1
Hypothesis Tests
Steps for a formal test of hypothesis:
1. State the null hypothesis
0
H
: (assume this until step 5)
and the alternate hypothesis
a
H
: (want to show this, hopefully, in step 6)
2. State the level of significance
α
(comfort level of what you would call a rare event) usually 1% or 5%
3. Give results from a sample.
Generally, this is
n
and
p
ˆ
for proportions,
n
and
x
and
x
S
for means.
4. Use the results to calculate the test statistic:
z-score for proportions
(
)
( )
n
pp
pp
z
00
0
1
ˆ
−
−
=
t-score for means
(
)
−
=
n
S
x
t
x
0
µ
Then use the test statistic to compute the
P-value: probability of getting the results from the sample based on assuming H
0
is true.
5. Reject or do not reject H
0
.
There are two outcomes for a hypothesis test as revealed by the table below.
6. Conclusion (state in real-life terms with no “math” notation).
_____________________________________________________________________________________
Conditions/Requirements for conducting a hypothesis test about a population proportion:
1. The sample proportion
p
ˆ
must be obtained from a random sample.
2.
10
0
≥np
, where
0
p
is the assumed population proportion from
0
H
.
3.
10)1(
0
≥− pn
, where
0
p
is the assumed population proportion from
0
H
.
4. The population size is at least ten times the sample size (
n
).
_____________________________________________________________________________________
The conditions/requirements for conducting a hypothesis test about a population mean are the same as the
conditions/requirements for using t-distributions (see t-distributions handout).
_____________________________________________________________________________________
P-value
α
≤
P-value
α
>
Sample is rare Sample is
NO
T
rare
Reject
0
H
Do NOT reject
0
H
There is significant
evidence to support
a
H
There is
NOT
significant
evidence to support
a
H