Question

A study of high blood pressure and smoking found the following: Smoker Nonsmoker Normal blood pressure 360 1000 High blood pressure 240 200 Are high blood pressure and smoking independent?

Answer 1

	Smoker	Non-Smoker	Total
Normal Blood Pressure	360	1000	1360
High Blood Pressure	240	200	440
Total	600	1200	1800

For two events to be independent P(AB) = P(A) * P(B)

Here A is High Blood Pressure

B is Smoker

P(AB) = 240 / 1800 = 0.13333

P(A) = 440 /1800

P(B) = 600 / 1800

P(A) * P(B) = (600 * 440) / (1800 * 1800)

= 0.08148

P(AB) is not equal to P(A) * P(B)

Hence A and B are not independent

Since there is a confusion on which set of values refers to which event, I would also test the other scenario out

	Normal Blood Pressure	High Blood Pressure	Total
Smoker	360	1000	1360
Non-Smoker	240	200	440
Total	600	1200	1800

For two events to be independent P(AB) = P(A) * P(B)

Here A is High Blood Pressure

B is Smoker

P(AB) = 1000 / 1800 = 0.5556

P(A) = 1200 /1800

P(B) = 1360 / 1800

P(A) * P(B) = (1200 * 1360) / (1800 * 1800)

= 0.503704

P(AB) is not equal to P(A) * P(B)

Hence A and B are not independent