≠
0
t
= 0.6402
p
= 0.5351
x
= 0.3583
X
σ
n1
= 1.9388
n
= 12
Solution
Critical value: At 1% level of
significance, t
crit
= t
0.01/2, 121
=  3.11
12
9388
.
1
35833
.
0
t
calc
Before we state the test statistics, we use the calculator to obtain the values:
1Sample tTest
μ
≠
0
t
= 0.6402
p
= 0.5351
x
= 0.3583
X
σ
n1
= 1.9388
n
= 12
= 0.6402
Let μ
1
=average time (mins) for oil and filter change by Procedure A
Let μ
2
=average time (mins) for oil and filter change by Procedure B
Condition: Normal and equal std dev but unknown
Ho:
D
= 0
(where
D
=
1

2
) – There is no diff in the means of two
related pop or the population mean difference
D
is 0.
Ha:
D
≠
0 (or Ho:
D
≠
1

2
) ) – the population difference
D
is not 0
Define rejection/nonrejection regions
Area=
α
/2=0.025
t
crit
= 3.11
t
crit
=3.11
Area=
α
/2=0.025
Z
t
calc
=0.640
Reject Ho
Reject Ho
Do Not Reject Ho
Decision
Area=
α
/2=0.025
t
crit
= 3.11
t
crit
=3.11
Area=
α
/2=0.025
Z
tcalc=0.640
Reject Ho
Reject Ho
Do Not Reject Ho
Decision: Do not reject Ho
The statistical evidence does not indicate that we may conclude there is
a difference in the average times for an oil and filter change.
Hypothesis Test
One Population
Hypothesis Test
Two Populations
Sample
Independent
Sample
dependent
Equal
2
?
unequal
2
1
and
2
known?
Ztest
Pooled Variance ttest
2 MEANS
2 Proportions
Check the 4
conditions
If yes
Ztest
Paired ttest
Normal?
Yes
No
STOP
No
Yes
Yes
No
Ttest
Pooled variance
Ztest of
two
Proportions
Hypothesis test for Differences
 Proportions for c Independent
Groups –
א
2
test
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1/31/2012
7
The sevenstep Method of Hypothesis Testing
Steps:
1.Define the parameters: π1and π22.State the hypothesis
3.
Determine the appropriate test (refer to the flowchart)
4.
State the conditions/assumptions: n
1
p
1
≥
5; n
1
(p
1
1)
≥
5 and
n
2
p
2
≥
5; n
2
(p
2
1)
≥
5
5.
Determine the critical value that divide the rejection and nonrejection regio
6.
Calculate the test statistics value
7
Make the statistical decision and Managerial conclusion
To reject Ho or DO NOT reject Ho
Compare the test statistics with the critical value (critical value approach)
or
compare pvalue with
α
(pvalue approach)
Hypothesis Test: Two Proportions
(Z test for the differences in Proportions for 2 independent Groups)
For a two tailed hypothesis test:
5
)
p
1
(
n
,
5
p
n
1
1
1
1
5
)
p
1
(
n
,
5
p
n
2
2
2
2
2
1
o
π
π
:
H
2
1
a
π
π
:
H
Are the four conditions
satisfied?
Let
π
2
= the population proportion of successes in group 2
Let
π
1
= the population proportion of successes in group 1
See page 484, section 11.3
Hypothesis Test: Two Proportions
(Z test for the differences in Proportions for 2 independent Groups)
Test statistics:
)
n
1
n
1
)(
p
1
(
p
)
π
π
(
)
p
p
(
z
2
1
2
1
2
1
2
1
2
2
1
1
2
1
2
1
n
n
p
n
p
n
n
n
x
x
p
Where usually
Л
1
–
Л
2
=0 since we hypothesis that
Л
1=
Л
2
Where p is called
the pooled estimate of the population proportion
Illustrative Example
Two printers are tested using the same paper and graphic
output. The results are then judged as conforming or
nonconforming. The results follow. Test for a difference
in proportion of nonconforming pages. Use 5% level of
significance.