11.1 Hypothesis Testing
•
In hypothesis testing, there is a preconceived idea about the value of the
population parameter.
For example, the dean of a business school claims
that the average weekly salary of his graduates is $800.
Based on the
evidence we saw, we suspect that the actual mean is lower than that.
•
Thus, there are two theories or hypotheses involved in a statistical study:
The first is what we assume to be true until we prove otherwise, called
the null hypothesis
, μ = 800, denoted
H
0
.
•
The second is the research or alternative
hypothesis
, μ < 800, denoted
H
a
.
•
The alternative hypothesis is what we are trying to prove is true.
•
Next, we present our evidence.
This is called the test statistic
.
This is
our ‘evidence’ to see if we can back up our alternative hypothesis.
That
is what the sample statistic does.
•
Then we set up a rejection region
.
The rejection region helps us make
our final decision, so that everyone comes to the same decision.
•
The final decision is our conclusion
.
In hypothesis testing, there are
only two possible conclusions we can make:
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We can reject the null hypothesis in favor of the alternative
hypothesis.
This is equivalent to the jury coming to the conclusion that
the defendant is guilty.
Or,
we can fail to reject the null hypothesis.
This means we don’t
have enough evidence to reject the null hypothesis and we don’t have
enough evidence to accept the alternative hypothesis.
The jury did not
have enough evidence to convict.
We
never
accept the null hypothesis!
That would be the equivalent to the prosecutor saying the defendant is
innocent.
If the prosecutor thought the defendant was innocent, he
wouldn’t be prosecuting him!
He just didn’t have enough evidence to
prove the guy was guilty.
•
There are two possible errors that can be made here:
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 Spring '08
 CathyDavis
 Statistics, Null hypothesis, Statistical hypothesis testing, Type I and type II errors, prosecutor

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