2 of
13
1.2 Testing a claims when
σ
is known
REVIEW
What is a hypothesis test?
A hypothesis test calculates the probability of observing our sample data
as
suming the null hypotheses
H
0
is true
. If the probability is low enough
(
p
value
≤
α
), we reject
H
0
and have evidence to support our alternative hy
pothesis
H
a
.
Eight simple steps
0. Write down what is
known
.
1. Determine which type of hypothesis
test
to use.
2. Check the test’s
requirements
.
3. Formulate the
hypothesis
:
H
0
,
H
a
4. Determine the
significance level
α
.
5. Find the
p
value
.
6. Make the
decision
.
7. State the final
conclusion
.
KTRHSPDC: “Know The Right Hypothesis So People Don’t Com
plain”
What is the
p
value?
The
p
value represents the probability of observing our sample data
assuming
H
0
is true.
We use the sampling distribution to determine if sampling error
could explain our observed sample statistic’s deviation from
H
0
’s claim about
the parameter. If we decide to reject
H
0
,
the
p
value is the actual Type I
error
for the study data.
1
The
p
value is calculated using the test statistic and it’s corresponding
distribution.
Common form of a test statistic
test statistic =
(sample statistic)

(null hypothesis of parameter)
(standard deviation of sample statistic)
(1)
What are the types of errors?
Type I error
α
/
p
value
occurs when we
reject
H
0
but
H
0
is actually
true
. The
p
value is the Type I error. (ex. Convicting a innocent person
— when
H
0
is innocence.)
Type II error
β
occurs when we
fail to reject
H
0
but
H
0
is actually false
.
(ex. Letting a criminal go free — when
H
0
is innocence.)
1.2
Testing a claims when
σ
is known
USE
Often used to help answer:
1
The
α
we use to make our decision is just the
maximum
Type I error we will accept.
It is the significance level, not the actual Type I error.
Anthony Tanbakuchi
MAT167
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Testing a claim about a population mean
3 of
13
1. Is the mean of a population equal to
μ
0
?
2. Is the mean of a population different than
μ
0
?
COMPUTATION
One sample hypothesis test,
σ
known.
Definition 1.1
requirements
(1) simple random sample, (2)
σ
known, (3) C.L.T.
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 Spring '11
 Tanbakuchi
 Statistics, Probability, Statistical hypothesis testing

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