Transcript Hypothesis Test Paper+Formulas

HYPOTHESIS TESTING PROCEDURE
STEP 1.
Establish the Hypothesis
a.) Null Hypothesis
Ho:
b.) Alternative Hypothesis
Ha:
=
STEP 2.
Choose a Significance Level
a=
STEP 3.
Plan the Test
a.) Choose the Test Statistic (formula)
b.) Determine the Rejection Region
Z
or
t
0
F
or
c2
0
STEP 4.
Collect data and
Calculate test statistic
STEP 5.
Draw conclusion
STEP 6.
Estimate the parameter of interest
and determine Confidence Interval
DATA BLOCK
Hypothesis Tests
Differences in the Means - Tests for One Population
Population Variance ( s )
known?
Yes
Test To Use
Formula
Z - Test
x - m0
s/ n
where:
x - Sample Mean
m 0 - Standard Mean
s - Population Standard Deviation
n - Sample Size
No
t - Test
2
Z=
t=
x - m0
s/ n
where:
x - Sample Mean
m 0 - Standard Mean
s - Sample Standard Deviation
n - Sample Size
Differences in the Means - Tests for Two Population s – Paired Data
Population
Variances
known?
N/A
Population
Variances
Equal?
N/A
Test to
Use
Paired
Sample t Test
Formula
d
s/ n
where :
t=
d - Sample Differences Mean
s - Sample Standard Deviation
n - Sample Size
Differences in the Means - Tests for Two Populations
Population
Variances
known?
Yes
Population
Variances
Equal?
N/A
Test to
Use
Two Pop.
Z-Test
Formula
For Equal Sample Sizes
Z=
x A - xB
1 2
(s A + s 2B )
n
where:
xi - Sample Mean
s i - Population Standard Deviation
n - Sample Size
For Unequal Sample Sizes
Z=
x A - xB
s 2A
nA
+
s 2B
nB
where:
xi - Sample Mean
s i - Population Standard Deviation
ni - Sample Size
No
Yes
Two –
Pop.,
Pooled
Variance
t-Test
For equal sample sizes
t=
x A - xB
s 2A + sB2
n
where:
xi - Sample Mean
si - Sample Standard Deviation
n - Sample Size
For unequal sample sizes
t=
x A - xB
 1
1  SS A + SS B

+ 
 n A nB  n A + nB - 2
where:
xi - Sample Mean
n i - Sample Size
Differences in the Means - Tests for More than Two Populations
.
Differences in the Dispersion
Comparison
Population Variance to a
Standard
Test To
Use
c2 - Test
Formula
c
2
=
( n - 1) s 2
s
2
0
where :
s - Sample Standard Deviation
s
- " Standard" or Population Standard Deviation
0
n - Sample Size
Two Population
Variances
2
2
F = s A sB
F - Test
where :
s i - Sample Standard Deviation
Differences in Proportions
Comparison
Population Proportion to a
Standard
Test To
Use
Z - Test
Formula
Z=
p - P0
P0 (1 - P0 ) / n
where:
p - Sample Proportion
n - Sample Size
Two Population
Proportions
Z - Test
(2 Pop’s)
Z=
p1 - p2
1 1
p(1 - p) + 
n1 n2 
where:
pi - Sample Proportion
ni - Sample Size
x +x
p= 1 2
n1 + n2
xi - Number of Sample Items with Characteristic of Interest