审计英语审计抽样

审计英语审计抽样
一、考情分析
从专业阶段历年考试情况来看,考点主要围绕样本量的设计和评价样本结果、PPS抽样、传统变量抽样等相关内容，重点掌握传统变量抽样计算方法以及重要的理论知识。

二、专业词汇
抽样风险：Sampling risk
非抽样风险：Non-sampling risk
信赖不足风险：Under reliance risk
信赖过度风险：Over reliance risk
控制测试：Tests of control
控制有效性：Effectiveness of control
重大错报：Material misstatements
实际水平：Actual level
审计结果：Audit result
审计效率：Audit efficiency
误拒风险：Rejection risk
误受风险：Acceptance risk
细节测试：Test of details
样本量：Samples size
偏差：Deviation
具体目标：Specific objectives
统计抽样：Statistical sampling
非统计抽样：Non-statistical sampling
成本效益：Cost benefit
证据的充分性：Sufficiency of the evidence
优点：Advantages
缺点：Disadvantages
可接受的抽样风险：Acceptable sampling risk
可接受误差（可容忍误差）：Acceptable error
认定层次：Assertion level
总体变异性：Population deviation
分层：Stratification
预计的总体误差：Expected population error
总体规模：Population size
专业判断：Professional judgment
上限：Upper limit
风险系数：Risk coefficient
可容忍偏差率：Tolerable deviation rate
修正重大错漏报风险评估程度：Modify material misstatement risk assessment level 实质性程序：Substantive procedures
差额：Difference
调整账目：Adjust book record
账面金额：Book value
实际金额：Actual value
概率比例规模抽样法: Probability-proportional- to-size sampling（PPS Sampling）零余额：Zero balance
负余额：Negative balance
高估：Overestimate
属性抽样：Attribute sampling
变量抽样：Variable sampling
三、重点、难点讲解
I.抽样风险和非抽样风险
1.抽样风险（由于采用抽样而引起的风险）
（1）抽样风险：指注册会计师根据样本得出的结论，可能不同于如果对整个总体实施与样本相同的审计程序得出的结论的风险。

Ⅰ.Sampling risk and non-sampling risk
1.Sampling risk（risk caused by sampling）
（1）Sampling risk: it is the risk arising from the possibility that the CPA’s conclusion, based on a sample, may be different from the conclusion that would be reached if the entire population were subjected to the same audit procedure.
（2）抽样风险的控制
抽样风险是抽出的样本不能完全代表总体的可能性。

抽样风险与样本量成反向关系，即样本量越大，抽样风险越低。

所以，只要有抽样就存在抽样风险。

（2）Control of sampling risk
Sampling risk is the possibility that samples selected may not completely represent the population. Relationship between sample size and sampling risk is opposite, the larger the sample size, the lower the sampling risk is. Therefore, sampling risk always exists because of sampling.
（3）抽样风险的类型
①注册会计师在进行控制测试时，主要面临信赖不足风险和信赖过度风险。

信赖过度风险：根据样本推断的控制有效性高于实际，评估的重大错报风险低于实际水平，从而影响审计效果（质量）。

信赖不足风险：根据样本推断的控制有效性低于实际，评估的重大错报风险高于实际水平，从而影响审计效率。

（3）Types of sampling risk
①CPA is mainly faced with under reliance risk and over reliance risk when conducting tests of control.
Over reliance risk: the expected effectiveness of control is higher than the actual level, risk assessed of material misstatements is lower than the actual level, thereby influencing the audit effectiveness（quality）.
Under reliance risk: the expected effectiveness of control is lower than the actual level，assessed risk of material misstatements is higher than the actual level, thereby influencing the audit efficiency.
②注册会计师在进行细节测试时，主要面临误拒风险和误受风险。

误受风险是指注册会计师推断某一重大错报不存在而实际上存在的风险，从而影响审计效果（质量）。

误拒风险是指注册会计师推断某一重大错报存在而实际上不存在的风险，从而影响审计效率。

②CPA is mainly faced with rejection risk and acceptance risk when conducting detailed testing.
Acceptance risk refers that CPA infers that the material misstatement is not existed but actually it is not, thereby influencing the audit effectiveness（quality）.
Rejection risk refers that CPA infers that the material misstatement is existed but actually it is not, thereby influencing the audit efficiency.
2.非抽样风险（不是由样本量引起的风险）
非抽样风险是指注册会计师由于任何与抽样风险无关的原因而得出错误结论的风险。

