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Ag engineering PE review:
Exam prep, I-C economics and statistics
Marybeth Lima, Ph.D., P.E.
Cliff & Nancy Spanier Alumni Professor
Biological & Agricultural Engineering
E-mail: [email protected]
Overview



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Exam preparation
Statistics
Economic analysis
Throughout:
You will be doing PE style problems (have your
references and calculators ready!)
 Ask questions

Part 1: Exam preparation



References (must have)
Time (in preparing for exam and during exam)
Strategies (preparation and test taking)
References


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Are an absolutely critical part of your
preparation; you will not pass the exam without
the proper references
There is a comprehensive list of references at
http://www.asabe.org/membership/careerresourcespe-licensure/pei.aspx
Some references are more useful than others
References I used for 80% of the
exam problems (must haves)


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
A Guide to Professional Licensure for Agricultural, Food, and
Biological Systems Engineers (see online material)
The notes from this on-line review course (bound)
ASABE Standards (I used the 2000 edition for the 2005 exam
and was fine)
The Civil Engineering Reference Manual for the PE exam (soil
and water, wastewater, pumps, econ tables, INDEX)
The Mechanical Engineering Reference Manual for the PE exam
(HVAC, machine systems, econ tables, fans, INDEX)

You don’t have to bring both PE manuals but have one; I’d recommend
civil over mechanical because of broad coverage of topics. If you pick the
civil manual, bring ASHRAE Fundamentals or another strong HVAC
book.
Other references I used






Wastewater Engineering, Metcalf and Eddy (used 3rd
edition)
Henderson, Perry and Young, Principles of Process
Engineering
Wood Engineering, Gurfinkel (any wood engineering
book will do; you need the tables at the back; you may
find in civil vs. ag parts of library)
A soil physics book
MWPS-1: Structures and Environment Handbook (op)
Schwab et al. Soil and water conservation engineering
(4th edition)
References I brought and did not use


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Irrigation Systems
NRCS handbook parts 650 and 651
Goering and Hansen, Engine and tractor power
Shuler and Kargi, Bioprocess Engineering Basic
Concepts
Salvendy, Handbook of Human Factors
MWPS-8, Swine Housing and Equipment
Handbook
Time: preparing for the exam







Get your references and get used to using them (tab Standards)
Make an index of where specific information is located so
that you don’t have to search during the exam
Do and re-do all the problems you are given in the on-line
course
Do problems in your reference books
Focus your time: general ag engineering knowledge, your
expertise area, your secondary knowledge areas
Don’t spend time on what you KNOW you won’t touch (there is
something you won’t)
The week before the test, do a sample test using the 8 hr exam
format (road test caffeine issues, etc.)
Time during the exam

The exam is designed such that each question takes an average of
six minutes


There are 1 minute problems and 15-20 minute problems
Go through the test and answer questions in the following order:



The quick, easy ones that you know you can do
The ones you know that you can do that take a little more time
Guess (with gusto!) at the ones that are beyond your scope



Guess the same letter every time
Go back and do the ones that you think you can do that are time
consuming
If there’s time, go back and check your answers; also go to the ones that
are bugging you (if there are any)
Strategies

You need to develop problem recognition

You need to develop flexible thinking

Pick what you will not answer and guess with pleasure (I guessed
at 10% of the questions on the exam)

Many times you can eliminate two of the four choices easily
(even with areas you know nothing about)

Knowing fundamental knowledge is critical (the PE reference
manuals in civil and mechanical were invaluable)
Strategies

You need to answer ~60% of the problems correctly to
pass



Having a strong base in general agricultural engineering
knowledge will “take you over the top”
My experience: for the various expertise areas, about 60% of
the problems were solvable without expert knowledge in the
area (as long as you had good references and knew where to
look for info)
The other 40% of the expertise questions were expert
knowledge level, involved problems (I skipped P&M,
irrigation, and structures/environment expert problems)
1-C: Economics and statistics

A broad area with applications “across the board” (5%
of exam questions)



Statistics is commonly used because you need descriptive
information to help interpret data
Economics is commonly used for making engineering
decisions
My suggestion for stats and econ: use the CE or ME
PE reference book (Lindeburg)

