1 | P a g e ME 350 Project 2 Posted February 26, 2019, Due March 5 2019 Higher level tools for roots of f(x) = 0 problems Q. 1. The velocity of a falling parachutist is given by the following formula: 1 Where g=9.81 m/s2, the drag coefficient c=13.5 kg/s. Compute the mass (m) of the parachutist so that v = 40.7 m/s when t = 12.8 s Hint. This is an f(x) = 0 type problem, with corresponding variables v(m) = 0 (a) Rearrange the terms and write a simple m-file, then use this file to use a regular plot command to locate the approximate root. Submit the m-file and the corresponding plot. Here you will need to experiment with a range of values of ‘m’ . (b) Modify the m-file from (a) into a function file that can be used with the fzero function to compute a refined root. Submit your function and the solution it displays in the MATLAB command window. Q.2. Consider the square cross section beam anchored on one end and supporting a 500 lb weight. Other details are shown in figure below. Ref. Musto ch. 6. This exercise will help you review methods for solving f(x) = 0 problems. According to strength of materials principles, the maximum bending stress experienced by the cantilever beam shown above is: 2 | P a g e σ = 335,000/x3 + 92,600/x (1) This reflects the suspended weight, the specific weight (weight per unit length), and the length of the beam. From materials science, the maximum allowable stress (i.e. limiting stress before the onset of yielding) for the beam material is 17,750 psi. We now need to determine the minimum dimension ‘x’ in inches that will satisfy this stress constraint. Solve this problem using four different techniques as itemized below. Hint: The solution approaches involve solving a problem of the form: f(x) = 0 a) Rewrite equation 1 in polynomial form in descending coefficients of the powers of x then use the built-in MATLAB function roots to compute the representative solution. b) Rewrite equation 1 into a MATLAB function file (beam2b.m) which can be used by MATLAB’s fzero function. Use the fzero function to compute the solution for this problem, using an initial guess of 43. c) Rationalize the denominators of beam2b.m to generate a more standard polynomial form and name it beam2c.m . Use fplot to generate a plot of the function in the range -5≤x≤15; insert grid lines to spot the approximate location of the real root. Use the fzero function to compute the solution for this problem using and initial guess of -125. Submit the function file, the plot and the solution computed using fzero. d) Refer to the plot from (c). Use the bisectrr function to compute a root for this function in the interval -5≤x≤5. i. Comment on the outcome of the attempt in (d). ii. Select an alternative range that would yield the root for this function. What is the solution? 3 | P a g e Q.3. In designing a spherical tank whose schematic i.

1. 1 | P a g e
ME 350 Project 2
Posted February 26, 2019, Due March 5 2019
Higher level tools for roots of f(x) = 0 problems
Q. 1. The velocity of a falling parachutist is given by the
following formula:
1
Where g=9.81 m/s2, the drag coefficient c=13.5 kg/s.
Compute the mass (m) of the parachutist so that v = 40.7 m/s
when t = 12.8 s
Hint. This is an f(x) = 0 type problem, with corresponding
variables v(m) = 0
(a) Rearrange the terms and write a simple m-file, then use this
file to use a
regular plot command to locate the approximate root. Submit
the m-file and
the corresponding plot. Here you will need to experiment with a
range of

2. values of ‘m’ .
(b) Modify the m-file from (a) into a function file that can be
used with the
fzero function to compute a refined root. Submit your function
and the
solution it displays in the MATLAB command window.
Q.2. Consider the square cross section beam anchored on one
end and supporting a
500 lb weight. Other details are shown in figure below. Ref.
Musto ch. 6. This
exercise will help you review methods for solving f(x) = 0
problems.
According to strength of materials principles, the maximum
bending stress
experienced by the cantilever beam shown above is:
2 | P a g e
σ = 335,000/x3 + 92,600/x (1)
This reflects the suspended weight, the specific weight (weight
per unit length),
and the length of the beam. From materials science, the
maximum allowable stress
(i.e. limiting stress before the onset of yielding) for the beam
material is 17,750
psi. We now need to determine the minimum dimension ‘x’ in
inches that will satisfy