在审计过程中，可能导致非抽样风险的原因包括下列情况：
2.Non-sampling risk（risk not caused by samples size）
Non-sampling risk refers the possible false decision made by CPA based on reasons not related to samples.
Following circumstances may cause non-sampling risk in audit:
（1）注册会计师选择的总体不适合于测试目标；
（2）注册会计师未能适当地定义误差（包括控制偏差或错报），导致注册会计师未能发现样本中存在的偏差或错报；
（1）The population selected by CPA is not suitable for the test target;
（2）CPA fails to properly define the error（including the control deviation or misstatement）, which makes CPA unable to find the deviation or misstatement;
（3）注册会计师选择了不适于实现特定目标的审计程序；
（4）注册会计师未能适当地评价审计发现的情况；
（5）其他原因。

（3）CPA performs audit procedures which are not suitable for the specific objectives;
（4）CPA does not adequately evaluate the audit result;
（5）Other reasons.
非抽样风险是由人为错误造成的，因而可以降低、消除或防范。

Non-sampling risk is caused by human error, which can be reduced, eliminated or prevented.
非抽样风险不能量化，但通过采取适当的质量控制政策和程序，对审计工作进行适当的指导、监督和复核，以及对注册会计师实务的适当改进，可以将非抽样风险降至可以接受的水平。

注册会计师也可以通过仔细设计其审计程序尽量降低非抽样风险。

Non-sampling risk cannot be quantified, but non-sampling risk can be reduced to an acceptable level through application of appropriate quality control policy & procedures and proper guidance, supervision and review of audit, as well as the appropriate improvement to CPA practice. CPA can also carefully design their audit procedures to minimize
non-sampling risk.
II.统计抽样和非统计抽样
1.统计抽样与非统计抽样方法的选用
注册会计师在统计抽样与非统计抽样方法之间进行选择时，主要考虑成本效益。

Ⅱ.Statistical sampling and non-statistical sampling
1.Selection between statistical sampling and non-statistical sampling method
Cost benefits are mainly considered when choosing between statistical sampling and non-statistical sampling method.
（1）统计抽样的优点：能够客观地计量抽样风险，并通过调整样本规模精确地控制风险，这是与非统计抽样最重要的区别。

统计抽样还有助于注册会计师高效地设计样本，计量所获取证据的充分性，以及定量评价样本结果。

（1）Advantages of statistical sampling: sampling risk can be measured objectively, and actually controlled by adjusting the sample size, which is the most important different from non-statistical sampling. Statistical sampling helps CPA to efficiently design samples, measure the sufficiency of the evidences obtained, and evaluate the sampling results quantificationally.
（2）统计抽样的缺点：统计抽样可能发生额外的成本。

（3）非统计抽样如果设计适当，也能提供与设计适当的统计抽样方法同样有效的结果。

注册会计师使用非统计抽样时，必须考虑抽样风险并将其降至可接受水平，但无法精确地测定出抽样风险。

（2）Disadvantages of statistical sampling: statistical sampling may incur extra cost.
（3）If the design of non-statistical sampling is appropriate, it can provide the same effective result as statistical sampling designed properly. When using non-statistical sampling, CPA must consider the sampling risk and reduce it to the acceptable level, however, the sampling risk cannot be accurately estimated.
2.审计抽样与职业判断
不管统计抽样还是非统计抽样，两种方法都要求注册会计师在设计、实施和评价样本时运用职业判断。

虽然传统上将非统计抽样称作判断抽样，但这并不代表统计抽样不需要职业判断。

2.Audit sampling and professional judgment
Professional judgment is required for CPA when designing, implementing and evaluating samples no matter the statistical sampling or non-statistical sampling is used. Although traditionally the non-statistical sampling is called judgment sampling, it does not mean that no judgment is required for statistical sampling.
III. 审计抽样的运用
影响样本规模的因素主要包括：
1.可接受的抽样风险
可接受的抽样风险与样本规模成反向变动关系。

注册会计师愿意接受的抽样风险越低，样本规模通常越大。

Ⅲ.Application of audit sampling
Factors affect the sample size:
1.Acceptable sampling risk
Acceptable sampling risk is in opposite relationship with sample size. The lower the sampling risk accepted by CPA, the larger the sample size is needed.
2.可容忍误差
（1）在控制测试中，它指注册会计师能够接受的最大偏差数量。