Chapter on statistics



Table at the back (z-chart)
Get a t-chart as well!!
Chapter on engineering economic analysis

Full interest tables at the back
Statistics basics

Measures of central tendency

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Measures of dispersion

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Mean, median, mode
Standard deviation, variance, range, coefficient of variance
For PE: have equations to determine measures of
central tendency and dispersion
There are slight differences in equations depending on
if you are working with a population or a sample
Statistics: Distributions

A number of distributions can be used to
describe various data sets or can be used to
solve engineering problems in relation to these
data sets

Sampling distributions involving means:
Normal (aka Gaussian): our focus
 Student t distribution


Sampling distributions involving variance:
F distribution
 Chi-Square

z
xm
s
Normal distribution: review


Symmetrical distribution with
mean m and standard deviation s
Area under curve represents 100%
of possibilities

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50% to the right of the mean
50% to the left of the mean
A value is higher than the mean for
this distribution to the right of the
mean, lower to the left of the mean
x represents where you are in the
distribution; z is the number of
standard deviations away from the
mean that you are


z is positive to right of mean
z is negative to left of mean
z
xm
s
Reading the z-chart
P(0.59  z  2.18)
Typical PE style problems

The population mean for college students’
heights is 67 inches, and the population standard
deviation is and 4 inches. These data are
normally distributed.

What percentage of college students have heights
less than 71 inches?
Solution

In what range would you find the middle 70% of the
data? (pick closest z value, do not interpolate)
Solution
You try this one:

90% of college students have heights greater
than what value?
Solution
Sampling


We almost never work with populations
We take samples and try to draw conclusions
about a population based on a sample
Use z chart for large samples (n>30)
 Use t chart for small samples


Your statistical equations change a little to
reflect the fact that you have a sample
z
xm
s
x m
z
s n
Confidence intervals

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
Commonly used in research and process control
95% confidence intervals are common
For example, what is the 95% confidence
interval of a set of 50 data points; the mean of
this data set is 150 and the standard deviation is
15.
m  zs
m  z
2
s
n
x  t
2
s
n
Solution
Hypothesis testing


Used to compare means values to each other to
determine if they’re significantly different
Considerations

What kind of hypothesis test is it?



Sample mean (large or small) compared to a standard
Sample mean (large or small) compared to another sample mean
(large or small)
Will you use a t chart or a z chart?
t

x m
s
n
Is the test one tailed (where directionality matters) or two
tailed (when only difference between values matters)
Steps to hypothesis testing

Ask, “what am I trying to show?”
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this is the alternate hypothesis
The null hypothesis contains all the other possibilities
Construct the acceptance and rejection region for the
hypothesis
Calculate the test statistic
Determine whether to accept or reject the null
hypothesis (you always test the null)
Reading a t chart
Example, hypothesis testing

A biodiesel plant has a standard daily production
rate that is normally distributed with a mean of
880 tons/day. Sampling the plant once a day for
35 days yielded a mean output of 870 tons/day
with a standard deviation of 20 tons per day. Do
the data present sufficient evidence to show that
the output is less than the standard?
1. Construct alternate and null
hypotheses

Problem statement: show output is less than
standard
Ha: m < 880
 Null is every other possibility: Ho: m ≥ 880

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From this statement, we can see that
directionality (< or >) matters: one-tailed test
If directionality doesn’t matter (show that the
means are different): two-tailed test
2. Construct acceptance/rejection
region


Start by drawing the standard that your sample is
being compared to
You need to know four things:
Which side of the mean your sample mean falls on
(to right/left of mean)
 What is alpha? (standard = 0.05)
 One-tailed or two tailed test
 Will you use the t-chart or z-chart?

