lab_handout_Treatment of Analytical Data

lab_handout_Treatment of Analytical Data -...

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C v n a, In“ . .; ’1 '— ‘- ‘M pm,» (4 <5‘ I /\/ I \/I \ X l \3 AREAS OF THE STANDARD NORMAL DENSITY FUNCTION 1 Q A(z)13 THE AREA UNDER THE CURVE BETWEEN 0 AND 2 ' 2 21(2) 2 A(Z) z A(Z) 2 A(Z) z A(Z) z A(2) 2 A(z) .00 .0000 .60 .2257 1.20 .3349 1 60 .4641 2.40 .4913 3.00 4967 3.60 .4993 .01 .0040 .61 .2291 1.21 .3669 1 11 .4643 2.41 .4920 3.01 4967 3 61 .4993 .02 .0030 .62 .2324 1.22 .3333 1.32 .4656 2.42 .4922 3.02 .4967 3.62 .4999 i .03 .0120 .63 .2357 1.23 .3907 1.93 .4664 2.43 .4926 3.03 .4936 3 63 .4999 i .04 .0160 .64 .2339 1.24 .3925 1.34 .4671 2.44 .4927 3.04 .4963 3.64 .4999 , . .05 .0199 .65 .2422 1.25 .3944 1.65 .4373 2.45 .4929 3.05 .4939 3.65 .4999 - .06 .0239 .66 .2454 1.26 .3962 1.66 .4636 2.46 .4931 3.06 .4939 3.63 .4999 5 .07 .0279 .67 .2436 1.27 .3930 1.37 .4693 2. 47 4932 3.07 . 4969 3. 67 . 4999 .08 .0319 .66 .2517 1.26 .3997 1.36 .4700 2.43 4934 3.03 .4990 3. 66 .4999 - .09 .0359 .69 .2549 1.29 .4015 1.39 .4706 2. 49 4936 3. 09 .4990 3. 69 . 4999 .10 .0393 .70 .2560 1.30 .4032 1.90 .4713 2.50 .4933 3 10 .4990 3 70 .4999 _ .11 .0433 .71 .2311 1.31 .4049 1.91 .4719 2.51 .4940 3.11 .4991 3.71 .4999 .12 .0473 .72 .2642 1. 32 .4066 1. 92 .4726 2. 52 .4941 3.12 .4991 3. 72 . 4999 .13 1051710524 .73 .2673 1.33 .4032 1.93 .4732 2.53 .4943 3 13 .4991 3.73 .4999 .14 ,.0557l/" .74 .2703 1.34 .4099 1.94 .4733 2.54 .4945 3 14 .4992 3.74 .4999 i .15 .0596 .75 .2734 1.35 .4115 1.95 .4744 2.55 4946 3.15 4992 3.75 .4999 . .16 .0636 .76 .2734 1.36 .4131 1.96 .4750 2.56 .4943 3 16 4992 3.76 .4999 : .17 .0675 .77 .2794 1.37 .4147 1.97 .4756 2.57 .4949 3 17 4992 3.77 .4999 .13 .0714 .76 .2323 1.33 .4162 1.96 .4762 2 53 4951 3 13 4993 3.73 .4999 .19 .0753 .79 .2352 1.39 .4177 1.99 .4767 2 59 4952 3 19 4993 3 79 .4999 . .20 .0793 .30 .2361 1. 40 .4192 2.00 .4772 2. 60 .4953 3. 20 .4993 3. 60 . 4999 ' .21 .0332 .31 .2910 1.41 .4207 2.01 .4773 2.61 .4955 3.21 .4993 3.31 .4999 = .22 .0371 .32 .2939 1.42 .4222 2.02 .4733 2.62 .4956 3.22 .4994 3.32 .4999 . g .23 .0910 .63 .2967 1.43 .4236 2.03 .4763 2.63 .4957 3.23 .4994 3.33 .4999 ~ - .24 .0943 .64 .2995 1.44 .4251 2.54 .4793 2.64 .4959 3.24 .4994 3.34 .4999 g .25 .0937 .85 .3023 1.45 .4265 2.05 . 4793 2. 65 .4960 3. 25 . 4994 3. 65 . 4999 .26 .1026 .86 .3051 v 1.46 .4273 2.06 .4303 2.66 .4961 3.26 .4994 3.36 .4999 .27 .1064 .37 .3073 1.47 .4292 2. 07 .4303 2. 67 .4962 3. 27 .4995 3. 37 . 4999 .26 .1103 .33 .3106 1.46 .4306 2.01 .4312 2.63 .4963 3.23 .4995 3.33 .4999 .29 .1141 .39 .3133 1.49 .4319 2.09 .4317 2.39 .4964 3.29 .4995 3.39 .5000 ./“‘ .30 .1179 .90 .3159 1.50 (.4332) 2.10 .4321 ‘ 2.70 .4965 3. 30 .4995 3.90 .5000 ‘ .31 .1217 .91 .3186 1.51 .4345 2 11 .4326 2.71 .4966 3.31 .4995 3.91 .5000 i .32 .1255 .92 .3212 1. 52 .4357 2.12 .4330 2. 72 .4967 3. 32 .4996 3. 92 . 