如果偏差超过这一数量则减少或取消对内部控制程序的信赖。

2.Acceptable error
（1）In control testing, it means the maximum deviation accepted by CPA. If the deviation exceeds that number then it would reduce or eliminate the reliance on the internal control procedures.
（2）在细节测试中，它指注册会计师确定的认定层次的重要性水平。

可容忍误差越小，为实现同样的保证程度所需的样本规模越大。

（2）In detailed testing, it refers to the level of significance determined by CPA at assertion level. The smaller the tolerable error, the larger the sample size is required to ensure the same level of assurance.
3.总体变异性
总体变异性是指总体的某一特征（如金额）在各项目之间的差异程度。

在控制测试中，注册会计师在确定样本规模时一般不考虑总体变异性。

3.Population deviation
The population deviation refers to the degree of deviation between projects of one parameter（like amount）.
In control testing, population deviation is not normally considered by CPA when determining the sample size.
在细节测试中，总体项目的变异性越低，通常样本规模越小。

注册会计师可以通过分层，降低每一组中变异性的影响，从而减小样本规模。

In detailed testing, the lower the population deviation, the smaller the sample size.
CPAs can use stratification to reduce the impact of deviation in each group, thereby reducing the sample size.
4.预计总体误差
在既定的可容忍误差下，当预计总体误差增加时，所需的样本规模更大。

5.总体规模
除非总体非常小，一般而言总体规模对样本规模的影响几乎为零。

4.Expected population error
In a given tolerable error, when the expected overall error increases, the required sample size is bigger.
5.Population size
Unless the population size is very small, it has no influence on the sample size.
Ⅳ.审计抽样在控制测试中的应用
1.在控制测试使用统计抽样方法——评价样本结果阶段
Ⅳ.Application of audit sampling in control testing
1.Statistical sampling methods used in control test using – stage of evaluating sample results
在控制测试中使用统计抽样评价样本结果计算
总体偏差率＝样本偏差率＝样本偏差数量÷样本规模
考虑抽样风险
公式法：总体偏差率上限＝风险系数÷样本规模＝总体偏差率＋抽样风险允许限度
The use of statistical sampling in control testing to evaluate sampling results Population deviation rate＝sampling deviation rate＝sampling deviation÷ sample size Considering sampling risk
Using formula：upper limit of population deviation＝risk coefficient÷sample size ＝population deviation rate + acceptable sampling risk level
查表法：使用样本结果评价表统计抽样的结果。

总体偏差率上限“低于”可容忍偏差率，则总体“可以接受”。

Using table: using the sample results evaluation table to evaluate the results of statistical sampling.
The upper limit of population deviation rate is less than the limit of tolerable deviation rate, so population is acceptable.
总体偏差率上限“低于但接近”可容忍偏差率，则“考虑是否接受”总体，并考虑是否需要扩大测试范围；总体偏差率上限“大于或等于”可容忍偏差率，则总体“不能接受”，应当修正重大错报风险评估水平，并增加实质性程序的数量；也可以对其他控制进行测试，以支持计划的重大错报风险评估水平。

If the upper limit of population deviation rate is lower than but close to tolerable deviation rate, then consider whether to accept the population and whether to expand the testing scope; If the upper limit of population deviation rate is equal to or higher than tolerable deviation rate, the population is unacceptable and should modify material misstatement risk assessment level, and increase the number of substantive procedures; or test other controls, to support the planned risk assessment level of material misstatements.
2.在控制测试中使用非统计抽样方法——评价样本结果阶段
在非统计抽样中，注册会计师同样将样本的偏差率作为总体偏差率的最佳估计。

ing non-statistical sampling method in test of controls—stage of evaluating sampling result
In non-statistical sampling, the CPA will also use the deviation rate of samples as the best estimate of the deviation rate of the population.
但在非统计抽样中，抽样风险无法直接计量。

