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STATISTICAL SAMPLING
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SAMPLING TEST PLAN - SAMPLE SIZE
IF YOUR SAMPLE TEST PLAN IS: Population Size: Sampling Error: Confidence Level: Expected (true) Error Rate: THEN THE SAMPLE SIZE SHOULD BE:
0 2.0% 90% 5.0%
323
SAMPLING TEST PLAN - SAMPLING ERROR
IF YOUR SAMPLE TEST PLAN IS: Population Size: Sample Size: Confidence Level: Expected (true) Error Rate: THEN THE SAMPLING ERROR WILL BE:
10,000 313 90% 5.0%
2.0%
SAMPLE SIZE CALCULATION - DOLLAR UNITS
IF YOUR SAMPLE TEST PLAN IS: Population Book Value: Maximum Allowable Error: Confidence Level: Expected or Actual Number of Errors: THEN THE SAMPLE SIZE SHOULD BE:
250,000.00 5.0% 95% 0
Required Maximum Tolerable Error Auditor Will Accept in Pop. 90%, 95% or 99% Max = 20 Random Samples Only
60
SAMPLE SIZE CALCULATION - DOLLAR UNITS
Maximum Tolerable Error Auditor Will Accept in Pop.
UPPER CONFIDENCE BOUND FOR MEAN ERROR - DOLLAR UNITS
IF YOUR SAMPLE TEST PLAN IS: Population Book Value: Sample Size: Confidence Level: Number of Dollar Unit Errors: A/R or INV?: UPPER BOUND OF ERROR WILL BE:
250,000.00 60
95%
Required Dollar Units - Random Samples Only '90%, 95% or 99% Max = 100 Enter "A/R" or "INV" Maximum Tolerable Error Acceptable to Auditor
0
A/R
4.92%
ERROR TAINTING VALUES
UPPER CONFIDENCE BOUND FOR MEAN ERROR - DOLLAR UNITS
UPPER CONFIDENCE BOUND FOR MEAN ERROR - DOLLAR UNITS
CONCEPTS
DEFINITIONS
Appraisal of sample results is necessary to determine the sampling precision achieved. This is because in order to calculate the sample size it was necessary for the auditor to estimate the rate of occurrence (expected error rate) in the field. Acceptance Sampling - A method of sampling in which if for a given sample size, if not more than a certain number of errors is found, then the population is considered acceptable, otherwise the population is rejected. Attributes Sampling - Estimation sampling that establishes the frequency of occurrence of some kind of event 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 fact depart 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 of assurance that at least one occurrence of a particular event will occur in the sample when it happens with at 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 the true rate of occurrence of the event (error) in the population being tested. This is the expected error rate anticipated 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 auditor can be comfortable. It is the sum of the expected universe error rate and the upper limit of the sampling precision. Multistage Sample - A sample taken on several levels, i.e., a random sample of branch offices and then a random sample of records at each branch selected. Population - The totality of observations from which the sample was drawn. Otherwise known as universe 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 the sample result. Denotes the degree to which the sample result (statistic) reflects the true population parameter (e.g., error rate). Standard Deviation - A measure of the dispersion of values about the arithmetic mean, specifically the average of the distance of all values from the arithmetic mean. Statistic - The value of the characteristic (average, percentage, proportion of some type, etc.) derived from the sample. Statistical Sampling - A sampling method that establishes the required sample size objectvely as well as appraises the sample results objectively. The sample taken is referred to as a probability or random sample. Stratefied Random Sample - Items are segregated into separate segments (or strata) of the population and 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 item beginning 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.
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STANDARD DEVIATION CALCULATION
Standard Deviation is:
#DIV/0!
