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### 36 Cards in this Set

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 Why do we use statistical sampling? to quantify risk -allows a measurement of degree of risk What are the 2 types of sampling? Attribute sampling (tests of controls, compliance) Variable sampling (substantive tests) Whats the first step in sampling? Define the population How many potential populations are there in a typical set of f/s? almost infinite What is the central limit theorem? The arithmetic means of all the samples drawn from the population would form a perfect normal curve What does "random" mean? every item in population must have an equal chance of being selected -one place where auditor judgment (bias) may not exist What is systematic sampling? randomly select a first item, and then select every Xth item after that weak form of randomness, if population has any order, misleading results Whats the strongest form of randomness? Get a random sample using a random number table What does variability increase? And what does it require? uncertainty, requires greater sample sizes How do you get the arithmetic mean? Audited sample value / sample size How do you calculate precision? # of Standard Deviations x Standard error of the mean = X x Population size = Precision What are the 3 different estimation types? Mean per unit estimation Ratio estimation Difference estimation What does stratifying do? Splits a highly variable population into 2 populations, reduces variablity in population -can use small sample size Why do you stratify? reduce variability, and use small sample sizes What is Alpha risk? f/s are correct in reality -sample says material error, so you modify opinion unncessarily -risk of incorrect rejection! What is Beta Risk? f/s are incorrect in reality -sample says correct, fail to modify opinion -risk of incorrect acceptance What is the relationship between variability and sample size? Direct Smaller the variability, smaller the sample size Greater the variability, larger the sample size What is the relationship between tolerable misstatement and sample size? Inverse relationship -smaller the tolerable misstatement, the larger the sample size -greater the tolerable misstatement, the smaller the sample size What is Alpha Risk in relation to Attribute sampling? -Internal control is effective -Sample says material weaknesses, so assess control risk too hight -risk of under-reliance, end up with too much substantive testing What is beta risk in relation to attribute sampling? Internal control is not effective -Sample says no material weaknesses, assess control risk too low -risk of over-reliance, effect is too little substantive testing What is the relatinoship between expected deviation rate and sample size? Direct -high expected deviation rate, high large sample -low, small sample What is ther relationship between Tolerable Error Rate and sample size INVERSE -high tolerable error, small sample -low tolerable error, large sample What is Discovery Sampling? -type of attribute sampling -predetermined probability of discovering one item, use with critical items -expect error rate to be very low What is PPS Sampling? Probability-proportional-to size -uses attribute sampling tables to assist in sampling variables How do you get a sampling interval? Tolerable misstatement / reliability factor = sampling interval How do you get a sample size? Population value / Samplng interval = sample size What are the advantages of PPS sampling? -easier than other methods -automatic stratification: larger value items have a higher chance to be selected -sample size not affected by variability -can start before entire population is available What are the 8 basic steps in any sampling plan? 1. Define the population 2. Choose method (mean-per-unit, difference, ratio, stratified) 3. Determine sample size, considering variable or attribute 4. Determine acceptable level of risk 5. Select the random sample 6. Audit the random sample 7. Evaluate the results 8. Document the procedures In performing tests of controls over authorization of cash disbursements, which of the following statistical sampling methods would be most appropriate? (variables, stratified, ratio, attributes) Attributes When performing tests of controls the auditor is looking for the deviation rate from established control procedures set by the client. For testing the controls, the auditor performs attributes sampling procedures Why would you use variable sampling? Variable sampling is used by the auditor to estimate the total dollar amount of a population at auditor-specified levels of precision and reliability Why would you use attribute sampling? Attribute sampling provides evidence of the rate of occurrence of a specified characteristic in a population at auditor-specified levels of precision and reliability. Why would you use discovery sampling? Discovery sampling is a form of attribute sampling that is designed to locate at least one exception if the rate of occurrence in the population is at or above a specified rate. This method is used to search for critical occurrences that may indicate the existence of an irregularity, and is appropriate when the expected occurrence rate is quite low (usually near zero) and the auditor wants a sample that will provide a specified chance to observe one occurrence. What is the principal advantage of statistical over nonstatistical sampling methods? statistical methods provide a model for determining sample size while explicitly recognizing relevant factors (e.g. risk of assessing control risk too low, tolerable rate, and expected deviation rate). In nonstatistical sampling, the auditor implicitly recognizes the relevant factors while determining the sample size based on his or her own judgment and experience. What is precision? the range within which the sample result is expected to be accurate. Hence, it provides a calculation of the maximum acceptable error in either direction. How do you calculate the sampling interval? dividing the population into equal groups of dollars and selecting a logical unit from each group. Each group of dollars is a sampling interval What are the 4 factors that affect sample size when using classic variables sampling? (1) desired precision, (2) desired sample reliability, (3) variability among item values in the population (the estimate of the population's standard deviation) and (4) population size.