注册会计师通常将样本偏差率（即估计的总体偏差率）与可容忍偏差率相比较，以判断总体是否可以接受。

在控制测试中使用非统计抽样评价样本结果：
But in a non-statistical sampling, sampling risk cannot be measured directly.The CPA usually compares deviation rate of samples（i.e., the deviation rate of the population estimated）with the tolerable deviation rate to judge whether the population can be accepted.
Using non-statistical sampling method in test of controls to evaluate sampling result 总体偏差率＝样本偏差率＝样本偏差数量÷样本规模
Population deviation rate ＝deviation rate of the samples＝deviation amount of the samples/sample size
非统计抽样的结果评价与结论（非统计抽样无法量化抽样风险）：
Evaluation and conclusion of non-statistical sampling result（the sampling risk of non-statistical sampling cannot be quantified）:
样本偏差率“大于”可容忍偏差率，总体“不能接受”；样本偏差率“大大低于”可容忍偏差率，总体“可以接受”；样本偏差率“低于但接近”可容忍偏差率，总体“不可接受”；
If deviation rate of the samples is higher than the tolerable deviation rate, the population cannot be accepted; if deviation rate of the samples is significantly lower than the tolerable deviation rate, the population can be accepted; if deviation rate of the samples is lower than but close to the tolerable deviation rate, the population cannot be accepted
样本偏差率“低于”可容忍偏差率，其差额“不大不小”，“考虑是否接受”总体，考虑扩大样本规模以进一步收集证据。

Deviation rate of the samples is lower than the tolerable deviation rate, but the difference is neither too big nor too small, consider whether to accept the population; consider expanding the sample size in order to collect further evidence.
V.审计抽样在细节测试中的运用
1.样本规模的确定
无论使用统计抽样还是非统计抽样方法，注册会计师都应当综合考虑影响样本规模的因素，运用职业判断和经验确定样本规模。

V.Application of audit sampling in test of details
1.Determination of the sample size
Regardless of the use of statistical sampling or non-statistical sampling method, certified public accountants should comprehensively consider factors that influence the sample size, using professional judgment and experience to determine the sample size.
在情形类似时，注册会计师考虑的因素相同，使用统计抽样和非统计抽样确定的样本规模通常是可比的。

In a similar situation, the certified public accountants consider the same factors, and the sample size determined by statistical sampling and non-statistical sampling is usually comparable.
（1）利用样本规模确定表
Using the determination table of sample size
细节测试货币单元抽样样本规模（误受风险10%）
（2）利用公式
Using the formula
样本规模=总体账面金额/可容忍错报*保证系数
Sample size＝Book value of the population/Tolerable misstatement×Assurance coefficient
例如，注册会计师确定的误受险为10%，可容忍错报与总体账面金额之比为8%，预计总体错报与可容忍错报之比为0.20，注册会计师确定样本规模为：
查表法：43
公式法：3.41/8%=42.63
For example, the riskof incorrect acceptance determined by CPA is 10%, the ratio of tolerable misstatement/book value of the population is 8%, the ratio of estimated misstatement of the population /tolerable misstatement is 0.2, the sample size determined by CPA is:
Using table method: 43
Using formula method: 3.41/8%=42.63
Assurance coefficient when determining sample size in monetary unit sampling
非统计抽样方法中推断总体错报
①比率法（错报金额与抽样单元的金额相关）
总体错报金额＝样本错报金额/样本账面金额×总体账面金额
Deduce misstatement of the population in non-statistical sampling method
①Ratio method（misstatement amount relates to sample unit value）
Misstatement amount of the population＝Misstatement amount of the sample/Book value of the sample×Book value of the population
②差异法（错报金额与抽样单元的多少相关）
总体错报金额＝（样本错报审定金额－样本账面金额）/样本规模×总体规模
②Difference method（misstatement amount relates to sample unit number）
Misstatement amount of the population＝（Approved misstatement amount of the sample-Book value of the sample）/Sample size×Population size
非统计抽样结果评价与结论
总体错报“大于”可容忍错报，总体“不能接受”，应建议被审计单位调整账面记录；修改进一步审计程序的性质、时间安排和范围，考虑对审计报告的影响；总体错报“大大低于”可容忍错报，总体“可以接受”；
Evaluation and conclusion of non-statistical sampling result
If misstatement of the population exceeds tolerable misstatement amount, the population cannot be accepted, and the auditor should suggest client to adjust book record; further modify the nature, timing and scope of audit procedures; consider the effect on audit report If misstatement of the population is significantly lower than tolerable misstatement amount, the population can be accepted.
总体错报“低于但接近”可容忍错报，总体“不能接受”，应建议被审计单位调查错报，调整账面记录，修改进一步审计程序的性质、时间安排和范围，考虑对审计报告的影响；总体错报“小于”可容忍错报，其差额“不大不小”，“考虑是否接受”总体，并考虑是否需要扩大细节测试的范围，以获取进一步的证据。

