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AP Statistics
Inference Review—Chapters 10-15
Procedure
When do I use it?
Confidence
Interval for
Population
Mean (  )
When population
standard deviation
(  ) is known
Z Interval
Confidence
Interval for
Population
Mean (  )
When population
standard deviation
(  ) is not known
T Interval
pˆ  z *
Confidence
Interval for
Population
Proportion (p)
Z-Test for
Population
Mean (  )
When population
standard deviation
(  ) is known
T-Test for
Population
Mean (  )
When population
standard deviation
(  ) is not known
Z-Test for
Population
Proportion (p)
Related Formulas (including conditions)
  

x  z * 
 n
Conditions:
1. SRS
2. Normality: stated for population OR n>30 OR check
distribution of sample
3. Independence: N>10n
 s 
 degrees of freedom = n – 1
x  t * 
 n
Conditions:
1. SRS
2. Normality: stated for population OR n>30 OR check
distribution of sample
3. Independence: N>10n
pˆ(1  pˆ)
n
Conditions:
1. SRS
2. Normality: npˆ ≥10 AND n (1  pˆ) ≥10
3. Independence: N>10n
x 
Test Statistic: z 

n
Conditions:
1. SRS
2. Normality: stated for population OR n>30 OR check
distribution of sample
3. Independence: N>10n
x 
Test Statistic: t 
degrees of freedom = n – 1
s
n
Conditions:
1. SRS
2. Normality: stated for population OR n>30 OR check
distribution of sample
3. Independence: N>10n
pˆ  p 0
Test Statistic: z 
p 0 (1  p 0 )
n
Conditions:
1. SRS
2. Normality: npo≥10 AND n(1-po) ≥10
3. Independence: N>10n
Two Sample
T-Test for
The
Difference
Between Two
Means
When population
standard deviation
(  ) is not known
x1  x2
s12 s2 2

n1 n2
df = smaller of n1  1 or n2  1
Conditions:
1. SRS
2. Normality: stated for population OR n>30 OR check
distribution of sample
3. Independence: N1>10n1 and N2>10n2
s12 s2 2
( x1  x2 )  t *

n1 n2
df = smaller of n1 – 1 and n2 – 1
Confidence
Interval for
the Difference
Between Two
Means
Conditions:
1. SRS
2. Normality: stated for population OR n>30 OR check
distribution of sample
3. Independence: N1>10n1 and N2>10n2
pˆ1 (1  pˆ1 ) pˆ2 (1  pˆ2 )

n1
n2
( pˆ1  pˆ2 )  z *
Confidence
Interval for
Comparing
Two
Proportions
Conditions:
1. SRS
2. Normality: n1 pˆ1 , n1 (1  pˆ1 ), n2 pˆ 2 , n2 (1  pˆ 2 ) are all ≥5
3. Independence: N1>10n1 and N2>10n2
pˆ1  pˆ2
Test Statistic: z 
1
1 
pˆc (1  pˆc )  
 n1 n 2 
Conditions:
1. SRS
2. Normality: n1 pˆ1 , n1 (1  pˆ1 ), n2 pˆ 2 , n2 (1  pˆ 2 ) are all ≥5
3. Independence: N1>10n1 and N2>10n2
Z-Test for
Two
Proportions
Goodness of
Fit Test
Test Statistic: t 
When there is only
one categorical
variable involved
Homogeneity When there is a
of Populations separate sample
from 2 or more
populations
Test Statistic: 2  
(observed  exp ected )2
exp ected
df = k – 1
Conditions:
1. SRS
2. All expected counts  5
(observed  exp ected )2
Test Statistic:   
exp ected
Conditions:
1. SRS
2. All expected counts  5
2
df = (r-1)(c-1)
Test for
When there is a
Association or single sample from a
Indpendence
single population
classified according
to two categorical
variables
Confidence
Interval for
Regression
Slope
(observed  exp ected )2
Test Statistic:   
exp ected
Conditions:
1. SRS
2. All expected counts  5
2
df = (r-1)(c-1)
b  t * SE b 
where SE b 
s
 (x
x)
2

 (y
 yˆ) 2
 (x
 x )2
n 2
df = n – 2
Conditions:
1. Observations should be independent
2. Roughly straight-line association between explanatory and
response variables
3. Standard deviation is the same for all values of explanatory
variable
4. Response values (residuals) should vary Normally
Test for
Regression
Slope
Test statistic: t 
b
SE b
df = n – 2
Conditions:
1. Observations should be independent
2. Roughly straight-line association between explanatory and
response variables
3. Standard deviation is the same for all values of explanatory
variable
4. Response values (residuals) should vary Normally