5000 1 .33 .1293 .93 .3233 1.53 .4370 2.13 .4634 2.73 .4966 3.33 .4996 3.93 .5000 .34 .1331 .94 .3264 1.54 .4332 2.14 .4333 2.74 .4969 3.34 .4996 ‘ 3.94 .5000 .35 .1366 .95 .3239 1.55 .4394 2.15 .4642 2.75 .4970 3.35 .4996 3.95 .5000 .36 .1406 .96 .3315 1.56 .4406 2.16 .4346 2.76 .4971 3.36 .4996 3.96 .5000 .37 .1443 .97 .3340 1. 57 .4413 2.17 .4350 2.77 .4972 3. 37 .4996 3.97 .5000 * .33 .1460 .93 .3365 1.53 .4430 2.13 .4354 2.73 .4973 3.36 .4996 3.93 .5000 .39 .1617 .99 .3339 1.59 .4441 2.19 .4357 2.79 .4974 3.39 .4996 3.99 .5000 .40 «1554) 1.00 .3413 1.60 .4452 2.20 .4361 2.30 .4974 3.40 .4997 4.00 .5000 ; .41 .1591 1.01 .3436 1.61 .4463 2.21 .4664 2.61 ,4975 3.41 .4997 s .42 .1623 1.02 .3461 1.62 .4474 2.22 .4363 2.32 .4976 3.42 .4997 . .43 .1664 1.03 .3465 1.63 .4434 2.23 .4371 2.33 .4977 3.43 .4997 I .44 .1700 1.04 .3506 1.64 .4495 2.24 .4374 2.34 .4977 3.44 .4997 4 1i 1 0'0.“ .45 .1736 1.05 .3531 1.65 .4506 2.25 .4676 2.35 .4973 3.45 4997 .46 .1772 1.06 .3554 1.66 .4515 2.26 .4331 2.36 .4979 3.46 4997 .47 .1603 1.07 .3577 1. 67 .4525 2. 27 .4334 2. 37 .4979 3. 47 4997 .46 .1344 1. 03 .3599 1.63 .4535 2. 23 .4637 2. 63 .4930 3. 43 .4997 e .49 .1379 1.09 .3621 1.69 .4545 2.29 .4390 2.69 .4931 3.49 .4993 i (50 .1915. 1.10 .3643 1.70 .4554 2. 30 .4693 2.90 .4931 3. 50 . 4996 ' .51 ''' ":1950 1.11 .3666 1.71 .4564 2.31 .4396 2.91 .4932 3.51 .4993 .52 .1935 1.12 .3666 1. 72 .4573 2. 32 .4393 2. 92 . 4962 3. 52 . 4996 .53 .2019 1.13 .3703 1.73 .4532 2 33 .4901 2.93 .4933 3.53 .4993 .64 .2054 1.14 .3729 1. 74 .4591 2. 34 .4904 2. 94 .4934 3. 54 .4996 .65 .2066 1.15 .3749 1.75 .4599 2.35 .4906 2.95 .4934 3.55 .4993 .56 .2123 1.16 .3770 1. 76 .4606 2. 36 .4909 2.96 .4965 3. 56 .4996 .57 .2157 1.17 .3790 1.77 .4616 2. :7 .4911 2.97 .4935 3.57 .4996 .53 .2190 1.16 .3610 1.73 .4625 2.36 .4913 2.93 .4936 3.53 .4996 . .59 .2224 1.19 .3630 1.79 .4633 2. 3 .4916 2.99 .4936 3.59 .4993 1 P l ( \1 22‘ +VZw/.z \«l ' ..__-—_..'_._....__.._._..- “C” Degrees of \ Freedom / 120 / E 31W VALUES OF ta FOR GIVEN PROBABILITY VALUES TABLE II D—‘HO—‘HH HHI—‘I—‘H HHHHH HHHHH HHHHH .44 .42 .40 .38 .37 .36 .36 .35 .34 .34 .34 .33 .33 .33 .32 .32 .32 .32 .32 .32 .32 .31 .31 .31 .31 .30 .30 .29 HI—al-dr-I HHHHH HHHHH HHHHH NMNNO} HHHHH .05 .31 .92 .35 .13 .01 .94 .90 .86 .83 .81 .80 .78 .77 .76 .75 .75 .74 .73 .73 .73 .72 .72 .71 .71 .71 .71 .70 .70 .70 .70 .6'8, .67 .66 NMNNN mommies; NpMNN :31 .26 .23 .20 .18 .16 .14 .13 .12 .11 .10 .09 .09 .07 .07 .06 .06 . 06 .- 05 . 05 . 04 . 04 .02 .00 .08. Probability of a value larger than t a .01 31.82 6.96 4.54 3.75 3.36 .14 .00 .90 .82 .76 NNNWOD .72 .68 .65 .62 .60 NNNNN .58 .57 .55 .54 .53 .52 .51 .50 .49 .48 'wamm NNNNN .48 .47 .47 .46 .46 NNNNN b3 .42 NNNNN NNNNN NIX)me 0309000300 NNNNN common» .ayp-azp.:> o .4 0300000393 4 .q 0305000000 0') 4 03 01 U1 Propagation of Error Summary Propagation Rule Table 5. 5~ The above expressions assume that C and D are constants, M, M1, and M2 are measure- ments with error 0 M, R is the result with error 0 R, and the relative error is 6, 2.9. 6R=0R/R. SQ, Qéaaa ...
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