How to Determine Sample Size

Part A. 

In case Phillips establishes that the acceptable risk of reliance is 5 percent, the expected population deviation rate is 3 percent and the tolerable rate of deviation is 9 percent, then the sample size will be 84. That can be established by examining the AICPA sample size table. 

Part B. 

Assessment of Parameters 

Assessment of the Risk of Overreliance 

To answer this part, let’s first start by defining the risk of overreliance. In auditing, the risk of overreliance is realized when the sample size portrays the control as effective when in reality it is not. It simply implies that the sample size is not good enough to measure the effectiveness of the control. This happens when the expected rate of population deviation is higher than the tolerable deviation rate. In auditing, the risk of overreliance is particularly a concerning issue as it can lead to giving wrong opinions and conclusions on financial records with material errors (Elder et al., 2013). 

To assess the risk of overreliance, Phillips will have to measure and identify the expected rate of population deviation as well as the tolerable deviation rate. The second step will be comparing them and identifying which one is larger than the other. Normally, the expected population deviation rate is expected to be close or equals to the tolerable deviation rate. So, if Phillips finds out that the expected rate of population deviation exceeds the tolerable deviation rate, he will conclude that there is a risk of overreliance. Depending on how wide the difference between the expected population deviation rate and tolerable deviation rate is, Phillips will decide whether to use 5 percent risk of overreliance or 10 percent risk of overreliance. Here the population deviation rate is 3 percent and tolerable deviation rate is equals to 9 percent. The difference is -6% 

In this case, Phillips risk of overreliance is -6%. This implies that Phillips underutilized the information given by Cowboy Company’s employees in regard to the company’s internal control. Therefore, there is a high likelihood that Phillips concluded that Cowboy Company has poor internal control system when in reality the company has an effective internal control (Elder et al., 2013). 

Assessment of the Expected Population Deviation Rate 

First, the expected population deviation rate refers to the amount of error or deviations in the population size. This is determined by relating the deviations in a population and the entire population. It is calculated using the formula: expected population deviation rate = deviation or error in the population size ÷ the presented population size. The larger the value the worst as it implies there is a lot of unreliability in the population size. As a result, the auditors can end up making wrong conclusions about the financial statements of the company in question (Pencina et al., 2014). 

To assess the population deviation rate, Phillips will first have to determine the number of employees working for Cowboy Company whose information was used to assess the internal control of Cowboy Company. The second step will be determining the deviation or error in the population. Next, is to determine the percentage of the ratio of the deviation in the population size and the actual sample (Pencina et al., 2014). 

Assessment of the Tolerable Rate of Deviation 

Tolerable rate of deviation is the highest error or deviation in the sample that the auditor will be willing to accept or tolerate. It is determined by examining the historical deviations that had insignificant impacts on the predictions or financial judgments (Pencina et al., 2014). 

Therefore, to determine the most effective tolerable rate of deviation, Phillips will identify the highest deviation in the sample that has historically had insignificant impacts when it comes to assessing Cowboy Company’s internal control system. The sample, in this case, is 84 and the standard deviation was 3. Therefore, the expected sample deviation rate will be = 3 ÷ 84 ×100% =3.57%. The expected sample deviation rate was 3.57%, which is smaller than what Philips has historically been accepting as the maximum error in its sampling procedure. In conclusion, the choice of 9 percent as the tolerable rate of division is perfect since the expected sampling deviation rate is quite lower (i.e. 3.57% lower than the highest acceptable error, 9%). 

Part C 

In case Phillips decides to increase the acceptable risk of reliance to 10 percent and keep the expected population deviation rate at 3 percent and tolerable rate of deviation at 9 percent, then the sample size will be 58. That can also be established by examining the AICPA sample size table. 

Part D 

The sample size in part C has reduced because the risk of overreliance increased. Normally, the smaller the sample size the higher the chances that the sample will give wrong/biased impressions about the population size (Elder et al., 2013). For example, it 84 sample size is more likely to give reliable predictions about the population than 58. So, the reduction in sample size simply implies that the chances for making wrong projections have increased (i.e., the risk of overreliance has increased from 5% to 10%). 

References 

Elder, R. J., Akresh, A. D., Glover, S. M., Higgs, J. L., & Liljegren, J. (2013). Audit sampling research: A synthesis and implications for future research. Auditing: A Journal of Practice & Theory , 32 (sp1), 99-129. 

Pencina, M. J., Neely, B., & Steyerberg, E. W. (2014). RE: net risk reclassification P Values: valid or misleading?. Journal of the National Cancer Institute , 107 (1), dju355.