STUDY UNIT SEVEN AUDIT SAMPLING - Gleim Exam Prep

1 STUDY unit SEVENAUDIT SAMPLING (23 pages of outline) of Probability.. SAMPLING .. SAMPLING .. SAMPLING -- Classical.. SAMPLING -- Monetary- unit .. the SAMPLING Method.. Control Techniques..235 The results of internal auditing work often have someuncertaintybecause resource limitationsrequire internal auditors to usesampling. The costs of a complete review of records, transactions,events, performance of control procedures, etc., may exceed both the benefits and the availableresources. In these cases, SAMPLING must be done. Thus, internal auditors may apply statisticalmethods that permit a quantitative assessment of the accuracy and reliability of the sample this way, the internal auditors can evaluate their hypotheses about the matters tested and reduceuncertainty to an acceptable FUNDAMENTALS OF is important to management decision making because of the unpredictability offuture events.

2 According to definitions adopted by some writers, making under conditions ofriskoccurs when the probability distribution ofthe possible future states of nature making under conditions ofuncertaintyoccurs when the probabilitydistribution of possible future states of nature isnot knownand must be provides a method for mathematically expressing doubt or assurance about theoccurrence of an probability of an event varies from 0 to probability of 0 means the event cannot occur. A probability of 1 means the event iscertain to probability between 0 and 1 indicates the likelihood of the event s occurrence. Forexample, when a fair coin is flipped, the probability that it will land with a given sideup is probabilitiesare based on judgment. In business, subjective probability mayindicate the degree of confidence a person has that a certain outcome will example, a manufacturer projecting demand for its product is developingexpectations about the overall economy.

3 Management estimates the probability of1% growth in GDP to be high, growth to be medium, and 2% growth to be probabilitiesare based on logic or actual example, in rolling fair dice, each face on a single die is equally likely to turn , the probability of that event is one in six (.166667).Coin TossOutcomeChancesDecimalSide A1 in B1 in RollOutcomeChancesDecimal1 Dot1 in Dots1 in Dots1 in Dots1 in Dots1 in Dots1 in DrawOutcomeChancesDecimal2 of Clubs1 in of Clubs1 in of Clubs1 in of Clubs1 in of Clubs1 in of Clubs1 in of Clubs1 in of Clubs1 in other card44 in events aremutually exclusiveif they cannot occur example, a flipped coin cannot land with both sides events areindependentif the occurrence of one has no effect on the probability of example, when two dice are rolled, the result of one does not affect the result ofthe probabilityof two events is the probability that one will occur given that theother has already example, the probability of drawing the queen of clubs from a 52-card deck is 1 in52 ( ).

4 But if the ace of spades has been removed from the deck, theprobability of drawing the queen of clubs is higher (1 in 51 or ). probabilityfor two events is the probability that both will occur. It equals theprobability (Pr) of the first event times the conditional probability of the second event, giventhat the first has already 60% of the students at a university are male, Pr(male) is 6 in 10 (.6). If 1 in 6 of the male students has a B average,Pr(B average given that a student is male) is 1 in 6 (.166667). Thus, the probability that any given student (male or female)selected at random is both male and has a B average isPr(male B) = Pr(male) Pr(B|male)= .6 .166667= .10218SU 7: AUDIT probability thateither one or bothof two events will occur equals the sum of theirseparate probabilities minus their joint that one side of a fair coin is heads and the other tails.

5 If two such coins are flipped, the probability that at leastone will come up heads is calculated as follows:Pr(one or both coins heads) = Pr(coin 1 heads) + Pr(coin 2 heads) Pr(coin 1 heads and coin 2 heads)= .5 + .5 (.5 .5)= .25= .75 EXAMPLEIn the earlier example, if 1 in 3 (.33334) of all students, male or female, has a B average [Pr(B average) is .33334], theprobability that any given student is male and has a B average is .2 (.6 .33334). Accordingly, the probability that anygiven student either is male or has a B average isPr(male or has B avg.) = Pr(male) + Pr(B avg.) Pr(B male)= .6 + .33334 .2= .7333 The term Pr(B male) must be subtracted to avoid double counting those students who belong to both Thesum of the probabilitiesof all possible mutually exclusive outcomes of a singleexperiment is two fair coins (H = heads, T = tails) are flipped, four outcomes are possible:Probability ofCoin #1 Coin #2 This (certainty)ExpectedValue11.

