Problem 10E

The article “High Cumulative Risk of Lung Cancer Death among Smokers and Nonsmokers” (P. Brennan, et al. American Journal of Epidemiology, 2006:1233– 1241) states that the probability is 0.24 that a man who is a heavy smoker will contract lung cancer. True or false:

a. In a sample of 100 men who are heavy smokers, exactly 24 of them will contract lung cancer.

b. In a sample of 100 men who are heavy smokers, the number who will contract lung cancer is likely to be close to 24, but not exactly equal to 24.

c. As more and more heavy-smoking men are sampled, the proportion who contract lung cancer will approach 0.24.

Answer:

Step 1 of 3:

(a)

In this question, we are asked to find whether the statement is true or false.

Statement: In a sample of men who are heavy smokers, exactly of them will contract lung cancer.

The probability is that a man who is a heavy smoker will contract lung cancer.

From the definition of probability,

We know that probability of an event is the proportion of time that the event would occur in long run, if the experiment were to be repeated over and over again.

Hence probability can not be exact since event sample space is small.

Hence statement is false.

(b)

Statement: In a sample of men who are heavy smokers, the number who will contract lung cancer is likely to be close to , but not exactly equal to .

Because of small sample space, we can conclude that the number is likely to be close to .

Hence statement is true.

(c)

Statement: as more and more heavy smoking men are sample, the proportion who contract lung cancer will approach .

Since the sample space is large, then the proportion who contract lung cancer will approach .

Hence statement is true.