3. this stress constraint. Solve this problem using four different
techniques as
itemized below.
Hint: The solution approaches involve solving a problem of the
form: f(x) = 0
a) Rewrite equation 1 in polynomial form in descending
coefficients of the
powers of x then use the built-in MATLAB function roots to
compute the
representative solution.
b) Rewrite equation 1 into a MATLAB function file (beam2b.m)
which can be
used by MATLAB’s fzero function. Use the fzero function to
compute the
solution for this problem, using an initial guess of 43.
c) Rationalize the denominators of beam2b.m to generate a more
standard
polynomial form and name it beam2c.m . Use fplot to generate a
plot of
the function in the range -5≤x≤15; insert grid lines to spot the
approximate location of the real root. Use the fzero function to
compute
the solution for this problem using and initial guess of -125.
Submit the
function file, the plot and the solution computed using fzero.
d) Refer to the plot from (c). Use the bisectrr function to
compute a root for
this function in the interval -5≤x≤5.

4. i. Comment on the outcome of the attempt in (d).
ii. Select an alternative range that would yield the root for this
function. What is the solution?
3 | P a g e
Q.3. In designing a spherical tank whose schematic is shown
below, you need to
determine the height of water in the tank if the radius R of the
tank is 2.7 m, and
the volume V is 37.8 m3. The equation for computing V as a
function of R and h is:
3
3
Treat this is an f(h) = 0 problem to compute the height of water
in the tank for
the given values of V and R
(a) Write a MATLAB function file that computes the volume the
fluid in the
spherical tank as a function h; and generates a plot of V versus
h.
(b) From your plot determine approximate of root for this

5. function.
(c) Use fzero with the aid of the approximate root from (b) to
compute the
desired root accurately.
Submit:
te root computed using fzero that is echoed to the
command window
Review each scenario and data set carefully and choose which
scenario you would like to work with. Begin Phase 1 of your
analysis by including the following information:
1. Introduce your scenario and data set.
. Provide a brief overview of the scenario you are given above
and the data set that you will be analyzing.
. Classify the variables in your data set.
. Which variables are quantitative/qualitative?
. Which variables are discrete/continuous?
. Describe the level of measurement for each variable included
in your data set.
· Discuss the importance of the Measures of Center and the
Measures of Variation.
· What are the measures of center and why are they important?
· What are the measures of variation and why are they
important?
· Calculate the measures of center and measures of variation.
Interpret your results in context of the selected topic.
· Mean
· Median

6. · Mode
· Midrange
· Range
· Variance
· Standard Deviation
· Conclusion
· Recap your ideas by summarizing the information presented.
Phase 2
1. Discuss the importance of constructing confidence intervals
for the population mean.
. What are confidence intervals?
. What is a point estimate?
. What is the best point estimate for the population mean?
Explain.
. Why do we need confidence intervals?
· Based on your selected topic, evaluate the following:
. Find the best point estimate of the population mean.
. Construct a 95% confidence interval for the population mean.
Assume that your data is normally distributed and σ is
unknown.
. Please show your work for the construction of this confidence
interval and be sure to use the Equation Editor to format your
equations.
. Write a statement that correctly interprets the confidence
interval in context of your selected topic.
· Based on your selected topic, evaluate the following:
. Find the best point estimate of the population mean.
. Construct a 99% confidence interval for the population mean.
Assume that your data is normally distributed and σ is
unknown.
. Please show your work for the construction of this confidence
interval and be sure to use the Equation Editor to format your
equations.
· Write a statement that correctly interprets the confidence

