MECE E3018辅导、讲解Python，Java语言编程、辅导c++程序
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Dr. Yesilevskiy
Fall 2019
LAB 1 MECE E3018 EXAM
Mechanical Engineering Lab I - MECE E3018 - Fall 2020 - Professor Yevgeniy Yesilevskiy
Due: October 20, 2020 by 1:10pm
Read the entire exam carefully before beginning to work. You may write directly on the exam paper, or
you may put your answers on separate sheets of paper.
This is an open-book exam.
All required tables are attached at the end of this exam.
By submitting this exam, you have agreed to the following statement:
I have neither given nor received aid on this examination, nor have I concealed any violation of the Honor
Code. I will not give any information about this exam to other students.
Problem 1 (2 points each) – Support or Rebut Questions
Please answer the following questions by circling either Support or Rebut. If you circle Support then you
must provide facts to show why you support the statement. If you circle Rebut, then you must provide
facts to show why the statement is false. One way to do this is to modify the statement to make it true
(supportable) and provide facts to show why the modified statement is supportable. If no support or rebut
facts are given, then no credit will be given.
I. The large scale approximation, which states that the t-value is approximately equal to 2, can be used
with the t-distribution when the degrees of freedom are greater than or equal to 9 and the confidence
level is 99%.
Support or Rebut
II. You conduct an experiment where you measure the weight of tires coming off of an assembly line.
After averaging the measurements, you find that the average weight is 97.8609 Newtons. After
calculating precision and bias uncertainties, you find that the total uncertainty is ±1.3027 Newtons to
95% confidence. The way to present this data is to state that:
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑊𝑒𝑖𝑔ℎ𝑡 = 97.8609 ± 1.3027 𝑁 (95%)
Support or Rebut
Name: ____________________________
3
III. You are working in a lab that measures the intensity of light passing through a particular material. After
extensive testing of many samples, you come up with an average intensity that is lower than the
manufacturer claimed value for the material. You decide to conduct a hypothesis test to see if it is in
fact lower. As always, your null hypothesis states that the true population mean 𝑥′, equals the claimed
value 𝑥𝑜′. Your alternate hypothesis states that the true population mean, 𝑥
′ < 𝑥𝑜′. After calculating
the test-statistic, 𝑡𝑒𝑥𝑝, you say you can reject the null hypothesis with 95% confidence if 𝑡𝑒𝑥𝑝 < 𝑡0.025,𝜈,
where 𝜈 is the degrees of freedom.
Support or Rebut
IV. The least squares regression method to best-fit a line to a set of data can only be used for data that
follows an underlying linear trend.
Support or Rebut
Name: ____________________________
4
V. In an experiment, you collect 17 measurements. From this data, you calculate a sample mean, 𝑥̅, and a
sample standard deviation, 𝑆𝑥. In order to estimate the range within which the 18th measurement
would fall, to a given confidence, you should use a corresponding t-value and the standard deviation of
the means, 𝑆𝑥̅= 𝑆𝑥/√𝑁, where N is the number of measurements.
Support or Rebut
VI. The standard deviation of the means is given by 𝑆𝑥̅= 𝑆𝑥/√𝑁 where 𝑆𝑥 is the sample standard deviation
and 𝑁 is the number of measurements. This value is the true population standard deviation.
Support or Rebut
Name: ____________________________
5
Problem 2 (15 points)
A car manufacturer is inspecting a key engine component to ensure that it will not fail under typical
loading conditions. The manufacturer takes 61 measurements and finds that the mean failure load is
44.72 Kilo-Newtons [kN] with a sample variance of 5.74 kN
2
a. Assuming the underlying distribution is normal, what is the probability that the next measurement
you take will be between 43.92kN and 45.20kN?
b. Determine the range (in kN) over which the true population mean will be, assuming 95%
confidence.
Name: ____________________________
6
c. Determine the range (in kN
2
) over which the true population variance will be, assuming 95%
confidence.
Name: ____________________________
7
Problem 3 (15 points)
During part of a thermocouple lab, you and your team collect the voltage of the thermistor, 𝑉𝐷𝐴𝑄, from a
data acquisition (DAQ) device. Using this value you then calculate the thermistor resistance, 𝑅𝑡ℎ𝑒𝑟𝑚 using
the following equation:
𝑅𝑡ℎ𝑒𝑟𝑚 =
𝑎 ∗ 𝑉𝐷𝐴𝑄
𝑏 − 𝑉𝐷𝐴𝑄
where 𝑎 and 𝑏 are fixed constants with no precision or bias error.
