Download S-300 Test 8-9 Formuals.cwk (WP)

Chapter 8 Test Formulas
The test Statistic for
the Population Proportion
z=
the Population Mean
( pˆ − p)
t=
⎛ p • q⎞
⎝ n ⎠
the population
must be normal
or
n • p ≥ 5 AND n • q ≥ 5
(x − µ )
⎛ sx ⎞
⎜
⎟
⎝ n⎠
the population
must be normal
or
n > 30
the Population Standard Deviation
χ2 =
(n − 1)• s2
σ2
the population
must be normal
Do Not Reject Ho :
There is not sufficient evidence at the α significance level to reject the “statement of equality”
Reject Ho:
There is sufficient evidence at the α significance level to support the “ statement of inequality”
or
P Method (optional)
Finding a P Value:
If it is a One Tail Test the P value is equal to the area to the right or left of the test statistic
If it is a Two Tail Test the P value is equal to twice the area to the right or left of the test statistic.
Reject H0 if P Value ≤ α
Do Not Reject H0 if P Value > α
A Type I Error Rejects a True H0.
A Type II Error Does Not Reject a False H0.
Chapter 9 Test Formulas
Chapter 8 and 9 Test Formulas
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© 2013 Eitel
Chapter 9
The Test Statistic for Two Population Proportions with H 0: p1 = p2
( pˆ 1 − ˆp2 )
Test Statistic: z =
p• q
p •q
+
n1
n2
ˆp1 =
x1
x
x + x2
and ˆp2 = 2 and p = 1
n1
n2
n1 + n 2
Creating a Confidence Interval to Estimate the value of
the Difference in 2 Population Proportions (p1 − p2 )
( pˆ 1 − pˆ 2 ) − E < ( p1 − p2 ) < ( pˆ 1 − ˆp2 ) + E
if
ˆp1 > pˆ 2
if
ˆp2 > pˆ 1
or
( pˆ 2 − pˆ1 ) − E < ( p2 − p1 ) < ( pˆ 2 − ˆp1 ) + E
⎛ pˆ • qˆ ⎞ ⎛ pˆ • qˆ ⎞
Where E = zα 2 • ⎜ 1 1 ⎟ + ⎜ 2 2 ⎟
⎝ n1 ⎠ ⎝ n2 ⎠
The Test Statistic for Two Population Means with H 0: µ1 = µ2
( x1 − x 2 )
Test Statistic: t =
2
2
( s1 ) + ( s2 )
n1
n2
at a significance level of α with DF = the smaller of { ( n1 −1) and ( n2 −1)}
Creating a Confidence Interval to Estimate the value of
the Difference in 2 Population Means µ1 − µ2
(x1 − x 2 ) − E < (µ1 − µ2 ) < (x1 − x 2 ) + E
if
x1 > x2
if
x2 > x1
or
(x 2 − x1 ) − E < (µ2 − µ1 ) < (x 2 − x1 ) + E
Where E = tα 2 •
( s1 )2
n1
+
(s 2 )2
n2
at a significance level of α with DF = smaller of { (n1 −1) and (n 2 − 1)}
Chapter 8 and 9 Test Formulas
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© 2013 Eitel
The Test Statistic for testing a Claim about the
Difference in 2 Population Standard Deviations
with H 0: σ 1 = σ 2
chose the population with the largest sample standard deviation to be
Population One with a sample standard deviation of s1 and degrees of freedom DF = n1 − 1
chose the population with the smallest sample standard deviation to be
Population Two with a sample standard deviation of s2 and degrees of freedom DF = n 2 − 1
Test Statistic:
F=
(s1 ) 2
(s2 )2
where s1 > s2
with the Numerators DF = n1 −1 and the Denominators DF = n 2 − 1
The Test Statistic for testing a Claim about the
Mean of the Differences between Matched Pairs
Dependent Samples
with H 0: µd = 0
Test Statistic:
t=
(d )
⎛ sd ⎞
⎜
⎟
⎝ n⎠
with DF = n − 1
Creating a Confidence Interval to estimate the value of the
Mean of the Differences between Matched Pairs
Dependent Samples
d − E < µd < d + E
Where E = tα 2 •
sd
n
with DF = n − 1
Chapter 8 and 9 Test Formulas
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© 2013 Eitel