HYPOTHESIS TESTING BACKGROUND
When most people think of inferential statistics, they think of hypothesis testing.
Hypothesis tests are used to
determine whether or not a drug is effective, whether a particular teacher’s students score better on the final than
another, etc.
In science class, you have a hypothesis that you must test to see if you are correct.
The same thing happens
in statistics.
Except, there is 2 hypotheses instead of 1 hypothesis; what we are testing and the opposite (it’s
complement).
By doing so, we are accounting for the possible outcomes.
For example, we are testing to see if a
particular drug lowers your cholesterol level.
One of the hypothesis is cholesterol level is lower and the other
hypothesis is the cholesterol level is the same or higher.
It works or it doesn’t.
These 2 hypotheses have names:
null hypothesis
(denoted
H
o
) and the
alternative hypothesis
(denoted H
a
or
H
1
, as in your text).
The alternative hypothesis is the hypothesis of change.
When we write the hypotheses, we
always write the null at the top and the alternative at the bottom.
Most of the time, the alternative is the thing you are
testing.
We will not study the tests where this is not the case.
The null hypothesis is the opposite of the alternative.
In the cholesterol example, H
1
: lower cholesterol so then H
o
: cholesterol level is the same or higher.
If our drug does
not work, then the cholesterol level would stay the same or get higher: the drug would have a null effect, hence the
name null hypothesis.
Our null hypothesis always has the “equal to” or the “or equal to”
Ex.:
pg 412 # 13 b)
The average income for accountants is $51497.
There is an equality given.
The change would be not equal.
497
,
51
:
&
497
,
51
:
1
0
≠
=
μ
μ
H
H
Ex:
pg 412 #13 c)
The average age for attorneys is greater than 25.4years.
The term is greater, so the change to test is greater.
4
.
25
:
&
4
.
25
:
1
0
>
≤
μ
μ
H
H
Note:
There is a table on pg. 402 to help you figure out if the words given refer to less than, greater
than, etc.
Note:
The null hypothesis always has the “equal to” or the “or equal to”.
Note:
Once we set up the alternative hypothesis, the null hypothesis is everything else.
When we conduct our tests, four things can happen.
1.
The test suggests the null is true and it is.
Fail to reject H
o
given H
o
is really true.
2.
The test suggests the null is true but the alternative is true.
Fail to reject H
o
given H
1
is true.
3.
The test suggests the alternative is true and it is.
Reject H
o
given H
1
is true.
4.
The test suggests the alternative is true but the null is true.
Reject H
o
given H
o
is true.
Two of these decisions are correct decisions and two are incorrect.
In statistics, we have names for these errors or
incorrect decisions.
Type I Error
:
Conclude H
1
is true but H
o
is true.
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 Spring '09
 Statistics, Inferential Statistics, Statistical hypothesis testing, critical value

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