Summary Table for Statistical Techniques
Inference
Parameter
Statistic
Type of
Data
Examples

Estimating a
mean
One
population
mean µ
sample mean
x
Quantitative


Test about a
mean
One
population
mean µ
sample mean
x
Quantitative


Estimating a
proportion
One
population
proportion
p
sample
proportion
categorical

p̂

Test about a
proportion
One
population
proportion
p
sample
proportion
p̂
categorical

Analysis
What is the average
weight of adults?
What is the average
cholesterol level of
adult females?
1-sample mean-interval
s
x  z*
n
Is the average GPA
of juniors at Penn
State higher than
3.0?
Is the average
Winter temperature
in State College
less than 42ْ F?
What is the
proportion of males
in the world?
What is the
proportion of
students that smoke?
Ho : µ = µo
Ha : µ  µo or Ha : µ > µo
or Ha : µ < µo
Is the proportion
of females different
from 0.5?
Is the proportion of
students who fail
Stat100 less than
0.1?
The one samplemean test:
x  0
z
s
n
1-proportion interval
pˆ  z *
pˆ (1  pˆ )
n
Ho : p = po
Ha : p  po or Ha : p > po
or Ha : p < po
The one proportion test:
z
pˆ  p0
p0 (1  p0 )
n
Inference
Parameter
Statistic
Type of
Data
Examples

Estimating the
difference of
two means
difference in
two
population
means
µ1-µ2
difference in
two sample
means

Quantitative
x1  x 2

Test to
compare two
means
Estimating a
mean with
paired data
Test about a
mean with
paired data
difference in
two
population
means
µ1-µ2
difference in
two sample
means
Quantitative

x1  x 2
mean of
paired
difference
µD
sample mean
of
difference
mean of
paired
difference
µD
sample mean
of
difference
What is the
difference
in pulse rates, on the
average, before and
after exercise?

Is the difference in
IQ of pairs of twins
zero?
Are the pulse rates
of people higher
after exercise?
Xd
Xd
Do the mean pulse
rates of exercisers
and non-exercisers
differ?
Is the mean EDS
score for dropouts
greater than the
mean EDS score for
graduates?

Quantitative
Quantitative
How different are
the mean GPAs of
males and females?
How many fewer
colds do vitamin C
takers get, on
average, than non
vitamin C takers?

Analysis
two-sample mean interval
( x1  x2 )  z*
Where
s12 s 22

n1
n2
SEM 12 
s12
s2
2
and SEM 2  2
n2
n1
Ho : µ1 = µ2
Ha : µ1  µ2 or Ha : µ1 > µ2
or Ha : µ1 < µ2
The two sample mean test:
(x  x2 )  0
z 1
s12 s 2 2

n1
n2
s12
s 22
2
Where SEM 
and SEM 2 
n2
n1
2
1
paired mean interval
s
X d  z* d
n
Ho : µD = 0
Ha : µD  0 or Ha : µD > 0
or Ha : µD < 0
z
Xd 0
sd
n
Inference
Parameter
relationship
between two
categorical
variables
Relationship
or
in a contingency
difference in
table
two or more
population
proportions
Correlation
Relationship
between two
Quantitative
Data
Statistic
Type of
Data
Examples
Analysis
Ho : The two variables are
the observed
counts in a
contingency
table
categorical
 Is there a relationship
between smoking and
lung cancer?
 Do the proportions of
students in each class
who smoke differ?
not related
Ha : The two variables are
related
The chi-square statistic:
2 

all
cells
Estimated
correlation
Quantitative
 is there a linear relation
Between father’s height
And son’s height?
(Observed  Expected) 2
Expected
Ho: correlation =0
Ha: correlation ≠ 0