If misstatement of the population is lower than but close to the tolerable misstatement amount, the population cannot be accepted, and the auditor should suggest client to investigate the misstatement and adjust book record; further modify the nature, timing and scope of audit procedures; consider the effect on audit report
If misstatement of the population is lower than the tolerable misstatement amount, but the difference is neither too big nor too small, consider whether to accept the population and whether to expand the scope of test of details in order to collect further evidence.
2.在细节测试中使用统计抽样方法——评价样本结果阶段
在细节测试中使用统计抽样评价样本结果
推断总体错报（传统变量抽样）
e statistical sampling method in test of details—stage of evaluating sampling result
Use statistical sampling method in test of details to evaluate sampling result
Deduce misstatement of the population（traditional variable sampling）
①均值法
样本审定金额平均值＝样本审定金额÷样本规模
总体金额估计值＝样本审定金额平均值×总体规模
推断的总体错报＝总体金额估计值-总体账面金额
①Mean method
Mean of sample approved amount ＝ Approved amount of sample/Sample size
Estimation of population value＝Mean of sample approved amount × Population size Misstatement of population deduced＝Estimation of population value-Book value of the population
②差额法
样本平均错报＝（样本账面金额-样本审定金额）÷样本规模
推断的总体错报＝样本平均错报×总体规模
估计的总体金额=总体账面金额-推断的总体错报
②Difference method
Average misstatement of sample ＝（ Book value of sample- Approved value of sample）/Sample size
Misstatement of population deduced＝Average misstatement of sample ×Population size Estimated population amount=Book value of population – Misstatement of population deduced
③比率法
比率＝样本审定金额÷样本账面金额
估计的总体金额＝总体账面金额×比率
推断的总体错报＝总体账面金额－估计的总体金额
③Ratio method
Ratio＝ Approved amount of sample/Book value of sample
Estimated population amount ＝Book value of the population×Ratio
Misstatement of population deduced＝Book value of the population - Estimated population amount
统计抽样结果评价与结论
总体错报上限“大于或等于”可容忍错报，总体“不能接受”，所测试的交易或账户余额存在重大错报, 注册会计师应建议被审计单位对错报进行调查，且在必要时调整账面记录；总体错报上限“低于”可容忍错报，总体“可以接受”。

Evaluation and conclusion of the statistical sampling result
If upper limit of the population misstatement exceeds or is equal to tolerable misstatement amount, the population cannot be accepted; If the transaction or account balance tested has material misstatement, CPA should suggest client to investigate the misstatement and adjust book record when necessary
If upper limit of the population misstatement is less than tolerable misstatement amount, the population can be accepted
VI.货币单元抽样
VI.Monetary unit sampling
货币单元抽样的优点：Advantages of monetary unit Sampling:
（1）货币单元抽样以属性抽样原理为基础，注册会计师可以很方便地计算样本规模和评价样本结果因而通常比传统变量抽样更易于使用。

（1）Monetary unit sampling is based on attribute sampling, it is convenient for certified
accountant to calculate the sampling size and assess the sample results.Therefore, it is usually easier to be used compared with traditional variable sampling.
（2）货币单元抽样在确定所需的样本规模时无需考虑总体的特征（如总体变异性），因为总体中的每一个货币单元都有相同的规模，而传统变量抽样的样本规模是在总体项目共有特征的变异性或标准差的基础上计算的。

（2）When determining the sample size of monetary unit sampling, it is not necessary to consider the characteristics of population （e.g.populationdeviation）.Because each monetary unit in the population has the same size, while the sample size in traditional variable sampling is calculated based on the deviation or standard deviation of common characteristics of population.
（3）货币单元抽样中项目被选取的概率与其货币金额大小成比例，因而无需通过分层减少变异性。

而传统变量抽样通常需要对总体进行分层以减小样本规模。

在货币单元抽样中，如果项目金额超过选样间距，货币单元系统选样自动识别所有单个重大项目。

（3）The probability that the items in monetary unit sampling are selected and the currency amount has a proportional relationship so there is no need to reduce deviation through stratification.While in traditional variable sampling, it is usually necessary to stratify population to reduce sample size.When using monetary sampling, if the item amount exceeds the sampling interval, monetary unit system will automatically identify the single material item.
（4）在货币单元抽样中使用系统选样法选取样本时，如果项目金额等于或大于选样间距，货币单元抽样将自动识别所有单个重大项目，即该项目一定会被选中。

