Sectio. True or False Questios (2 pts each). For a populatio the meas is defied as i= μ = i but for a small sample of the populatio, the mea is defied as: = i= i 2. For a logormal distributio, the media equals the mea. 3. If the media equals the mea, the data must be ormally distributed. 4. The stadard error is always bigger tha the stadard deviatio. 5. A r 2 value of.85 always idicates that the correlatio is statistically sigificat. 6. A systematic error ca lead to bias i the data. 7. Precisio depeds o the magitudes of both systematic ad radom errors. ( /4)
Sectio 2. Multiple choice questios: circle all correct aswers. (3 pts each) 8. Circle all that are true or correct. a. The total error equals the square root of the sums of the squares of the systematic ad radom errors; b. The total error equals the product of the systematic ad radom errors; c. The total error equals the sum of the systematic ad radom errors; d. The total error equals the larger of the systematic ad radom errors; e. Noe of the above; 9. Circle all that are true or correct. a. The COV is the costraits o variatio; b. The COV is the coefficiet of veracular; c. The COV is the coefficiet of variatio; d. The COV equals the stadard deviatio divided by the mea; e. Noe of the above.. Circle all that are true or correct. a. Radom errors are predictable; b. I a large sample, radom errors are likely to be ormally distributed; c. All radom errors are beyod the cotrol of the data collector; d. Radom errors occur relatively seldom; e. Radom errors are likely i all data sets.. Circle all that are true or correct. a. Accurate implies freedom from all errors; b. Accurate implies freedom from radom errors; c. Accurate implies freedom from systematic errors; d. Accurate implies freedom from bias; e. Accurate implies highly precise. 2. Circle all that are true or correct. a. High precisio implies that all errors are small; b. High precisio implies that radom errors are small; c. High precisio implies that systematic errors are small; d. High precisio implies that bias is small; e. High precisio implies high accuracy. ( /5) 2
Sectio 3. Short-aswer questios 3. The results of 7 replicate measuremets of Mied Liquor Volatile Solids (MLVS) cocetratios are show i the graph below. The idividual measuremets are show as black circles; the mea is show as a hollow bo, ad the error bars represet S.D. You wish to determie whether the highest value should be cosidered a outlier. MLVS (mg/l) 8 6 4 2 8 6 4 2 a. What is the criterio that you would use to determie if poit 7 (the highest value) should be regarded as a outlier? (5 pts) b. Based o the data tabulated below, is the highest poit a outlier? Show all calculatios. (8 pts) Group MLVS (mg/l) Mea ( to i ) S.D. ( to i ) 865 865 NA 2 956 9 64 3 46 956 9 4 87 989 99 5 39 9 9 6 372 78 74 7 585 5 249 --------------------------------------------------------------------------------------------- ( /3) 3
4. A histogram of all of the idividual measuremets of mied liquor suspeded solids cocetratios is show below. You wish to determie if the data are ormally distributed. Number of measuremets 4 3 2 5 7 9 3 5 7 9 2 23 25 MLSS (mg/l) You costruct a probability plot (show below) to help determie if the data are ormally distributed. Q (i) or Normal MLSS (mg/l) 25 2 5 5 y =.97 + 49.98 R 2 =.95 5 5 2 25 MLSS (mg/l) a. What should the slope of the regressio lie i the probability plot be if the data are ormally distributed? (4 pts) a..5 b..75 c.. d..25 e. There is o fied value that the slope should have f. Caot tell from the iformatio give b. What two criteria must the probability plot meet for you to decide that the data are ormally distributed? (2 pts each). 2. ( /8) 4
5. List four tests that you ca apply to determie if a set of data is ormally distributed. (8 pts). 2. 3. 4. 6. The results from your measuremets of SRP i the ifluet to the wastewater treatmet plat are tabulated below. Ca you say with 95% cofidece that the mea is less tha 4. mg/l? Eplai ad show clearly the basis for your aswer. (5 pts) Coc (mgp/l) 3.7 2.27 2.24 3.26 3.36 3.25 2.87 3. 6.8 Mea 3.3 S.D..6 N 9 ( /23) 5
7. The historical record for aual sowfall i Houghto Couty is show below. Output from a regressio aalysis i ecel is show below the graph. Base your aswers to the followig questios o either the graph or the regressio aalysis. Yearly Sowfall for Houghto, MI (Oct-May) Sowfall (i) 4 35 3 25 2 5 5 88 9 92 94 96 98 2 22 Year Regressio Statistics Multiple R.652 R Square.425 Adjusted R Squ.42 Stadard Error 44.48 Observatios 7 ANOVA df SS MS F igificace F Regressio 68456 68456 85.443.64E-5 Residual 5 227524 978 Total 6 39598 Coefficietstadard Erro t Stat P-value Lower 95%Upper 95% Itercept -24 237-8.48685 8.47E-4-2484 -544 X Variable.2.2 9.23.64E-5.88.37 a. Based o the statistics table provided, is the tred toward icreasig sowfall statistically sigificat? Eplai the basis for your aswer. ( pts) b. Is the rate of icrease i aual sowfall sigificatly differet from zero? Eplai the basis for your aswer. (8 pts) c. Based o the regressio, how may iches of sow do you predict will fall i 225? (4 pts) d. What is the error (iches) i your predictio? (5 pts) 6
EQUATIONS X i i = = σ = ( ) 2 i SE = σ CI = t να, s ε = ε + ε 2 2 2 total radom systematic t t k j = t k + = j j t = ( φφ ) t j j= S DL = mi mi Bl m S = Bl+ K s Bl MDL = t s να, m f( ) = e σ 2π ( μ ) 2 2 2σ 2 2 2 2 2 2 2 = a + b + c ε ε ε ε a b c P= + zi s UTL = + ki s k = tνα, i + 7
Pearso Product-Momet Correlatio Coefficiet Table of Critical Values df= N-2 Level of sigificace for two-tailed test N = umber of pairs of data..5.2..988.997.9995.9999 2.9.95.98.99 3.85.878.934.959 4.729.8.882.97 5.669.754.833.874 6.622.77.789.834 7.582.666.75.798 8.549.632.76.765 9.52.62.685.735.497.576.658.78.476.553.634.684 2.458.532.62.66 3.44.54.592.64 4.426.497.574.628 5.42.482.558.66 6.4.468.542.59 7.389.456.528.575 8.378.444.56.56 9.369.433.53.549 2.36.423.492.537 2.352.43.482.526 22.344.44.472.55 23.337.396.462.55 24.33.388.453.495 25.323.38.445.487 26.37.374.437.479 27.3.367.43.47 28.36.36.423.463 29.3.355.46.456 3.296.349.49.449 35.275.325.38.48 4.257.34.358.393 5.23.273.322.354 6.2.25.295.325 7.95.232.274.32 8.83.27.256.284 9.73.25.242.267.64.95.23.254 5.78.234 8
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