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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 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 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) 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 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 Measures of dispersion 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 xm s Normal distribution: review Symmetrical distribution with mean m and standard deviation s Area under curve represents 100% of possibilities 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 xm 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 xm s x m z s n Confidence intervals 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?” 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 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: 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 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) Tabulated in the ME reference manual, A-132-150 or CE manual A-112130 Types of problems in engineering economic analysis 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) 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 (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 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 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 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 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 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.