Type I error:
Rejecting H
0
when it is true.
Type II error:
Failing to
reject H
0
when it is false.
α=P(type I error) = P(reject H
0
when H
0
is true)
Pvalue
is smallest level of significance that would lead to rejection
of H
0
.
1)
Parameter of interest
2)
Null Hypothesis
3)
Alternative Hypothesis
4)
Test statistic
5)
Reject H0 if…
6)
Computations
7)
Conclusions
Inference on the mean of a population, variance known
Random sample size n, normally distributed.
= 
/
Z0 X μ0σ n
Pvalue:
(  (
))
2 1 ϕ Z0
for twosided. 1sided = 1Φ(Z
0
) when µ > µ
o
,
or Φ(Z
0
) when µ < µ
0
.
Reject α if z
0
is > z
α/2
or z
0
is < z
α/2
and fail to reject if –z
α2
<= z
0
<= z
α/
2
(twosided). } Critical
For onesided, reject if z
0
> z
a
(µ > µ
0
), reject if z
0
< z
a
(µ < µ
0
).
} regions!
Probability of Type II Error for TwoSided Alternative
Hypothesis on the Mean, Variance Known
=

 

β
ϕZα2 δnσ ϕ Zα2 δnσ
For Onesided:
=

β
ϕZα δnσ
Sample Size for TwoSided Alternative Hypothesis on the Mean,
Variance Known
= (
+
)
n
Zα2 Zβ 2σ2δ2
, where Z
β
=
(

)
Zα2 δnσ
and
= 
δ μ μ0
For Onesided:
= (
+
)
n
Zα Zβ 2σ2δ2
Confidence Interval on the Mean, Variance Known

/
≤ ≤ +
/
x zα 2σn μ x zα 2σn
Sample Size for a Specified E on the Mean, Variance Known
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 Spring '06
 andersonrowland
 Normal Distribution, Statistical hypothesis testing, 1 degrees

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