Download Hypothesis Tests Steps and Notation (1

Hypothesis Tests
Steps and Notation
(1-Sample)
STEP 1, Null and Alternate Hypotheses
State the
“Null Hypothesis”
H0 :
and
“Alternate Hypothesis”
Ha :
STEP 1, Null and Alternate Hypotheses
The Null Hypothesis is
what we assume.
We will try to reject this
assumption (i.e., reject
the Null) with significant
evidence.

TIP: Always put an equal
sign for the Null.
Fill out the Null
Hypothesis AFTER filling
out the Alternate
Hypothesis.
H0 :
STEP 1, Null and Alternate Hypotheses
The Alternate Hypothesis
is what we want to show.
This comes from the
question in the paragraph.
In filling out the Alternate
Hypothesis, we are limited
to three different
inequality signs to choose
from:
Less Than
Greater Than
Not Equal To



Ha :
NOTE: “a” for
“alternate”
STEP 1, Null and Alternate Hypotheses
Both the Null and Alternate
Hypotheses are statements
about the POPULATION.
Therefore, the symbols that you
use will be either
p
population proportion
Ho : p 
Ha : p
STEP 1, Null and Alternate Hypotheses
Both the Null and Alternate
Hypotheses are statements
about the POPULATION.
Therefore, the symbols that you
use will be either
p
population proportion
or

population mean
H o : 
Ha : 
STEP 1, Null and Alternate Hypotheses
While reading the question
in the paragraph, you will
choose the inequality for the
Alternate Hypothesis which
best represents what the
question wants to show.
Once an inequality sign is
chosen, the entire
hypothesis test takes on a
nickname.
These nicknames tell you
which tail you shade in the
bell-shaped curve in STEP 4.
TIP: During STEP 4,
remember to look back at
the inequality in the
Alternate Hypothesis for
shading.
Ha : 
“Left-tailed”
Ha : 
“Right-tailed”
Ha : 
“Two-tailed”
STEP 1, Null and Alternate Hypotheses
Recall that you will fill out
the Alternate hypothesis
first by reading the
question in the paragraph
and seeing what it is that
you want to show.
For example, if you want to
show that
“…the percentage of all
college students that own
a cell phone
is less than 99%.”
Ho :
Ha :
p
 0.99
then fill out the Alternate
Hypothesis as follows.

STEP 1, Null and Alternate Hypotheses
Recall that you will fill out
the Alternate hypothesis
first by reading the
question in the paragraph
and seeing what it is that
you want to show.
For example, if you want to
show that
“…the percentage of all
college students that own
a cell phone
is less than 99%.”
then fill out the Alternate
Hypothesis as follows.
Ho : p 
H a : p  0.99
STEP 1, Null and Alternate Hypotheses
The comparison number
that you put into the
Alternate Hypothesis will
then be copied into the
Null Hypothesis.
So we will assume that the
percentage of all college
students that own a cell
phone is equal to 99% until
STEP 5.
During STEP 5 we hope to
reject this assumption H 0 .
TIP: The Alternate
Hypothesis H a is not
referenced again until
STEP 6 (the conclusion).
Ho : p 
H a : p  0.99
STEP 1, Null and Alternate Hypotheses
Recall that you will fill out
the Alternate hypothesis
first by reading the
question in the paragraph
and seeing what it is that
you want to show.
For example, if you want to
show that
“…the average cover price
for all comic books
published in 2012
is greater than $2.”
then fill out the Alternate
Hypothesis as follows.
Ho :
Ha :

2

STEP 1, Null and Alternate Hypotheses
Recall that you will fill out
the Alternate hypothesis
first by reading the
question in the paragraph
and seeing what it is that
you want to show.
For example, if you want to
show that
“…the average cover price
for all comic books
published in 2012
is greater than $2.”
then fill out the Alternate
Hypothesis as follows.
Ho :  
Ha :   2
STEP 1, Null and Alternate Hypotheses
The comparison number
that you put into the
Alternate Hypothesis will
then be copied into the
Null Hypothesis.
So we will assume that the
average cover price for all
comic books is equal to $2
until STEP 5.
During STEP 5 we hope to
reject this assumption H 0 .
TIP: The Alternate
Hypothesis H a is not
referenced again until
STEP 6 (the conclusion).
Ho :  
Ha :   2
STEP 2, Significance Level
State your Level of
Significance.
This is the comfort level
of what you would call a
“rare event.”
TIP: This is usually 1% or
5%.
TIP: The Significance
Level is not used again
until Step 5 where we
compare it against the Pvalue.

STEP 3, Statistics
State your statistics.
These will be the
numbers which describe
your SAMPLE.
Sample size
and either
n
sample proportion
p̂
or
sample mean
and sample
standard deviation
x
Sx
n
p̂ 
STEP 3, Statistics
State your statistics.
These will be the
numbers which describe
your SAMPLE.
Sample size
and either
n
sample proportion
p̂
or
sample mean
and sample
standard deviation
x
Sx
n
x
Sx 
STEP 4, Part 1, Test Statistic
Step 4 is done in two
parts, and each part is a
calculation.
Part 1: Calculate the
TEST STATISTIC:
z
 pˆ  p0 
p0 1  p0 
n
z-score for proportions
or
t-score for means
t
x  0 
 Sx



n

STEP 4, Part 1, Test Statistic
Note that
and
p0 and
0 numbers come
from the Null
Hypothesis H . The
0
subzero in the notation
is to remind you that
you are assuming these
values from the Null
Hypothesis.
z
 pˆ  p0 
p0 1  p0 
n
t
x  0 
 Sx



n

STEP 4, Part 2, P-value
Part 2: Use the Test
Statistic to calculate the Pvalue (Probability value).
The P-value will be the
shaded area in the curve.
TIP: Look back at the
Alternate Hypothesis H a
in STEP 1 to see where to
shade (left-tailed, righttailed, or two-tailed).
You will shade the area of
the tail after where the
Test Statistic is (and its
mirror image if “TwoTailed”) as indicated
from H a .
STEP 5, To reject or not to
reject the Null Hypothesis
Now that you have
calculated the P-value
from STEP 4, compare it
with the Level of
Significance from STEP 2.
If the P-value < α then the
probability of your sample
occurring is small.
In other words, your
sample is “rare”, or
“statistically significant”
enough to reject your Null
Hypothesis H 0 .
P - value  
STEP 5, To reject or not to
reject the Null Hypothesis
If the P-value > α then
the probability of your
sample occurring is
more common.
In other words, your
sample is “NOT rare”, or
“NOT statistically
significant” enough to
reject your Null
Hypothesis H 0 .
P - value  
STEP 6, The conclusion
In STEP 6 you state your
conclusion in real-life
terms.
If, from STEP 5, the
P-value < α then there is
significant evidence to
conclude H a .
In other words…
P - value  
There is significant
evidence to conclude
(whatever the question in
the paragraph wanted to
show).
STEP 6, The conclusion
If, from STEP 5, the
P-value > α then there is
NOT significant evidence
to conclude H a .
In other words…
P - value  
There is NOT significant
evidence to conclude
(whatever the question in
the paragraph wanted to
show).
THE END