,Hy pothesis
Tests
,Sample distribution of j2
O O
I
E (5) i .d
X
-N( , 8) =
I U
population
.
identical) distribution
sample
Mean mean
so
↓ independent
Infinite population [E(x I ,
+
. ..
+
Ecn)] Central Limit Theorem (CLT)
standard L
error of the
if = 0 05 =
is when
large simple
random sample
M
.
-
mean
↓ (n 30) is used (approx by XN)
>
.
identical
(X x n) = 52 because
+ -
.. . to
Var I Small sample is when 30 and
= (n() =
..
X +
varn)] can be considered normal ONLY If
since var (c) = population is assumed to have X2N
var([Y) = Var(x) + Var(Y)
independent
When 2> 0 When 0
· P(z <* ) should be added with
· P(2 <* ) should ignore 1-) and
0 5 to whatever out from
. the table gives subtract whatever the table gives
(0 .
5 + v = P) 0 5
. Even if Pof 2 is () it should be
·
P(z >* ) should be subtracted (0 5 .
- V =
P)
with 0 5 *
.
to whatever the table
gives
·
p(z > 2 ) should ignore (-) and
out (0 5 v P) add 0 5 to whatever from the
given
-
=
.
.
table Even if P of 2 is (-) it should
be (0 . 5+ v =
P)
8 vs2S z
Z x
2 > s2 82
M
>
s uses + p P
F
>
, Hypothesis tests
Hypothesis tests used to determine whether a statement about the
value of a population parameter should or not be rejected
assumption/hypothesis
Null hypothesis(o)-
· :
a tentative aboutone
Assuming Ho is correct but attempts to
reject it
.
Reject Ho ,
conclude (accept) Hi
Can't Ho can't conclude Hi
reject
. .
,
·
Alternative
hypothesis (H ,
or Ha) : an
assumption that is the
of null
opposite hypothesis
The conclusion that the research (alternative) hypothesis is true
comes from sample data that contradict the null
hypothesis
our evidence
The conclusion that the claim is false comes from sample
data that contradict the null
hypothesis => Conclude/Accept H ,
A
hypothesis test about the value of a population a
mean
must take one of the following forms (Mo is the hypothesized
mean)
·
One tailed (lower tail) ·
One tailed (uppertail) ·
Two tailed
Ho :
M2 Mo Ho M & Ho =
MO M Mo
: :
H1 :
M
<
Mo H1 :
M
>
Mo Hi :
M NO
Tests
,Sample distribution of j2
O O
I
E (5) i .d
X
-N( , 8) =
I U
population
.
identical) distribution
sample
Mean mean
so
↓ independent
Infinite population [E(x I ,
+
. ..
+
Ecn)] Central Limit Theorem (CLT)
standard L
error of the
if = 0 05 =
is when
large simple
random sample
M
.
-
mean
↓ (n 30) is used (approx by XN)
>
.
identical
(X x n) = 52 because
+ -
.. . to
Var I Small sample is when 30 and
= (n() =
..
X +
varn)] can be considered normal ONLY If
since var (c) = population is assumed to have X2N
var([Y) = Var(x) + Var(Y)
independent
When 2> 0 When 0
· P(z <* ) should be added with
· P(2 <* ) should ignore 1-) and
0 5 to whatever out from
. the table gives subtract whatever the table gives
(0 .
5 + v = P) 0 5
. Even if Pof 2 is () it should be
·
P(z >* ) should be subtracted (0 5 .
- V =
P)
with 0 5 *
.
to whatever the table
gives
·
p(z > 2 ) should ignore (-) and
out (0 5 v P) add 0 5 to whatever from the
given
-
=
.
.
table Even if P of 2 is (-) it should
be (0 . 5+ v =
P)
8 vs2S z
Z x
2 > s2 82
M
>
s uses + p P
F
>
, Hypothesis tests
Hypothesis tests used to determine whether a statement about the
value of a population parameter should or not be rejected
assumption/hypothesis
Null hypothesis(o)-
· :
a tentative aboutone
Assuming Ho is correct but attempts to
reject it
.
Reject Ho ,
conclude (accept) Hi
Can't Ho can't conclude Hi
reject
. .
,
·
Alternative
hypothesis (H ,
or Ha) : an
assumption that is the
of null
opposite hypothesis
The conclusion that the research (alternative) hypothesis is true
comes from sample data that contradict the null
hypothesis
our evidence
The conclusion that the claim is false comes from sample
data that contradict the null
hypothesis => Conclude/Accept H ,
A
hypothesis test about the value of a population a
mean
must take one of the following forms (Mo is the hypothesized
mean)
·
One tailed (lower tail) ·
One tailed (uppertail) ·
Two tailed
Ho :
M2 Mo Ho M & Ho =
MO M Mo
: :
H1 :
M
<
Mo H1 :
M
>
Mo Hi :
M NO
