You are performing a cohort study to look at risk factors for breast cancer in postmenopausal women. If the probability of developing breast cancer among smokers is .05 for the study duration, then if you sample 100 smokers, how many do you expect to develop the disease? Give the expected value +/- 1 standard deviation.

Question

You are performing a cohort study to look at risk factors for breast cancer in postmenopausal women. If the probability of developing breast cancer among smokers is .05 for the study duration, then if you sample 100 smokers, how many do you expect to develop the disease? Give the expected value +/- 1 standard deviation.

5±60
10±6
5±2
10±5
5±6

Answer 1

To determine the expected value and the standard deviation, we need to use the formula for the expected number of events in a given sample:

Expected Value = Sample Size * Probability

In this case, the sample size is 100 smokers, and the probability of developing breast cancer among smokers is 0.05. Let's calculate the expected value:

Expected Value = 100 * 0.05
Expected Value = 5

So, you would expect 5 out of the 100 smokers to develop breast cancer over the study duration.

To calculate the standard deviation, we use the following formula:

Standard Deviation = sqrt(Sample Size * Probability * (1 - Probability))

Standard Deviation = sqrt(100 * 0.05 * (1 - 0.05))
Standard Deviation = sqrt(100 * 0.05 * 0.95)
Standard Deviation = sqrt(4.75)
Standard Deviation = 2.18 (rounded to 2 decimal places)

The standard deviation represents the spread of values around the expected value.

Therefore, the expected value +/- 1 standard deviation would be:

5 +/- 2

So, the answer is 5 +/- 2.