consumption more common among those without cancer?
D. What are the chances of an individual not to get colon or rectal cancer, if he consumes high amounts of olive oil?

2. Plan: Which of the following techniques should we use to find the answer?
A. Calculate and compare the marginal distribution from the two-way table.
B. Calculate and compare the conditional distribution of the three groups of people for the three levels of olive oil consumption.
C. Calculate and compare the conditional distributions of olive oil consumption for the colon cancer, rectal cancer and control group.
D. Calculate the total number of people that consumed olive oil and then relative to this total, find the proportion of people with colon cancer, rectal cancer and control group.

3. Solve: Calculate your distribution.
Match your answers below:
1. 34.3%
2. 68.3%
3. 20.7%
4. 32.9%
5. 18.3%
6. 32.4%
7. 35.1%
8. 33.9%
9. 12%
10. 32.6%
11. 19.7%
12. 20.1%
13. 32.5%
14. 11.6%
15. 33.1%

A. Colon cancer / Low
B. Rectal cancer / Low
C. Control / Low
D. Colon cancer / Medium
E. Rectal cancer / Medium
F. Control / Medium
G. Colon cancer / High
H. Rectal cancer / High
I. Control / High

4. Conclude: What is your conclusion based on your analysis?
True or False:
"High olive oil consumption is more common among those without cancer than among those with colon rectal cancer."