(a) Develop a symbolic expression for the relative uncertainty in 𝑅𝑡ℎ𝑒𝑟𝑚 as a function of:
a. 𝑉𝐷𝐴𝑄
b. the absolute uncertainty in the voltage, 𝑈𝑉𝐷𝐴𝑄
c. constants
[Note: do NOT waste your time simplifying the expression OR getting the expression in terms of the
relative uncertainty on the voltage, it is not required].
Name: ____________________________
8
(b) As the lab proceeds, you are able to use this resistance value to calculate the temperature of the
thermistor, 𝑇. This temperature is in turn used to calculate a voltage, 𝐸, using an equation similar
to the one below:
𝐸 = 2 + 3𝑇 + 7𝑇
2 + 9𝑇
3
Assuming you took 12 temperature measurements, and found a mean of 𝑇̅ = 97.34 degrees
Celsius, with a sample standard deviation of 𝑆𝑇 = 1.03 degrees C, and a bias uncertainty of ±0.57
degrees C, what is 𝑒𝐸, the relative uncertainty in the voltage measurement?
Name: ____________________________
9
Problem 4 (15 points)
You are tasked with investigating the drag force 𝐹𝐷 on a small-scale airplane wing as a function of speed.
From aerodynamic theory, you know that this force should depend on airplane speed, 𝑣, according to the
following relationship:
𝐹𝐷 = 𝑎𝑣
𝑏
where 𝑎 and 𝑏 are unknown constants.
(a) You take 11 measurements at different speeds and observe the resulting drag force. Using these
measurements, explain (with words and equations) how you would calculate 𝑎 and 𝑏. NOTE: you
do not have to actually calculate the numerical values of a and b, just explain how you would do
it.
Name: ____________________________
10
(b) The small-scale airplane wings you received for this experiment come from two different
manufacturers. In order to see if they are indeed the same, you take a random sample from each
of the manufacturers and measure their length. From the first manufacturer, you find that there
is a mean length of 𝑥̅1 = 15.7mm and a standard deviation of 𝑆1 = 0.2mm based on 14
measurements. From the second manufacturer, you find that there is a mean length of 𝑥̅2 =
15.3mm and a standard deviation of 𝑆2 = 0.1mm based on 19 measurements. You calculate the
combined degrees of freedom and find that it is 𝜈 = 17.79. Are these two populations equivalent
with a 95% confidence level?
Name: ____________________________
11
(c) In words, how would your analysis change if there was a third population?
Name: ____________________________
12
Distribution Tables
[Table of values on the next page]
Dr. Yesilevskiy
Fall 2019
LAB 1 MECE E3018 EXAM
Mechanical Engineering Lab I - MECE E3018 - Fall 2020 - Professor Yevgeniy Yesilevskiy
Due: October 20, 2020 by 1:10pm
Read the entire exam carefully before beginning to work. You may write directly on the exam paper, or
you may put your answers on separate sheets of paper.
This is an open-book exam.
All required tables are attached at the end of this exam.
By submitting this exam, you have agreed to the following statement:
I have neither given nor received aid on this examination, nor have I concealed any violation of the Honor
Code. I will not give any information about this exam to other students.
Problem 1 (2 points each) – Support or Rebut Questions
Please answer the following questions by circling either Support or Rebut. If you circle Support then you
must provide facts to show why you support the statement. If you circle Rebut, then you must provide
facts to show why the statement is false. One way to do this is to modify the statement to make it true
(supportable) and provide facts to show why the modified statement is supportable. If no support or rebut
facts are given, then no credit will be given.
I. The large scale approximation, which states that the t-value is approximately equal to 2, can be used
with the t-distribution when the degrees of freedom are greater than or equal to 9 and the confidence
level is 99%.
Support or Rebut
II. You conduct an experiment where you measure the weight of tires coming off of an assembly line.
After averaging the measurements, you find that the average weight is 97.8609 Newtons. After
calculating precision and bias uncertainties, you find that the total uncertainty is ±1.3027 Newtons to
95% confidence. The way to present this data is to state that:
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑊𝑒𝑖𝑔ℎ𝑡 = 97.8609 ± 1.3027 𝑁 (95%)
Support or Rebut
Name: ____________________________
3
III. You are working in a lab that measures the intensity of light passing through a particular material. After
extensive testing of many samples, you come up with an average intensity that is lower than the
manufacturer claimed value for the material. You decide to conduct a hypothesis test to see if it is in
fact lower. As always, your null hypothesis states that the true population mean 𝑥′, equals the claimed
value 𝑥𝑜′. Your alternate hypothesis states that the true population mean, 𝑥
′ < 𝑥𝑜′. After calculating
the test-statistic, 𝑡𝑒𝑥𝑝, you say you can reject the null hypothesis with 95% confidence if 𝑡𝑒𝑥𝑝 < 𝑡0.025,𝜈,
where 𝜈 is the degrees of freedom.
