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8/13/2019 Stats Amp

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ST TISTIC L S MPLING

8/13/2019 Stats Amp


SAMPLING TEST PLAN - SAMPLE SIZE

IF YOUR SAMPLE TEST PLAN IS:Population Size: 10,000Sampling Error: 2.0%

Confidence Level: 90%Expected (true) Error Rate: 5.0%

THEN THE SAMPLE SIZE SHOULD BE: 313

8/13/2019 Stats Amp


SAMPLING TEST PLAN - SAMPLING ERROR

IF YOUR SAMPLE TEST PLAN IS:Population Size: 10,000

Sample Size: 313Confidence Level: 90%

Expected (true) Error Rate: 5.0%

THEN THE SAMPLING ERROR WILL BE: 2.0%

8/13/2019 Stats Amp


SAMPLE SIZE CALCULATION - DOLLAR UNITS

IF YOUR SAMPLE TEST PLAN IS:Population Book Value: 250,000.00 Required

Maximum Allowable Error: 5.0% Maximum Tolerable Error Auditor Will Accept in Pop.

Confidence Level: 95% 90%, 95% or 99% Expected or Actual Number of Errors: 0 Max = 20

THEN THE SAMPLE SIZE SHOULD BE: 60 Random Samples Only

8/13/2019 Stats Amp


SAMPLE SIZE CALCULATION - DOLLAR UNITS

8/13/2019 Stats Amp


UPPER CONFIDENCE BOUND FOR MEAN ERROR - DOLLAR UNITS

IF YOUR SAMPLE TEST PLAN IS: Population Book Value: 250,000.00 Required

Sample Size: 60 Dollar Units - Random Samples Only

Confidence Level: 95% '90%, 95% or 99%

Number of Dollar Unit Errors: 0 Max = 100

A/R or INV?: A/R Enter "A/R" or "INV"

UPPER BOUND OF ERROR WILL BE: 4.92% Maximum Tolerable Error Acceptable to Auditor

ERRORTAINTINGVALUES

8/13/2019 Stats Amp



8/13/2019 Stats Amp


CONCEPTS

DEFINITIONS Appraisal of sample results is necessary to determine the sampling precision achieved. This isbecause in order to calculate the sample size it was necessary for the auditor to estimate the rate ofoccurrence (expected error rate) in the field.

Acceptance Sampling - A method of sampling in which if for a given sample size, if not more than acertain number of errors is found, then the population is considered acceptable, otherwise the populationis rejected.Attributes Sampling - Estimation sampling that establishes the frequency of occurrence of some kind ofevent or type of item.

Cluster Sample - Groups of items (not individual items) are drawn from the population at random points.Confidence Level - The probability (expressed in %) that the value obtained from the sample will in factdepart from the true population value by no more than the amount of the sample precision.Discovery Sampling - Used to determine the sample size which will give any desired degree ofassurance that at least one occurrence of a particular event will occur in the sample when it happens withat least a certain frequency in the population.

Estimation Sampling - Used to answer the question of how many or how much.Expected Error Rate - In Attribute Sampling, used in calculating sample size. Auditor's estimate of thetrue rate of occurrence of the event (error) in the population being tested. This is the expected error rateanticipated by the auditor.Judgment Sample - Any sample not meeting the criteria of a probability sample.Maximum Tolerable Error Rate - The maximum true rate of error in the universe with which the auditorcan be comfortable. It is the sum of the expected universe error rate and the upper limit of the samplingprecision.Multistage Sample - A sample taken on several levels, i.e., a random sample of branch offices and thena random sample of records at each branch selected.Population - The totality of observations from which the sample was drawn. Otherwise known asuniverse or field.Sample - The observations drawn from the entire group.Sample Precision - Error in a statistical sample. Usually expressed as a +/- percentage in relation to thesample result. Denotes the degree to which the sample result (statistic) reflects the true populationparameter (e.g., error rate).Standard Deviation - A measure of the dispersion of values about the arithmetic mean, specifically theaverage of the distance of all values from the arithmetic mean.Statistic - The value of the characteristic (average, percentage, proportion of some type, etc.) derivedfrom the sample.Statistical Sampling - A sampling method that establishes the required sample size objectvely as well asappraises the sample results objectively. The sample taken is referred to as a probability or randomsample.Stratefied Random Sample - Items are segregated into separate segments (or strata) of the populationand any item within a segment has an equal probability of being selected.