（4）When using system sampling method to select sample in the monetary unit sampling, if the item amount equal to or greater than the sampling interval, monetary unit sampling will automatically identify all individual major items, namely the item will be certain to be selected.
（5）如果注册会计师预计不存在错报，货币单元抽样的样本规模通常比传统变量抽样方法更小。

（5）If the auditor expects that the misstatement does not exist or is little, the sample size of monetary unit sampling is smaller than that of traditional variable sampling.
（6）货币单元抽样的样本更容易设计，且可在能够获得完整的总体之前开始选取样本。

（6）The sample of monetary unit sampling is easier to design and may select samples before obtaining completed population.
货币单元抽样的缺点：
Disadvantages of monetary unit Sampling:
（1）货币单元抽样不适用于测试总体的低估，因为账面金额小但被严重低估的项目被选中的概率低，如果在货币单元抽样中发现低估，注册会计师在评价样本时需要特别考虑。

（1）Monetary unit sampling is not suitable for the understatement of population, because the probability of being chosen for a small book value but grossly understated project is low.If understatement is discovered in monetary unit sampling, certified public accountants need special consideration when evaluating samples.
（2）对零余额或负余额的选取需要在设计时特别考虑。

（2）The selection of zero balance and negative balance needs to be considered specially.
（3）当发现错报时，如果风险水平一定，货币单元抽样在评价样本时可能高估抽样风险的影响，从而导致注册会计师更可能拒绝一个可接受的总体账面金额。

（3）When misstatements are identified, if the risk level is fixed, monetary unit sampling may overestimate the effect of sampling risk when evaluating samples, which may lead to that CPA may refuse an acceptable book value of the population.
（4）在货币单元抽样中注册会计师通常需要逐个累计总体金额，以确定总体是否完整并与财务报表一致，不过如果相关会计数据以电子形式储存，就不会额外增加大量的审计成本。

（4）CPA needs to accumulate total amount one by one in monetary unit sampling, in order to determine whether the population is complete and consistent with the financial statements.But if the relevant accounting data is stored in electronic form, there is no additional cost of auditing.
（5）当预计总体错报的金额增加时，货币单元抽样所需的样本规模也会增加。

在这些情况下，货币单元抽样的样本规模可能大于传统变量抽样所需的规模。

（5）When the volume of misstatements in the population increase, the sampling size of monetary unit sampling will also increase.Under these situations, the sample size of monetary unit sampling may be greater than that of traditional variable sampling.
在货币单元抽样中，计算总体错报的上限：
Calculate the upper limit of population misstatements in monetary unit sampling: （1）如果在样本中没有发现错报，总体错报的上限= 保证系数x选样间隔。

例如：误受险为5%，选样间隔为3000元（下同），注册会计师没有在样本中发现错报，总体错报的上限为9000元（3x3000），称基本精确度。

（1）If no misstatement is discovered in the sample, the upper limit of population misstatements =Assurance coefficient x Sampling interval.For example, risk of incorrect acceptance is 5%, sampling interval is 3000 Yuan （ the same below）, CPAs haven't found any misstatement in the sample, then the upper limit of population misstatements is 9000 Yuan （3x3000）, which is called basic accuracy.
（2）如果在账面金额大于或等于选样间隔的逻辑单元中发现了错报，无论该错报的百分比是否为100%，总体错报的上限=事实错报+基本精确度。

例如：注册会计师在样本中发现1个错报，该项目的账面金额为5000元，审定金额为4000元，总体错报的上限为10000元（1000+3x3000）（2）If a misstatement is found in a logical unit that is larger than or equal to the sample interval, no matter whether the percentage of the misstatement is 100%, the upper limit of population misstatements = factualmisstatement+ basic accuracy.For example, CPA found one misstatement in sample, the book value of the item is 5000 Yuan, approved amount is 4000 Yuan, the upper limit of population misstatements is 10000 Yuan （1000+3X3000）（3）如果在样本（排除账面金额大于或等于选样间隔的逻辑单元）中发现了错报百分比为100%的错报，总体错报的上限=保证系数x选样间隔。

例如：注册会计师在样本中发现1个错报，该项目的账面金额为20元，审定金额为0元，则总体错报的上限为14250元（4.75x3000）（3）If a misstatement with 100% misstatement percentage in sample （ excluding logical unit that is larger than or equal to the sample interval）is found, the upper limit of population misstatements = Assurance coefficient x Sampling interval.For example, CPA found one misstatement in sample, the book value of the item is 20 Yuan, approved amount is 0 Yuan, then the upper limit of population misstatements is 14250 Yuan （4.75X3000）.
（4）如果在样本（排除账面金额大于或等于选样间隔的逻辑单元）中发现了错报百分比低于100%的错报，注册会计师先计算推断错报，再将推断错报按金额降序排列后，分别乘以对应的保证系数增量（即在既定的误受风险水平下，特定数量的高估错报所对应的保证系数与上一行保证系数之间的差异），加上基本精确度之后，最终计算出总体错报的上限。

总体错报的上限= 推断错报x 保证系数的增量+ 基本精确度。

（4）If a misstatement with the misstatement percentage lower than 100% in sample （ excluding logical unit that is larger than or equal to the sample interval）is found, CPA should first calculate projected misstatements, then after arranging projected misstatements in descending order according to amount, multiply the incremental quantity of corresponding assurance coefficient respectively （ i.e.Under the given level of risk
of incorrect acceptance, the difference between the assurance coefficient corresponding specified number of overstatement misstatements and the assurance coefficient of above line）, plus basic accuracy, calculate the upper limit of population misstatements at last.
The upper limit of population misstatements = projectedmisstatements X incremental quantity of assurance coefficient + basic accuracy.
例如：误受险为5%，选样间隔为3000元，注册会计师在样本中发现2个错报，账户A的账面金额为2000元，审定金额为1500元，推断错报为750元（500÷2000x3000）；账户B的账面金额为1000元，审定金额为200元，推断错报为2400元（800÷1000x3000）。

将推断错报按金额降序排列后，由表可知，在5%的误受风险水平下，账户A对应的保证系数增量为1.55，账户B对应的保证系数增量为1.75。

因此，总体错报的上限为14363元（750×1.55＋2400×1.75＋3×3000）。

For example, risk of incorrect acceptance is 5%, sampling interval is 3000 Yuan, CPA found two misstatements in sample, the book value of account A is 2000 Yuan, approved amount is 1500 Yuan, projected misstatement is 750 Yuan （500÷2000x3000）；the book value of account B is 1000 Yuan, audited value is 200 Yuan, projected misstatement is 2400 Yuan （800÷1000x3000）.
After arranging project misstatements in descending order according to amount, from the table, under the 5% level of risk of incorrect acceptance, the incremental quantity of corresponding assurance coefficient of account A is 1.55, the incremental quantity of corresponding assurance coefficient of account B is 1.75.Therefore, the upper limit of population misstatements is 14363 Yuan（750×1.55＋2400×1.75＋3×3000）如果样本中既有账面金额大于或等于选样间隔的逻辑单元，又有账面金额小于选样间隔的逻辑单元，而且在账面金额小于选样间隔的逻辑单元中，既发现了错报百分比为100% 的错报，又发现了错报百分比低于100%的错报。

如何解决？
If there are both logical units with book value greater than or equal to the sampling interval, and logical units with book value less than the sampling interval, and in the logical unit with book value less than the sampling interval, misstatement with misstatement percentage is 100% is discovered and misstatement with misstatement percentage less than 100% is also discovered.How to solve?
注册会计师可以将所有样本项目分成两组：
CPA could divide all the sample items into two groups:
第一组是账面金额大于或等于选样间隔的逻辑单元，注册会计师计算出该组项目的事实错报；
The first group is made up of logical units with book value greater than or equal to the sampling interval.CPA could calculate the factual misstatement of items in this group.
第二组是账面金额小于选样间隔的逻辑单元，无论该组项目的错报百分比是否为100%，注册会计师都先计算出各项目的推断错报，再将所有推断错报按金额降序排列后，分别乘以对应的保证系数增量，并将计算结果累计起来。

用这个累计结果加上基本精确度，再加上第一组项目中的事实错报，就是最终总体错报的上限。

The second group is made up of logical units with book value less than the sampling interval.No matter whether the misstatement percentage of items in this group is 100%, CPA should first calculate the projected misstatement of each item, then after arranging all the projected misstatements in descending order according to amount, multiply the incremental quantity of corresponding assurance coefficient respectively, and add up the calculation results.
Use this cumulative result to add basic accuracy, and add the factual misstatement in the first group, then is the upper limit of population misstatements.。