The four things:

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Sample mean is 870, which is less than 880, so
you’re to the left of the mean
Alpha is not given, assume 0.05
Directionality matters, (<), one-tailed
n = 35, >30, use the z chart
Acceptance/rejection region
Calculate the test statistic
Draw the conclusion: accept or reject
the null hypothesis

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z-crit = -1.645
z-calc = -2.95
If you draw z-calc on your acceptance/rejection region,
it falls into the portion of the curve in which the null is
rejected
Thus, reject the null and conclude that Ha is true: yes,
sufficient evidence exists for showing that the mean
output of the plant is less than 880
Drawing
Statistics summary

General Tips:

Get a general reference with equations and make
sure you have a z chart and a t chart
get z from A, and A from z
 Know confidence intervals
 Look at process control (2 and 3 sigma limits)

Statistics summary,
hypothesis testing


Very cookbook approach
When you draw the acceptance/rejection region,
draw the mean that you are comparing your
sample to first
When comparing two small samples, arbitrarily
choose one and make sure you keep the means
properly situated from a numerical standpoint
 Also remember that sample size is POOLED or
added, so df = n1 + n2 - 2
Remember that you always test the null hypothesis,
which leads to a conclusion about the alternate


1-C: Engineering
economic analysis

Typically easy questions on the exam if you know how to use
factor tables (slang, interest tables)

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Tabulated in the ME reference manual, A-132-150 or CE manual A-112130
Types of problems in engineering economic analysis
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Decision making: you have a material you’re trying to choose, or a part, or
a machine. Compare which is most economical given present cost,
maintenance costs, etc.
Replacement/retirement analysis (when should you replace or retire a
product?)
Rate of return problem (to find percentage return on an investment)
Break even point on an investment
Loan repayment (how long will it take)
Economic life analysis (life cycle costs)
Benefit/cost analysis (do the benefits outweigh the costs)
Engineering econ


Almost all engineering econ problems will involve cash flows; it
is like a material balance using money instead of mass.
Types of cash flows:

Single payment cash flows (P or F)

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Uniform series cash flow (A)


An amount that is the same every month, like a house or car payment
Gradient series cash flow (not used much) (G)


P = present value of money
F = future value of money
A value that goes up or down the same amount every time period
You use types of cash flows to compare alternatives and solve
econ problems
Engineering econ

Cash flow problems can
be calculated using
equations or are
tabulated for fast
problem solving

Example


If you put $1,000 into a savings account and the
annual interest rate on the account was 6%, how
much money would be in the account after 5 years?
The equation to convert a present value to a
future value is
F  P (1  i )
n
Engineering econ

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
(1 + i)n is called the single payment compound amount
factor, and is tabulated for various combinations of i
(interest rate) and n (time period)
The notation (symbol) for the single payment
compound factor is (F/P, i%, n)
This notation indicates that F (future $ amount) is
unknown, that you have P (the present value), and
given the interest rate (i) in percent and the time period
(n), you can find F.
Engineering econ



Back to our example: If you put $1000 into a
savings account and the annual interest rate on
the account was 6%, how much money would
be in the account after 5 years?
Solve by equation: F = 1000(1 + 0.06)5 =
$1338.23
Solve by interest table
Engineering econ
F  P (F/P, i%, n)
Engineering econ

Example solve by interest table:

Go to F/P column with n = 5, for table with i =
6%: Factor = 1.3382
F  P (F/P, i%, n)

F = ($1000) 1.3382 = $1338.2
Engineering econ
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Biggest thing to keep in mind: make sure that
your UNITS match; interest rate, n, and dollar
amounts may be given on a different basis
You try: How much should you put into a 10%
effective annual rate savings account in order to
have $10,000 in four years? (10% interest table
included on next page)
Engineering econ
Engineering econ
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
You are given a future amount of money (F) and
ask to solve for a present amount of money
Solve using the i = 10% interest table, with n =
4 years; (P/F, 10%, 4) = 0.6830
P = F (P/F, 10%, 4) = $10,000*0.6830 = $6,830
Notice that n is given in years and i is given as
an annual interest rate (per year); units match
Engineering econ

Maintenance costs for a machine are $250/year.
What is the present worth of these maintenance
costs over a 12 year period if the annual interest
rate is 10%?
Given:
 Find:

Engineering econ


You have A, you need P: Go to i = 10%
interest chart and go to the P/A column
(remember in this notation your unknown
comes first): (P/A, 10%, 12) = 6.8137
P = A (P/A) = -250*6.8137 = -$1703 (negative
sign indicates a cash sink or loss of $)
More complicated

