Ag engineering PE review: Exam prep, I-C economics and statistics

1. 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: mlima1@lsu.edu

2. Overview • Exam preparation • Statistics • Economic analysis • Throughout: • You will be doing PE style problems (have your references and calculators ready!) • Ask questions

3. Part 1: Exam preparation • References (must have) • Time (in preparing for exam and during exam) • Strategies (preparation and test taking)

4. 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/career-resourcespe-licensure/pei.aspx • Some references are more useful than others

5. 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.

6. 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)

7. 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

8. 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.)

9. 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)

10. 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)

11. 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)

12. 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

13. Statistics basics • Measures of central tendency • Mean, median, mode • Measures of dispersion • 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

14. 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

15. 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

16. Reading the z-chart

17. 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?

18. Solution

19. In what range would you find the middle 70% of the data? (pick closest z value, do not interpolate)

20. Solution

21. You try this one: • 90% of college students have heights greater than what value?

22. Solution

23. 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

24. 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.

25. Solution

26. 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? • Is the test one tailed (where directionality matters) or two tailed (when only difference between values matters)

27. 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)

28. Reading a t chart

29. 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?

30. 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

31. 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?

32. 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

33. Acceptance/rejection region

34. Calculate the test statistic

35. 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

36. Drawing

37. 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)

38. 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

39. 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-112-130 • 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)

40. Engineering econ • Almost all engineering econ problems will involve cashflows; it is like a material balance using money instead of mass. • Types of cash flows: • Single payment cash flows (P or F) • P = present value of money • F = future value of money • 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) • 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

41. Engineering econ • Cash flow problems can be calculated using equations or are tabulated for fast problem solving

42. 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

43. 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.

44. 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

45. Engineering econ

46. Engineering econ • Example solve by interest table: • Go to F/P column with n = 5, for table with i = 6%: Factor = 1.3382 • F = ($1000) 1.3382 = $1338.2

47. 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)

48. Engineering econ

49. 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

50. 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: