School

University of Cincinnati, Main Campus **We aren't endorsed by this school

Course

ENED 3061

Subject

Statistics

Date

Sep 25, 2023

Type

Other

Pages

6

Uploaded by bhertrick on coursehero.com

1
ENED 3061 Probability & Statistics
HW 10: NHST Two Means - p.
Spring 2023, Murphy
due by 8:00AM on Thursday April 6
Save this Word document as
HW10_NHST_TwoMeans_UCusername
, where
UCusername
is
the character string that goes at the beginning of your @mail.uc.edu email address. Submit your
completed work (as a Word doc or PDF) to the HW 10: NHST Two Means link in Canvas.
Either type your work and answers or include pictures of your hand-written work (make sure it's
legible and well organized).
Note: This is an individual assignment. The work you submit must be your own. Your
submission of work for this assignment indicates your affirmation of the CEAS Honor Code
statement, which is provided verbatim below.
https://ceas.uc.edu/about/info-current-students/academic-action-criteria.html
College of Engineering and Applied Science
Honor Code
As students of the University of Cincinnati's College of Engineering and Applied Science, we
honor the high standards required by our future profession.
We pledge to uphold those high standards by practicing integrity within our classrooms, our
communities, and our careers.
We believe in honest representation of individual work and in fair advancement of academic
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We expect academic integrity from our peers who share the responsibilities of this code.
Our commitment to this pledge entitles us to trust from our peers, our instructors, and our
institution. We maintain the right and share the responsibility to report any unfair advantage
with anonymity and without retribution.
I hereby affirm that this is my own work in accordance with the Honor Code of the University of
Cincinnati College of Engineering and Applied Science.

2
ENED 3061 Probability & Statistics
HW 10: NHST Two Means - p.
Spring 2023, Murphy
due by 8:00AM on Thursday April 6
Complete the following two problems. You can either (a) type in this document or (b) print the
document, write your answers by hand, and submit a legible scan.
(1) Modification of textbook exercise 5-23. Note that the data are already in the file,
MRH5e_Chapter5_exercises_part1.csv
, and use Minitab for step 6 (computations).
Include your Minitab output in your solutions.
Problem Statement
: In semiconductor manufacturing, wet chemical etching is often used to
remove silicon from the backs of wafers prior to metalization. The etch rate is an important
characteristic in this process and
known to follow a normal distribution.
Your job is to conduct a hypothesis test to determine if the
mean etch rate is different for two
different (independent) etching solutions.
Assume that the two population variances are
unknown but equal.
Write out all 7 steps. For Step 5, use α = 0.05. For Step 6, use Minitab for the computations -
be sure to check your settings under Options. For Step 7, be sure to include both a statistical
conclusion and a practical interpretation.
Sample Data
: Two random samples of 10
wafers for etch solution have been
collected. The observed etch rates are in the
table (in mils/min).

3
ENED 3061 Probability & Statistics
HW 10: NHST Two Means - p.
Spring 2023, Murphy
due by 8:00AM on Thursday April 6
1.
Parameters of interest ate mean etching rate
μ
1
and
μ
2
with
∆
0
=
0
2.
H
0
:
μ
1
=
μ
2
3.
H
1
:
μ
1
≠μ
2
4.
Test statistic: t because the population variances are unknown but assumed equal (Case 1)
t
calc
=
´
x
1
−´
x
2
−
∆
0
s
p
√
1
n
1
+
1
n
2
and
df
=
n
1
+
n
2
−
2
5.
Rejection region (two-sided):
α
=
0.05
and
df
=
n
1
+
n
2
−
2
=
10
+
10
−
2
=
18
t
0.025,18
=
±
2.101
t
calc
<
t
0.025,18
Or the p-value is less than
α
=
0.05
6.
Used Minitab
t
calc
=
9.970
−
10.400
−
0
(
0.340
)
√
1
10
+
1
10
=−
2.83
p
−
value
=
0.011
7.
Conclusion:
t
calc
is less than -2.101 so we reject
H
0
and conclude that there is a
statistically significant difference in mean etching rate at
α
=
0.05
Also note that the p-value (0.011) is less than
α
=
0.05
, which also indicates a
statistically significant difference.
Practical Conclusion: The mean etching rates are not equal

4
ENED 3061 Probability & Statistics
HW 10: NHST Two Means - p.
Spring 2023, Murphy
due by 8:00AM on Thursday April 6
(2) Continued from (1): Modification of textbook exercise 5-23. Note that the data are already in
the file,
MRH5e_Chapter5_exercises_part1.csv
, and use Minitab for step 6 (computations).
Include your Minitab output in your solutions.
In the above problem, following assumptions were made:
(a)
The etch rate is known to follow a normal distribution.
(b) It was assumed that the two population variances are unknown but equal.
Conduct a hypothesis test to determine if the two population variances are equal. Write out
all 7 steps. For Step 5, use
α
= 0.05. For Step 6, use Minitab for the computations - be sure to
check your settings under Options. For Step 7, be sure to include both a statistical conclusion
and a practical interpretation.
Be sure to address whether the assumption of equal variances that we made in problem (1)
was valid.

5
ENED 3061 Probability & Statistics
HW 10: NHST Two Means - p.
Spring 2023, Murphy
due by 8:00AM on Thursday April 6
1.
Parameters of interest: The two population variances
σ
A
2
and
σ
B
2
in
mils
min
2.
H
0
:
σ
A
2
=
σ
B
2
but since we are using F which is a ration, we can also think of it as
H
0
:
σ
A
2
σ
B
2
=
1
3.
H
0
:
σ
A
2
σ
B
2
≠
1
4.
Test Statistic:
F
calc
=
s
1
2
s
2
2
5.
Rejection Region: We will compare the calculated p-value to our alpha of 0.05
6.
p
−
value
=
0.087
7.
Conclusion: Fail to reject
H
0
and conclude that Sample 1 has the same variability as
Sample 2
Practical Conclusion: The variances of the two samples are the same

6
ENED 3061 Probability & Statistics
HW 10: NHST Two Means - p.
Spring 2023, Murphy
due by 8:00AM on Thursday April 6