.
This is the case where nothing has changed. In the example above
means the drug does nothing.7.6 Hypothesis Testing
Ex 1 It is known that the recovery rate from a certain disease is 33%. A newly-developed drug is claimed to improve the recovery rate based on 15 people recovering in a sample of 40 patients.
We can test this claim by going through a procedure called Hypothesis Testing. The Test is designed to help us determine whether or not the events could have occurred through random chance.
An analogy would be a jury: The defendant is assumed innocent until that assumption is no longer believable.
The procedure involves several steps:
1)
State the null hypothesis, represented by
.
This is the case where nothing has changed. In the example above
means the drug does nothing.
2)
State the alternative hypothesis, represented by
.
This is the case being presented by the question. In the example
above
means the drug helps patients recover faster.
3)
State the significance level, denoted by
.
This is almost always given by the question. For the given example
above, let's say that the significance level is 0.01. This means we
allow ourselves to be wrong 1% of the time. The compliment of the
significance level is called the confidence level-we expect to be
right 99% of the time. Typical significance levels are 1%, 5%, 10%.
4) Conduct an experiment. Okay, not really. The question tells you about an experiment that was conducted.
5)
Assume
is
true. Calculate the probability of
occurring.
6)
Compare the results from Step 5 to the significance level in Step
3.Accept
if P(H1)>,
otherwise accept
.
If the probability of
occurring randomly is very small then it must have an impact.
7) State you conclusion based on Step 6.
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