Inference Formulas-my Chart
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Transcript of Inference Formulas-my Chart
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Inference Formulas & Conditions
Test Conditions Null
Hypothesis
Test Statistic p-value Confidence Interval
One-Sample z-test
(for a populationmean)
1.) known
2.) SRS3.) population is normal, orlare sample si!e (n " 3#)
$.) Independence
%o ' 'oZ= x o
n
normalcdf
(lower limit,upper limit)
x z*
n
Two-Sample z-test
(for a difference in 2
population means)
1.) 21 and are known
2.) SRS
3.) population is normal, or
lare sample si!e ( 21,nn "
3#)
$.) Samples areIndependent
%o '1 '2
2
2
2
1
2
1
21
nn
xx
z
+
=
normalcdf
(lower limit,
upper limit)2
2
2
1
2
1
21nn
zxx
+
One-Sample t-test
(for a population
mean)
1.) SRS2.) population is normal, or
lare sample si!e (n " 3#)
3.) Independence
%o ' 'ot=
x o
s
n
wit* n+ 1 df
tcdf((lowerlimit, upper
limit, derees of
freedom
x tn1
* s
n
Two-Sample t-test
(for a difference in 2population means)
1.) SRS
2.) population is normal, or
lare sample si!e ( 21,nn "
3#)
3.) Samples areindependent
21# & =H or
#& 21# =H
t=x
1x
2
s1
2
n1
+s2
2
n2
it* smaller of
11n or 12n df
tcdf((lower
limit, upperlimit, derees of
freedom
(x1x
2) t*
s1
2
n1
+s2
2
n2
Matched Pairs t-test 1.) samples are not
independent (t*e- are
matc*ed)2.) SRS
3.) differences are normalor lare sample si!e (n " 3#)
# =dH
t=x
o
s
n
wit* n+ 1 df
tcdf((lower
limit, upper
limit, derees offreedom
x tn1
* s
n
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Test Conditions Null Hypothesis Test Statistic p-value Confidence Interval
One
Proportion z-
test
1.) SRS2. ) Independence pop
1# times sample
3. ) /ormalit- 1#)1(1# pnnp
## & ppH =
n
pp
ppz
)1(
0
##
#
=
normalcdf(lower
limit, upper
limit)
n
ppzp
)01(00
/ote t*e condition for CI is
1#)01(1#0 pnandpn
Two
Proportion z-
test
1.) SRS2. ) Independence pop
1# times sample
3. ) /ormalit-)01(0
11 cc pnpn
)01(022 cc pnpn
21# & ppH = or
#& 21# = ppH
+
=
21
21
11)01(0
00
nnpp
ppz
cc
/ote21
210nn
xxp
c
+
+=
normalcdf(lower
limit, upper
limit)
( )
2
22
1
11
21
)01(0)01(0
00
n
pp
n
ppz
pp
+
Chi Suare
!oodness of"it Test
1.) SRS or data is from
an entire population.2. ) all epected countsare "
,...,& 21# ppppH ba ==
= .ep
.)ep.( 2
2 obsv
df of cateories 4 1
56cdf(56
statistic,1#####,df)
Chi Suare
test for
independence
1.) all epected counts"
#H t*ere is no
association 7etween t*e
8aria7les (independent)
=.ep
.)ep.( 2
2 obsv
df ( rows + 1)(columns + 1)
56cdf(56statistic,
1#####,df)
t-test for the
slope of a
linear
re#ression
euation
1.) - responses areindependent.
2.) - responses arenormal.
3.) standard de8iation
a7out t*e reression lineremains constant.
$.) 8aria7les arelinearl- related
# =H
bSE
bt=
9erees of freedom 2n
tcdf((lowerlimit, upper
limit,derees of
freedom b t*SE
b`