Support or Rebut
IV. The least squares regression method to best-fit a line to a set of data can only be used for data that
follows an underlying linear trend.
Support or Rebut
Name: ____________________________
4
V. In an experiment, you collect 17 measurements. From this data, you calculate a sample mean, 𝑥̅, and a
sample standard deviation, 𝑆𝑥. In order to estimate the range within which the 18th measurement
would fall, to a given confidence, you should use a corresponding t-value and the standard deviation of
the means, 𝑆𝑥̅= 𝑆𝑥/√𝑁, where N is the number of measurements.
Support or Rebut
VI. The standard deviation of the means is given by 𝑆𝑥̅= 𝑆𝑥/√𝑁 where 𝑆𝑥 is the sample standard deviation
and 𝑁 is the number of measurements. This value is the true population standard deviation.
Support or Rebut
Name: ____________________________
5
Problem 2 (15 points)
A car manufacturer is inspecting a key engine component to ensure that it will not fail under typical
loading conditions. The manufacturer takes 61 measurements and finds that the mean failure load is
44.72 Kilo-Newtons [kN] with a sample variance of 5.74 kN
2
a. Assuming the underlying distribution is normal, what is the probability that the next measurement
you take will be between 43.92kN and 45.20kN?
b. Determine the range (in kN) over which the true population mean will be, assuming 95%
confidence.
Name: ____________________________
6
c. Determine the range (in kN
2
) over which the true population variance will be, assuming 95%
confidence.
Name: ____________________________
7
Problem 3 (15 points)
During part of a thermocouple lab, you and your team collect the voltage of the thermistor, 𝑉𝐷𝐴𝑄, from a
data acquisition (DAQ) device. Using this value you then calculate the thermistor resistance, 𝑅𝑡ℎ𝑒𝑟𝑚 using
the following equation:
𝑅𝑡ℎ𝑒𝑟𝑚 =
𝑎 ∗ 𝑉𝐷𝐴𝑄
𝑏 − 𝑉𝐷𝐴𝑄
where 𝑎 and 𝑏 are fixed constants with no precision or bias error.
(a) Develop a symbolic expression for the relative uncertainty in 𝑅𝑡ℎ𝑒𝑟𝑚 as a function of:
a. 𝑉𝐷𝐴𝑄
b. the absolute uncertainty in the voltage, 𝑈𝑉𝐷𝐴𝑄
c. constants
[Note: do NOT waste your time simplifying the expression OR getting the expression in terms of the
relative uncertainty on the voltage, it is not required].
Name: ____________________________
8
(b) As the lab proceeds, you are able to use this resistance value to calculate the temperature of the
thermistor, 𝑇. This temperature is in turn used to calculate a voltage, 𝐸, using an equation similar
to the one below:
𝐸 = 2 + 3𝑇 + 7𝑇
2 + 9𝑇
3
Assuming you took 12 temperature measurements, and found a mean of 𝑇̅ = 97.34 degrees
Celsius, with a sample standard deviation of 𝑆𝑇 = 1.03 degrees C, and a bias uncertainty of ±0.57
degrees C, what is 𝑒𝐸, the relative uncertainty in the voltage measurement?
Name: ____________________________
9
Problem 4 (15 points)
You are tasked with investigating the drag force 𝐹𝐷 on a small-scale airplane wing as a function of speed.
From aerodynamic theory, you know that this force should depend on airplane speed, 𝑣, according to the
following relationship:
𝐹𝐷 = 𝑎𝑣
𝑏
where 𝑎 and 𝑏 are unknown constants.
(a) You take 11 measurements at different speeds and observe the resulting drag force. Using these
measurements, explain (with words and equations) how you would calculate 𝑎 and 𝑏. NOTE: you
do not have to actually calculate the numerical values of a and b, just explain how you would do
it.
Name: ____________________________
10
(b) The small-scale airplane wings you received for this experiment come from two different
manufacturers. In order to see if they are indeed the same, you take a random sample from each
of the manufacturers and measure their length. From the first manufacturer, you find that there
is a mean length of 𝑥̅1 = 15.7mm and a standard deviation of 𝑆1 = 0.2mm based on 14
measurements. From the second manufacturer, you find that there is a mean length of 𝑥̅2 =
15.3mm and a standard deviation of 𝑆2 = 0.1mm based on 19 measurements. You calculate the
combined degrees of freedom and find that it is 𝜈 = 17.79. Are these two populations equivalent
with a 95% confidence level?
Name: ____________________________
11
(c) In words, how would your analysis change if there was a third population?
Name: ____________________________
12
Distribution Tables
[Table of values on the next page]