RANDOM NUMBER LIST
366 710 415 988 794 106 653 864 997 406 534 80 799 12 861 533 746 602 75 385 729 850 413 791 820 606 158 199 599 84 110 205 530 506 113 843 103 500 517 848 992 15 846 95 775 85 395 880 428 713 80 142 333 95 84 776 868 957 294 438 643 736 967 104 869 985 995 596 126 923 931 653 138 707 446 922 940 137 590 793 759 319 754 302 424 524 667 24 191 960 482 220 888 872 23 709 993 836 133 372 989 260 882 101 457 813 882 672 462 212 246 992 949 662 901 595 88 133 933 605 464 842 324 888 147 721 475 215 686 827 397 677 372 314 940 193 279 689 486 589 930 512 560 615 592 789 733 647 594 777 291 805 903 609 393 730 423 304 948 251 987 121 667 168 443 127 600 399 526 356 777 111 838 563 446 732 97 603 549 763 572 900 506 624 906 973 612 599 634 904 393 664 72 848 474 354 405 592 759 48 135 204 657 83 90 979 551 353 584 616 504 680 159 171 516 399 12 848 701 215 303 20 964 453 356 725 442 852 431 45 252 47 978 633 861 112 563 22 865 249 966 360 205 502 560 120 653 88 510 959 712 344 224 56 456 929 248 851 767 620 766 823 228 839 149 300 529 491 230 493 905 551 30 126 803 36 421 384 111 322 861 330 528 524 208 640 124 759 937 977 402 255 976 538 286 932 937 854 264 43 885 167 272 858 936 636 728 802 710 271 6 915 808 292 472 653 393 398 337 361 372 360 439 167 140 348 561 465 753 618 84 116 478 61 101 244 506 575 265 784 871 966 822 148 868 309 838 165 945 491 443 130 633 235 849 59 569 420 590 978 553 96 975 872 75 670 4 165 102 464 309 512 270 393 559 911 320 440 239 693 42 131 356 125 510 588 981 484 524 1 639 438 588 968 417 776 931 254 380 291 55 348 489 26 644 550 315 617 3 22 926 962 673 642 829 811 341 144 592 595 791 157 314 898 492 194 517 671 759 626 928 629 583 274 17 60 134 538 721 749 54 750 91 768 826 264 330 535 344 799 742 640 634 529 140 434 574 375 210 354 911 547 808 827 412 794 35 279 277 415 557 968 710 902 783 137 236 789 280 561 785 946 372 415 20 720 295 39 260 634 793 13 789 123 849 888 183 21 330 371 107 778 241 329 239 678 632 282 327 882 527 677 350 706 841 769 167 750 396 726 310 260 427 678 948 325 806 247 461 31 123 725 121 824 321 275 62 642 736 273 30 563 470 554 166 694 314 802 890 95 590 990 19 283 970 892 934 333 486 111 126 91 455 124 319 143 903 385 464 720 768 31 456 173 223 238 959 501 6 533 818 668 511 630 631 476 733 942 152 536 165 955 504 407 527 439 595 331 648 66 690 649 428 411 17 866 550 821 390 990 290 891 229 850 750 789 220 179 700 859 864 742 192 267 132 525 37 32 934 771 677 323 244 849 155 277 93 121 489 159 188 684 265 536 141 655 807 510 75 480 566 830 728 417 851 817 615 115 217 477 739 320 190 876 114 724 245 119 113 894
RANDOM NUMBER LIST
618 373 361 490 154 479 284 983 404 717 18 704 728 632 250 951 857 344 638 527 399 485 555 769 910 84 1 552 246 988 628 735 236 158 356 983 666 901 710 321 315 36 719 971 665 765 197 561 14 675 161 837 325 490 47 86 836 732 497 820 352 997 741 957 153 293 200 935 662 785 50 943 531 969 895 562 747 315 322 526 13 592 588 263 162 414 66 204 514 741 510 543 220 431 595 444 136 605 594 781 176 331 347 667 757 102 700 726 358 252 978 725 412 764 723 56 777 381 645 166 379 506 465 73 247 396 719 40 214 431 172 46 197 134 27 234 570 666 610 610 763 406 179 187 330 536 470 48 477 995 174 579 43 258 74 311 176 630 499 35 261 568 110 132 261 133 328 881 797 333 914 822 697 387 428 190 379 326 488 575 207 575 966 742 702 627 792 83 617 595 902 71 483 610 930 853 332 647 270 925 580 615 603 973 46 903 252 12 417 989 293 953 151 228 66 343 363 424 193 134 260 228 897 48 810 981 316 190 166 211 35 106 867 346 190 185 317 745 806 419 247 157 325 396 695 841 589 847 995 746 275 719 436 432 102 127 691 314 231 826 550 887 274 265 992 918 497 214 817 169 10 835 913 781 481 61 815 150 878 213 79 708 72 315 638 541 473 819 703 464 31 484 670 686 585 325 89 528 847 820 127 296 710 955 538 260 371 207 134 695 300 260 180 861 839 510 669 945 931 364 730 667 882 302 920 769 86 124 474 531 296 854 828 834 751 926 155 728 541 812
Sample Size Calculation - Variables Sample
IF YOUR SAMPLE TEST PLAN IS: Population Size (No. of values): Sampling Error (In dollars, days, etc.): Confidence Level: Estimated Standard Deviation THEN THE SAMPLE SIZE SHOULD BE:
0.00 10.00 95% 50.00
If unknown, enter 0. Range of error (+/-) of the sample result - keep it small. 90%, 95% or 99% Worst case population error rate expected. Random Samples Only
95
SAMPLING ERROR CALCULATION - VARIABLES SAMPLE
IF YOUR SAMPLE TEST PLAN IS: Population Size: Sample Size: Confidence Level: Estimated Standard Deviation: THEN THE SAMPLING ERROR WILL BE:
5,000.00 94 95% 50.00
If unknown, enter 0. Random Samples Only 90%, 95% or 99% From pilot sample of 50 items. Range of error (+/-) of the sample result - keep it small.
10.01
SAMPLE SIZE CALCULATION - DISCOVERY SAMPLE
IF YOUR SAMPLE TEST PLAN IS: Population Size: Level of Assurance: Rate of Occurrence: THEN THE SAMPLE SIZE SHOULD BE:
10,000
95%
Required - Amounts up to 50,000 90%, 95% or 99% Required - Up to 5% Random Samples Only
3.0% 99