Question 104, webinar questions on general Ag Eng principles

As manager of a large fleet of farm equipment, you are contracting with
an outside mechanics shop to have all complete engine overhauls for
tractors, combines, and harvesters at the rate of $7,200 per engine. You
have determined the investment needed to construct a new building and
equip it to overhaul the equipment yourself would be $180,000. The
estimated annual cost for taxes and insurance for the facilities and
equipment is 1.25% of the purchase price. The operating cost to perform
engine overhauls at a facility that you own would be $5,500 per engine.
The equipment and facilities are assumed to have a life of 12 years with a
salvage value of $35,000. Interest rate is 7% per year. The minimum
number of engines to be overhauled per year to make the investment in
equipment and facilities economically feasible is:

NOTE: use 7% interest table (extra handout)
Solution

Approach:

You are comparing two alternatives, outsourcing vs. doing it
yourself

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
Outsourcing: $7200 per engine
“in-sourcing”: $5500 per engine, plus facilities, equipment, taxes, and
insurance (and minus salvage value)
You have to compare these two alternatives using the same
basis

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Choose A
Identify which type of cash flow you have in each situation
Set the outsourcing term = in-sourcing term
Solve for x, where x is the number of engines needed to break even
Solution


Outsourcing: $7200/engine * x engines, or $7200x
“In-sourcing:”


$5500/engine * x engines, or $5500x
New building and equipment = $180,000 (P)


Interest = 1.25% of building/equipment per year (A)


0.0125*180,000 = $2250
Salvage value = $35,000 12 years from now (F)


Convert to A
Convert to A
Use equations (as in solution online) OR (EASIER):
use interest tables!
Solution
Solution
Engineering economics summary



Also very cookbook approach, like statistics
Identify which factors you’re working with (F,
A, P, G) and ensure that you use the same basis
(usually annual)
Interest tables speed the solving of these
problems; obtain a set of interest tables!
Take home points


If your brain feels like it’s leaking out of your
ears right now, don’t worry, it’s normal 
Best things I did for the PE:
Had a reference book with a great index
 Had a list of where to find critical equations and
important information


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Time management tips
GOOD LUCK!!
Exam prep exercises
“Use of your PE reference books” exercise



On the PE exam, you want the “1 minute questions” that appear
on the test to take 1 minute to answer
These questions are testing your basic knowledge of the field and
your ability to bring and use the proper references
Practice: find the answers to the questions on the following
slides
 Approach


First, classify the problem: in which area of the Ag PE do you think the
problem is contained? In which references might you find the information?
When you find the answer, record the value, the reference in which you
found the answer, AND descriptive information within the reference (page
number, table number, figure number, equation number, etc.)
Question 1

What is the heat of combustion of propane?

NOTE: heat of combustion is also referred to
as heating value
Heat of combustion
Question 2

The Atterburg limit test measures what?
Question 3

What is the Young’s modulus of elasticity of
stainless steel?
Question 4

What is the density of air at 10° C?
Question 5

What is the curve number for contoured row
crops in good hydrologic condition for
hydrologic soil group B?
Question 6

For a relatively uniform distribution of soil
particles 1 mm in diameter, what is the largest
sieve size that these particles would not pass
through?
Question 7

What is the typical concentration of suspended
solids (SS) in septage?
Question 8

What is the equilibrium moisture content of
rough rice at 30° C and 80% RH?
Question 8
Questions on this exercise?

In my experience, 10-20% of the questions on
the exam were of this nature

Fast if you had the right references and knew where
to find the information
Hypothesis testing problems

Suppose you take dissolved oxygen (DO)
samples in a stream; the mean DO is 4.9 mg/l
and the standard deviation is 0.3 mg/l. Your
data sample consists of 8 samples. The minimal
DO level necessary in the stream is 5.0 mg/l.
Does your sample data meet this minimal
standard? Use standard hypothesis testing
conditions.
Hypothesis testing question

You took a second set of samples (same
location) at the same stream a month later. This
time, your data show a mean DO level of 5.2
mg/l with a standard deviation of 0.5 mg/l. This
data set also has 8 samples. Complete a
hypothesis test to show if the DO levels in the
stream are different (between last month and
this month). Use standard hypothesis testing
conditions.