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日期：2020-10-18 06:37

LAB 1 MECE E3018 Final

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:

?????????????? ??????????? = 97.8609 ± 1.3027 ?? (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 ??′, equals the claimed

value ????′. Your alternate hypothesis states that the true population mean, ??

′ < ????′. After calculating

the test-statistic, ????????, you say you can reject the null hypothesis with 95% confidence if ???????? < ??0.025,??,

where ?? 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, ???, and a

sample standard deviation, ????. 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, ?????= ????/√??, where N is the number of measurements.

Support or Rebut

VI. The standard deviation of the means is given by ?????= ????/√?? where ???? is the sample standard deviation

and ?? 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, ????????, from a

data acquisition (DAQ) device. Using this value you then calculate the thermistor resistance, ??????????? using

the following equation:

??????????? =

?? ? ????????

?? ? ????????

where ?? and ?? are fixed constants with no precision or bias error.

(a) Develop a symbolic expression for the relative uncertainty in ??????????? as a function of:

a. ????????

b. the absolute uncertainty in the voltage, ??????????

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, ??. This temperature is in turn used to calculate a voltage, ??, using an equation similar

to the one below:

?? = 2 + 3?? + 7??

2 + 9??

3

Assuming you took 12 temperature measurements, and found a mean of ??? = 97.34 degrees

Celsius, with a sample standard deviation of ???? = 1.03 degrees C, and a bias uncertainty of ±0.57

degrees C, what is ????, the relative uncertainty in the voltage measurement?

Name: ____________________________

9

Problem 4 (15 points)

You are tasked with investigating the drag force ???? on a small-scale airplane wing as a function of speed.

From aerodynamic theory, you know that this force should depend on airplane speed, ??, according to the

following relationship:

???? = ????

??

where ?? and ?? 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 ?? and ??. 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 ???1 = 15.7mm and a standard deviation of ??1 = 0.2mm based on 14

measurements. From the second manufacturer, you find that there is a mean length of ???2 =

15.3mm and a standard deviation of ??2 = 0.1mm based on 19 measurements. You calculate the

combined degrees of freedom and find that it is ?? = 17.79. Are these two populations equivalent

with a 95% confidence level?

Name: ____________________________

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(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]