N= Number sampled
Sx=
µ= median
X=
X
(x bar)= sample statistic
α = level of significance
Zc= level of confidence
Alpha
Tail
Z
0.10
Left
Right
Two
 1.28
+1.28
± 1.645
0.05
Left
Right
Two
 1.645
+1.645
± 1.96
0.01
Left
Right
two
2.33
+2.33
±2.575
Left tail
FAIL TO
H0: μ≥k
Reject Ho
REJECT Ho
Ha
: μ<k
Right Tail
FAIL TO
Reject Ho
H0: μ≤k
REJECT Ho
Ha
: μ>k
ALWAYS 1Z VALUE
to
get
FAIL TO
PVALUE
Reject Ho
REJECT Ho
Reject Ho
Two Tailed
H0: μ=k
If
P
≤
α
, then reject
H
0
.
Ha
: μ≠k
If
P
>
, then fail to reject
H
0
.
ZTEST
ON CALC
Null hypothesis 
H
0
:
A statistical hypothesis that contains a
statement of
equality
such as
≤
, =, or
≥
.
Alternative hypothesis 
H
a
:
A statement of
inequality
such as
>,
≠
, or <
Ex
Find the critical value (t
o
) for a left tail test α=0.025, n=19
d.f= (n1) = 191=18 (use ttable with d.f. =18 and 0.025) t
o
=
2.101 (
left tail means 
)
Ex
Find the critical value (t
o
) for a two tail test α=0.01, n=27
d.f= (n1) = 271=26 (use ttable with d.f. =26 and 0.01) t
o
=
±2.779 (
two tail means ±
)
Ex
Find the critical value (t
o
) for a right tail test α=0.10, n=20
d.f= (n1) = 201=19 (use ttable with d.f. =19 and 0.10) t
o
=1.328
(
right tail means +
)
Ex
state whether the standardized test statistic t indicates that
you should reject the null Hypothesis.
T
o
= 2.086
Ex
The Pew Research Center claims that more than 30% of US adults
regularly watch the weather channel.
You decide to test this claim and
ask a random sample of 75 adults whether they regularly watch the
weather channel.
Of the 75 adults, 27 responded yes.
At α=0.01, is
there enough evidence to support the claim?
N=75
X= 27
P=0.30
NP= 75(.3) =22.5
YES
Ho P≤ 0.30
Q=0.70
NQ= 75(.7) =52.5
Ha P> 0.30 (claim)
α=0.01
Critical value
z=1.13
α=0.01
Zo= 2.33
fail to reject Ho
Zo=2.33
Rejection region Z >2.33 (in alpha chart)
P
= 27/25 = 0.36
(0.360.30)
/
√(0.30)(0.7)/75
= Z= 1.13
Fail to reject Ho.
Not enough evidence to
support the claim.
Ex
A company specializing in parachute assembly state that it’s main
parachute failure rate is not more than 1%.
Perform a hypothesis test to
determine whether the company’s claim is false.
P= failure rate
Ho: P≤ 0.01 (claim)
Ha: P>0.01
Type 1 error:
reject Ho P≤0.01
when actually P≤ 0.01
Type 2 error:
fail to reject Ho P≤0.01
When actually P≤0.01
Ex
Find the pvalue for a left tailed hypothesis test with a test statistic of
z= 1.62.
Decide whether to reject Ho if the level of significance is α=0.05
Ho µ ≥K
Ha µ <K
z= 1.62
P= 0.0526
P Value = 0.0526 (z on chart)
P Value= 0.0526 > 0.05 =α
Fail to reject H
o
Ex
find the pvalue for a two tailed hypothesis test with a test statistic of
z=2.31.
Decided whether to reject Ho if the lever of significance is
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 Fall '10
 Raney
 Statistics, Statistical hypothesis testing, Reject Ho, Ho D.F.

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