6 The expected value of a decision (a choice among options) is a weighted average of thepayoffs. Each weight is the probability of the related highest expected value is )The decision is under the manager s )A state of nature is a future event associated with a )A payoff is the financial result of (a) the manager s decision and (b) the state 7: AUDIT expected value of a decision is calculated by multiplying the probability of eachstate of nature by its payoff and adding the is considering the purchase of two identically priced pieces of property, Bivens Tract and Newnan Tract. Theirvalues will change if a road is following are the states of nature and their probabilities:Future Stateof Nature (SN)EventProbabilitySN 1No road is ever 2A road is built this 3A road is built more than 1 year from following are estimates of values for each state of nature:PropertySN 1SN 2SN 3 Bivens TractUS $10,000US $40,000US $35,000 Newnan Tract$20,000$50,000$30,000 The following are the expected values:ExpectedValueBivens Tract.

7 1(US $10,000) + .2($40,000) + .7($35,000) =US $33,500 Newnan Tract: .1(US $20,000) + .2($50,000) + .7($30,000) =US $33,000 Thus, the Bivens Tract is the better calculation is a payoff probabilities are based on judgment. Objective probabilities are based on logic oractual events are mutually exclusive if they cannot occur events are independent if the occurrence of one has no effect on the probability ofthe conditional probability of two events is the probability that one will occur given thatthe other has already joint probability for two events is the probability that both will sum of the probabilities of all possible mutually exclusive outcomes of a singleexperiment is expected value of a decision (a choice among options) is a weighted average of thepayoffs associated with states of nature (future events).

8 Each weight is the probability ofthe related and review! You have completed the outline for this subunit. STUDY multiple-choicequestions 1 and 2 on page 7: AUDIT distributionspecifies the values of a random variable and their respectiveprobabilities. Certain standard distributions seem to occur frequently in nature and haveproven useful in business. These distributions may be classified according to whether therandom variable is discrete or the relative frequency of occurrence of the values of a variable can be specified, thevalues taken together constitute a function, and the variable is a random variable isdiscreteif it can assume only certain values in an interval. For example,the number of customers served is a discrete random variable because fractionalcustomers do not exist.

9 Probability distributions of discrete random variables includethe following:1)Uniform outcomes are equally likely, such as the flipping ofone coin or even of two coins, as in the example under item 9. in Subunit )Binomial trial has only two possible outcomes, , acceptor reject. This distribution shows the likelihood of each of the possiblecombinations of trial results. It is useful in quality )Poisson event may occur more than once with randomfrequency during a given period. Examples of applications are the arrival ofcustomers at a service window and the frequency with which trucks areinvolved in traffic random variable iscontinuousif no gaps exist in the values it may assume. Forexample, the weight of an object is a continuous variable because it may beexpressed as an unlimited continuum of fractional values as well as whole )Thenormal distributionis the most important of all distributions and describesmany physical phenomena.

10 It has a symmetrical, bell-shaped curve centeredabout the mean (see Figure 7-1 on the next page). shape, height, and width of a population s curve are related to itsmeasures of the arithmetic average of a set of the halfway value if raw data are arranged in numerical order fromlowest to highest. Thus, half the values are smaller than the median and half arelarger. It is the 50th the most frequently occurring value. If all values are unique, no investor has eight investments and calculates the measures of central tendency for returns on the = Arithmetic average of population values= (US $43,500 + $52,100 + $19,800 + $41,600 + $52,100 + $66,700 + $33,900 + $54,900) 8= US $364,600 8= US $45,575 Median = Midpoint between two central-most population valuesValues ranked: US $19,800; $33,900; $41,600; $43,500; $52,100; $52,100; $54,900; $66,700= (US $43,500 + $52,100) 2= US $95,600 2= US $47,800 Mode = Most frequent value in population= US $52,100SU 7: AUDIT anormal distribution, the mean, median, and mode are the same, and the tailsare Distributions1)In some frequency distributions, the mean is greater than the mode.