Summary Table for Statistical Techniques
Inference
1
Estimating a
mean
Parameter Statistic
One
population
mean µ
sample mean
x
Type of
Data
Quantitative
Analysis

What is the average
weight of adults?
What is the average
cholesterol level of
adult females?
1-sample t-interval
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


2
Test about a
mean
One
population
mean µ
sample mean
x
Quantitative


3
Estimating a
proportion
One
population
proportion
p
sample
proportion
categorical

p̂

4
Test about a
proportion
One
population
proportion
p
sample
proportion
p̂
categorical
Minitab
Command
Examples

Is the proportion
of females different
from 0.5?
Is the proportion of
students who fail
Stat200 less than
0.1?
x t
*
s
n
The one sample t test:
x  0
t
s
n
1-proportion Z-interval
pˆ  z *
pˆ (1  pˆ )
n
Ho : p = po
Ha : p  po or Ha : p > po
or Ha : p < po
The one proportion Z-test:
z
pˆ  p0
p0 (1  p0 )
n
Stat
→Basic
statistics
→1-sample t
Stat
→Basic
statistics
→1-sample t
Stat
→Basic
statistics
→1
proportion
Stat
→Basic
statistics
→1
proportion
Conditions



Data approximately normal
or
have a large sample
size (n ≥ 30)

Data approximately normal
or
have a large sample
size (n ≥ 30)

n p̂ and n (1- p̂ ) ≥ 5,
but preferably ≥ 10

np0 and n (1- p0) ≥ 5,
but preferably ≥ 10
Inference
Parameter Statistic
Type of
Data
Examples

5
Estimating the
difference of
two means
difference in
two
population
means
µ1-µ2
difference in
two sample
means

Quantitative
x1  x 2

6
Test to
compare two
means
difference in
two
population
means
µ1-µ2
difference in
two sample
means
Quantitative

x1  x 2

7
Estimating a
mean with
paired data
mean of
paired
difference
µD
sample mean
of
difference
Quantitative
d

8
Test about a
mean with
paired data
mean of
paired
difference
µD
sample mean
of
difference
d
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?
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?
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?
Minitab
Command
Analysis
two-sample t-interval
( x1  x 2 )  t *
s1 2 s 2 2

n1 n2
Ho : µ1 = µ2
Ha : µ1  µ2 or Ha : µ1 > µ2
or Ha : µ1 < µ2
The two sample t test:
t
( x1  x 2 )  0
s1 2 s 2 2

n1 n 2
paired t-interval
d  t*
sd
n
Ho : µD = 0
Ha : µD  0 or Ha : µD > 0
or Ha : µD < 0
d 0
t
sd
n
Stat
→Basic
statistics
→2-sample t
Conditions



Stat
→Basic
statistics
→2-sample t


Stat
→Basic
statistics
→Paired t


Stat
→Basic
statistics
→Paired t

Independent samples from
the two populations
data in each sample are
about normal or large
samples (ni ≥ 30)
independent samples from
the two populations
data in each sample are
about normal or large
samples (ni ≥ 30)
differences approximately
normal
or
have a large number
of pairs (n ≥ 30)
differences approximately
normal
or
have a large number
of pairs (n ≥ 30)
9
10
Inference
Parameter Statistic
Estimating the
difference of
two
proportions
difference in
difference in
two
population two sample
proportions proportions
p1-p2
pˆ 1  pˆ 2
Test to
compare two
proportions
Relationship
11 in a contingency
table
12
Regression
Test the slope
difference in difference in
two
two sample
population proportions
proportions
pˆ 1  pˆ 2
p1-p2
relationship
between two
categorical
variables
or
difference in
two or more
population
proportions
Type of
Data
Examples
 How different are
the percentages of
male and female
categorical smokers?
 How different are
the percentages of
upper- and lowerclass binge drinkers?
 Is the percentage of
males with lung
cancer higher than the
Percentage of females
categorical
with lung cancer?
 Are the percentages of
upper- and lower-class
binge drinkers
different?
Analysis
Minitab
Command
Conditions
two-proportions Z-interval
( pˆ 1  pˆ 2 ) 
z
*
pˆ 1(1  pˆ 1) pˆ 2(1  pˆ 2)

n1
n2
Ho : p1 = p2
Ha : p1  p2 or Ha : p1 > p2
or Ha : p1 < p2
The two proportion z test:
z
pˆ 1  pˆ 2
pˆ (1  pˆ ) pˆ (1  pˆ )

n1
n2
Stat→Basic
statistics
→2 proportions

independent samples
from the two populations

n1 p̂1 , n1(1- p̂1 ), n2 p̂ 2
and
n2(1- p̂ 2 )≥ 5, preferably 10
Stat→Basic
statistics
→2 proportions
 independent samples
from the two populations
 n1 p̂1 , n1(1- p̂1 ), n2 p̂ 2 and
p̂ 2 )≥ 5, preferably 10
Ho : The two variables are
the observed
counts in a
contingency
table
Relationship
between two Estimated
Quantitative Slope b1
Data
 Is there a relationship
between smoking and
lung cancer?
categorical  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
Stat
→Tables
→CrossTabulation
And Chi-Square

Stat
→Regression
→Regression
 Linearity
 No extreme outliers
 Constant Var. and Normality
(Observed  Expected) 2
Expected
Ho: β1=0
 is there a linear relation
Ha: β1≠ 0
Quantitative Between father’s height
Know how to find the test
And son’s height?
Statistic from Minitab output

all expected counts should
be greater than 1
at least 80% of the cells
should have an expected
count greater than 5