Systematic Sampling - A method of obtaining a probability sample consisting of drawing every n th itembeginning with a random start. Otherwise known as interval sampling.Unrestricted Random Sample - All items in the population have an equal probability of being selected,without segregating any portion of the field.Variables Sampling - Estimation sampling that provides an estimate of an average or total value.

8/13/2019 Stats Amp


STANDARD DEVIATION CALCULATION

Standard Deviation is: #DIV/0!

8/13/2019 Stats Amp


RANDOM NUMBER LIST

579016 587307 563650 527223 593084 588825 500406 548089 520013 520192561582 520226 561423 595699 577272 551857 505044 523232 571555 572384536471 597970 565805 577823 575004 578732 592867 561892 590290 538157525804 504342 502485 553080 518911 546484 535269 525727 596604 516170534284 578082 573435 540266 527273 556884 598976 524683 551338 519888504020 560826 521224 597365 500900 510088 531453 536762 558087 561758509652 550678 513127 576754 542673 518538 530049 541646 591389 561250543206 568704 560098 558424 580999 564961 557162 594365 522793 536757523137 551212 591381 550459 532713 510163 540179 583283 521605 533117540644 526250 593582 526409 526038 563135 515032 558231 558966 568506554398 596158 500564 529062 537902 583236 532051 579136 501773 569208559598 587101 514109 517819 547398 554293 598453 554623 557979 506787505863 546417 596948 580954 564558 531661 558512 529921 563584 509556512049 564805 578197 560463 577843 588439 505984 522904 598980 506510507165 563311 558366 594864 537126 501164 564412 510910 515873 576575544686 536896 501699 576174 585820 512418 502536 541931 588415 522314552164 587820 550021 519637 572458 556575 559299 582640 571224 519827531736 563209 551084 558229 513322 545315 538059 535378 515753 512095551197 532241 565561 579853 565052 528696 547357 563053 581552 596413

544681 553491 557433 501629 558695 500554 514180 562261 561391 527595543729 552574 551391 558564 562521 545551 504575 595995 552154 589808548776 587205 521091 523392 521395 543461 534960 548236 595825 578360581434 575383 583340 570815 505421 525663 540235 584782 505158 543435521950 522021 552365 552564 519611 598887 548708 572750 596056 524639564795 551527 587480 516841 559659 557480 561975 501312 546899 589634511896 543097 593485 586272 546189 599042 554138 521239 532367 513157584234 544256 510319 544096 547975 585530 563575 578340 526327 540868554728 569406 526838 503736 555608 542931 531180 509291 512835 581623593015 585886 580722 595952 554412 565912 565477 552281 580822 545432556940 571432 596789 527896 581189 535070 547944 521195 504510 554472547792 514128 552752 597520 569160 503463 547060 592582 524491 530766543747 541115 585822 589855 575349 544758 573441 509807 551590 554186560146 593537 575841 599217 572424 503409 530815 561262 588996 553706577052 504531 584727 525099 574023 500740 521814 509062 582873 517116

522720 559832 505765 544063 568192 538865 541427 513856 598198 587441573567 535566 592804 500642 590969 564391 549370 551246 563053 594979541055 573817 549037 521485 534134 536953 530558 532595 590092 591083518694 563655 597931 552371 504654 582493 579602 569568 584399 524250586005 551593 569821 583715 556125 554078 550402 559721 515937 562225573381 573786 566730 594203 564804 554526 512629 598231 509434 519004510822 523086 567684 543128 556256 578038 558341 540649 554283 535377537359 572959 540424 589022 565140 533250 556436 586008 549809 584899531176 564790 533049 591047 533874 596327 593007 565952 591149 546808587881 564572 529491 509750 583831 522235 584279 514271 581057 555444547034 543526 540042 539857 522073 572803 526647 588623 544006 519547556591 522154 595056 504917 554797 569092 525248 564502 560793 566971521281 565670 574234 510520 586113 571741 529708 580423 596469 526870548090 507304 542174 504787 549003 588532 536375 525096 529536 507628568693 597583 577464 518135 522272 528539 539017 526708 557654 528531520062 573127 569050 515313 579701 551509 528791 563287 561225 568410576110 584214 512195 520906 567721 539992 523343 570588 598553 569319551067 513627 580784 511501 544305 597285 553902 538598 507099 572795574730 572707 584884 532702 582665 589955 598632 593694 533769 519330544468 584227 554982 572301 539055 564690 549352 506427 582618 583197564204 564707 565419 597583 581735 547748 598722 510724 579037 567917510461 565975 504424 595595 505801 504617 561034 555359 534946 519202505822 583061 529194 576936 516575 588508 550752 583157 547870 550032502442 592909 578401 507330 567507 533221 572335 501345 572644 588119582196 549025 570947 539147 595990 590118 544112 534904 511721 521971587876 597409 508566 528260 510465 596268 522602 551286 531064 599104531197 534849 579415 557095 550763 583488 546552 563273 539689 521441542411 544671 581899 504247 556515 501347 515274 559924 509552 578460517862 537155 544081 503097 546657 530327 534555 552978 530518 587512509396 562866 581443 583756 581655 595479 577044 523711 516199 590564538732 555014 508718 582554 561168 572975 584826 569535 543621 594581