7. interval in context of your selected topic.
· Compare and contrast your findings for the 95% and 99%
confidence interval.
· Did you notice any changes in your interval estimate? Explain.
· What conclusion(s) can be drawn about your interval estimates
when the confidence level is increased? Explain.
Be sure to show all of your work in Excel and use the Equation
Editor to format your equations in Word.
Phase 3
Discuss the process for hypothesis testing.
Discuss the 8 steps of hypothesis testing?
When performing the 8 steps for hypothesis testing, which
method do you prefer; P-Value method or Critical Value
method? Why?
Perform the hypothesis test.
If you selected Option 1:
Original Claim: The average salary for all jobs in Minnesota is
less than $65,000.
Test the claim using α = 0.05 and assume your data is normally
distributed and σ is unknown.
If you selected Option 2:
Original Claim: The average age of all patients admitted to the
hospital with infectious diseases is less than 65 years of age.
Test the claim using α = 0.05 and assume your data is normally
distributed and σ is unknown.
Based on your selected topic, answer the following:
Write the null and alternative hypothesis symbolically and
identify which hypothesis is the claim.
Is the test two-tailed, left-tailed, or right-tailed? Explain.
Which test statistic will you use for your hypothesis test; z-test
or t-test? Explain.
What is the value of the test-statistic? What is the P-value?
What is the critical value?
What is your decision; reject the null or do not reject the null?
Explain why you made your decision including the results for

8. your p-value method or the critical value method.
State the final conclusion in non-technical terms.
Be sure to show all of your work in Excel and use the Equation
Editor to format your equations in Word.
Phase 4
1. introduce your scenario and data set.
1. Provide a brief overview of the scenario you are given above
and the data set that you will be analyzing.
2. Classify the variables in your data set.
1. Which variables are quantitative/qualitative?
2. Which variables are discrete/continuous?
3. Describe the level of measurement for each variable included
in your data set.
2. Discuss the importance of the Measures of Center and the
Measures of Variation.
1. What are the measures of center and why are they important?
2. What are the measures of variation and why are they
important?
3. Calculate the measures of center and measures of variation.
Interpret your results in context of the selected topic.
1. Mean
2. Median
3. Mode
4. Midrange
5. Range
6. Variance
7. Standard Deviation
4. Discuss the importance of constructing confidence intervals
for the population mean.
1. What are confidence intervals?
2. What is a point estimate?
3. What is the best point estimate for the population mean?
Explain.
4. Why do we need confidence intervals?

9. 5. Based on your selected topic, evaluate the following:
1. Find the best point estimate of the population mean.
2. Construct a 95% confidence interval for the population mean.
Assume that your data is normally distributed and σ is
unknown.
1. Please show your work for the construction of this confidence
interval and be sure to use the Equation Editor to format your
equations.
3. Write a statement that correctly interprets the confidence
interval in context of your selected topic.
6. Based on your selected topic, evaluate the following:
1. Find the best point estimate of the population mean.
2. Construct a 99% confidence interval for the population mean.
Assume that your data is normally distributed and σ is
unknown.
1. Please show your work for the construction of this confidence
interval and be sure to use the Equation Editor to format your
equations.
3. Write a statement that correctly interprets the confidence
interval in context of your selected topic.
7. Compare and contrast your findings for the 95% and 99%
confidence interval.
1. Did you notice any changes in your interval estimate?
Explain.
2. What conclusion(s) can be drawn about your interval
estimates when the confidence level is increased? Explain.
8. Discuss the process for hypothesis testing.
1. Discuss the 8 steps of hypothesis testing?
2. When performing the 8 steps for hypothesis testing, which
method do you prefer; P-Value method or Critical Value
method? Why?
9. Perform the hypothesis test.
1.
1. If you selected Option 1:
1. Original Claim: The average salary for all jobs in Minnesota
is less than $65,000.

10. 2. Test the claim using α = 0.05 and assume your data is
normally distributed and σ is unknown.
2. If you selected Option 2:
1. Original Claim:The average age of all patients admitted to
the hospital with infectious diseases is less than 65 years of age.
2. Test the claim using α = 0.05 and assume your data is
normally distributed and σ is unknown.
3. Based on your selected topic, answer the following:
1. Write the null and alternative hypothesis symbolically and
identify which hypothesis is the claim.
2. Is the test two-tailed, left-tailed, or right-tailed? Explain.
3. Which test statistic will you use for your hypothesis test; z-
test or t-test? Explain.
4. What is the value of the test-statistic? What is the P-value?
5. What is the critical value?
6. What is your decision; reject the null or do not reject the
null?
1. Explain why you made your decision including the results for
your p-value and the critical value.
7. State the final conclusion in non-technical terms.
10. Conclusion
1. Recap your ideas by summarizing the information presented
in context of your chosen scenario.
STA3215 Advanced Statistics and Analytics – Option 2
Introduction:
As a healthcare professional, you will work to improve and
maintain the health of individuals, families, and communities in
various settings. Basic statistical analysis can be used to gain
an understanding of current problems. Understanding the
current situation is the first step in discovering where an
opportunity for improvement exists. This course project will
assist you in applying basic statistical principles to a fictional
scenario in order to impact the health and wellbeing of the
clients being served.

