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If 120 similar people were observed over 10 years, how many deaths from heart attacks would you expect?
There are several different ways to approach this question. Two methods are shown below.
Method 1 is a long method but it can help you to think through one step at a time, and you can apply this same method to more complex examples when Method 2 or alternative methods may become too difficult to think through. Given the relatively nice numbers used in this example, many students prefer Method 2 here.
Important principle: if the numbers involved are horrible, investigate what the strategy would be with very simple numbers, and exactly the same method will work for the horrible numbers.
Method 1
First make people the unit.
How many deaths from heart attacks would you expect if 1 person was observed over 5 years?
We expect less people to die from heart attacks if just 1 person is observed instead of 40 people so we need to divide the number of heart attacks by 40:
EMBED Equation.3
So we expect 0.05 death from heart attacks if 1 person is observed over 5 years.
(Note: Do not worry about the numbers being less than 1 death at this stage in the method since we will multiply up later on).
Next make years observed the unit.
How many deaths from heart attacks would you expect if observing 1 person over 1 year?
We expect less people to die from heart attacks if only observing over 1 year rather than 5 years so we need to divide the number of heart attacks by 5:
EMBED Equation.3
So we expect 0.01 death from heart attacks if 1 person is observed over 1 year.
Alternatively, you might prefer to first make years observed the unit and then make people the unit.
If 120 similar people were observed over 10 years, how many deaths from heart attacks would you expect?
Keeping people the unit, how many deaths from heart attacks would you expect if 1 person was observed over 10 years?
We expect more people to die from heart attacks if they are observed over 10 years rather than 1 year so we need to multiply the number of heart attacks by 10:
EMBED Equation.3
So we expect 0.1 death from heart attacks if 1 person is observed over 10 years.
Finally, we want to know how many deaths from heart attacks would be expected if 120 people were observed over 10 years.
We expect more people to die from heart attacks if 120 people are observed rather than observing only 1 person so we need to multiply the number of heart attacks by 120:
EMBED Equation.3
So we expect 12 deaths from heart attacks if 120 people are observed over 10 years.
Method 2
In 5 years, 2 out of 40 people die from heart attacks.
The question asks us what we expect after 10 years, which is a doubling of the observation timeframe, so we would expect twice as many people to die from heart attacks:
EMBED Equation.3
In 10 years, 4 out of 40 people die from heart attacks.
A group of 120 people is 3 times as many as 40, so 3 times as many people are likely to die from heart attacks:
EMBED Equation.3
In 10 years, 12 out of 120 people die from heart attacks.
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