591998 574410 525953 579705 594160 542398 510463 502690 530810 541954524343 506476 552936 514062 545992 586400 595996 507716 574271 541786

8/13/2019 Stats Amp


RANDOM NUMBER LIST

534573 556123 549008 587979 565422 528499 559027 569798 548211 541780567844 530905 569313 565299 533915 585485 544636 571226 511837 593572528694 502240 503050 560430 530087 599918 543931 563833 576095 575935575932 546891 569430 518610 510130 577442 503740 513278 530754 589048562882 508659 557928 521383 519266 551796 511659 551216 530722 524124539894 568912 599715 505012 595443 518344 533709 541619 554353 551826521286 533472 556854 543649 582694 552577 521276 501676 563763 513173572319 592742 556046 591314 599957 591255 597807 504938 517744 587733519277 577014 569381 564833 523580 580600 532572 576130 584879 585427543731 559589 598212 520418 515830 516603 544937 544981 520521 570008581004 565739 524582 582251 558270 502576 531483 583385 547643 565470571369 571556 597063 561557 591805 560493 534135 577964 574767 531695530259 501943 519413 522669 578557 587430 541263 531585 516177 543629599206 546734 535445 574213 587301 516636 569003 535138 593667 520719528496 542585 538127 569471 503520 593414 597272 528332 543450 575166595471 593545 583097 553042 562875 586656 599584 536560 549480 575570553961 505692 555864 578013 508773 592235 593748 577552 553771 585296521233 591821 579865 539169 534430 564585 580375 523491 589068 524188573713 503037 557827 595366 589215 525014 539764 504840 564740 585672

595439 582691 521311 548071 537728 529975 537111 570648 565761 593492549704 561359 520121 553039 535107 523605 569691 556464 557760 573854558620 599044 534815 507097 541823 559143 596282 512187 549498 586393548026 592445 509043 596239 561332 586269 500049 542563 541106 577041598926 561184 509462 582906 542682 570104 500270 515328 548452 530641567346 531887 588347 517337 505219 584747 547266 557673 561394 503544566283 500212 541259 594263 566935 516217 556750 584638 569421 573184547569 565261 573031 500837 593071 586688 552103 508572 541758 586971553368 568669 534479 575889 520216 515485 582323 538417 568572 563345521647 579200 512361 516893 547437 553583 542743 564517 560132 545248516974 519842 540101 542325 527938 502318 557235 515998 571191 549637520546 504307 520027 526658 557949 557054 562458 596974 570822 563242571422 567790 591758 574718 549916 569559 500611 597736 508106 557017529703 549905 567028 562505 531813 545655 518144 593707 598462 532928520729 545149 516875 533738 583436 512628 513243 526876 542089 568497

8/13/2019 Stats Amp


Sample Size Calculation - Variables Sample

IF YOUR SAMPLE TEST PLAN IS:Population Size (No. of values): 0.00 If unknown, enter 0.

Sampling Error (In dollars, days, etc.): 10.00 Range of error (+/-) of the sample result - keep it small.

Confidence Level: 95% 90%, 95% or 99% Estimated Standard Deviation 50.00 Worst case population error rate expected.


8/13/2019 Stats Amp


SAMPLING ERROR CALCULATION - VARIABLES SAMPLE

IF YOUR SAMPLE TEST PLAN IS:Population Size: 5,000.00 If unknown, enter 0.

Sample Size: 94 Random Samples Only

Confidence Level: 95% 90%, 95% or 99% Estimated Standard Deviation: 50.00 From pilot sample of 50 items.

THEN THE SAMPLING ERROR WILL BE: 10.01 Range of error (+/-) of the sample result - keep it small.

8/13/2019 Stats Amp


SAMPLE SIZE CALCULATION - DISCOVERY SAMPLE

IF YOUR SAMPLE TEST PLAN IS: Population Size: 10,000 Required - Amounts up to 50,000

Level of Assurance: 95% 90%, 95% or 99%Rate of Occurrence: 3.0% Required - Up to 5%


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