11. This assignment will be completed in phases throughout the
quarter. As you gain additional knowledge through the didactic
portion of this course, you will be able to apply your new
knowledge to this project. You will receive formative feedback
from your instructor on each submission. The final project will
be due on week 5.
Scenario:
You are currently working at NCLEX Memorial Hospital in the
Infectious Diseases Unit. Over the past few days, you have
noticed an increase in patients admitted with a particular
infectious disease. You believe that the ages of these patients
play a critical role in the method used to treat the patients. You
decide to speak to your manager and together you work to use
statistical analysis to look more closely at the ages of these
patients. You do some research and put together a spreadsheet
of the data that contains the following information:
· Client number
· Infection Disease Status
· Age of the patient
You need the preliminary findings immediately so that you can
start treating these patients. So let’s get to work!!!!
Background information on the Data:
The data set consists of 65 patients that have the infectious
disease with ages ranging from 35 years of age to 81 years of
age for NCLEX Memorial Hospital. Remember this assignment
will be completed over the duration of the course.
Review of Basic Statistics

12. o Qualitative Data
o Quantitative Data
ts of measurement
o Only takes on countable values
o Can take on any value within an interval
o Nominal
o Ordinal
rder, but differences either can’t be
found or are
meaningless
o Interval
starting point and
ratios are meaningless

13. o Ratio
o Mean
o Median
o Mode
al cells in a row, then enter
=MODE.MULT(data
range) and then press Ctrl+Shift+Enter
o Mid-Range
-way point between the lowest and highest values
range) and

14. =MIN(data range) and then enter =(Maximum+Minimum)/2
o Range
range) and
=MIN(data range) and then enter =Maximum-Minimum
o Variance
to the square of the standard deviation
o Standard Deviation
o A bell curve distribution whose shape is determined by a
mean and a standard
deviation
o Standard Normal Deviations and �-scores

15. called a standard
normal distribution. Measurements on this scale are identified
by the
variable �
o Find a �-score
-score from a probability with
=NORM.S.INV(probability)
-scores are not percentages, do not change the decimal
place when computing a z-score.
o Area and probability
-score with =NORM.S.DIST(z,
TRUE)
o A parameter is a measurement (usually a proportion, a mean,
or a standard
deviation) of an entire population. Usually these values are
either impossible or
unrealistic to find.

16. o A statistic is a measurement used to estimate a parameter that
is based on a
sample taken from a population.
Measurement Parameter Statistic
Mean (average) Mu (�) x-bar (�̅�)
Proportion � p-bar (�̅�)
Standard Deviation Sigma (�) �
Variance Sigma squared (�2) �2
NamesPatient #Infectious
DiseaseAge1Yes692Yes353Yes604Yes555Yes496Yes607Yes72
8Yes709Yes7010Yes7311Yes6812Yes7213Yes7414Yes6915Yes
4616Yes4817Yes7118Yes5519Yes4920Yes6021Yes7222Yes702
3Yes7624Yes5625Yes5926Yes6427Yes7128Yes6929Yes7130Ye
s6131Yes7032Yes5533Yes4534Yes6935Yes5436Yes4837Yes60
38Yes6139Yes5040Yes5941Yes6042Yes6243Yes6344Yes5345Y
es6446Yes5047Yes6948Yes5249Yes6850Yes7151Yes6952Yes5
953Yes5854Yes6955Yes6556Yes6157Yes5958Yes7159Yes7160
Yes6861Yes4962Yes7363Yes6464Yes8165Yes71