 Hello and welcome to the session. This is Professor Farhad in which you would look at monetary unit sampling. This topic is covered on the CPA exam as well as an auditing course. In this session, I would look at it from a simulation perspective or an exercise perspective. You might see on the exam, but going over the simulation, you'll be able to answer multiple choice questions as well. Monetary unit sampling is also known as dollar unit sampling. It means you're using the dollar as a unit rather than the account as a unit. So the sampling is based on the dollar. This means the higher the dollar amount and the population, the higher the probability that amount getting selected. And this is a common statistical method for test of details. Now, when you take this course in college, most of the students find hard time either understanding it or retain this information by the time to get to the CPA exam. What I suggest you do, if you're having any issues with this topic, I'm going to go over this exercise and explain everything in details as much as possible. I suggest you visit my website and check out my auditing and attestation course, which I explained this topic in details. As always, I would like to remind you to connect with me only then. If you haven't done so, YouTube is what I suggest you subscribe. I have 1,700 plus accounting, auditing, tax, finance, as well as Excel tutorial. If you like my lectures, please like them, share them, put them in playlist. If they benefit you, it means they might benefit other people. Connect with me on Instagram. On my website, farhatlectures.com, this is what I have additional lectures and resources to help you understand the material. The difference between what I offer in a CPA prep course is I teach you the material. The CPA prep course assumes you know the material and they move on review it with you. That's the difference. So check out my course. If you are looking to add 10 to 15 points to your CPA exam. So let's take a look at this question and try to answer and explain what's what we are being given here. There's a lot of information, although it's going to be asking only to compute the sample size, but in order to compute the sample size, we're going to have to learn a lot of material. An auditor is determined the appropriate sample size for testing inventory valuation using monetary unit sampling. As I said, it's a dollar, it's a dollar unit sampling. The population has 3,140 inventory item. This is how many items we have. The dollar value is 19,325. The tolerable misstatement is 575,000 and we are at a 10% acceptable risk of incorrect acceptance and no misstatements are accepted in the population zero misstatement. We have a lot of variables here. We have the number of unit items, 3,140. We have the population value, 19 million. We have the tolerable misstatement. We have ARIA, the acceptable risk of incorrect acceptance. I'm just going to call it ARIA for now and in the future. And the expected misstatement is zero. And all we have to do is compute N, which is the sample size. So simply put, how many units are we going to be selecting from this 3,140 inventory unit? The first thing is you have to know the formula on how to compute the sample size. So let's look at the formula first, then we'll explain every variable in the tails and see how does it affect the formula. Simply put, the formula is something called the confidence interval. Hold on a second. You just added a new factor, the confidence interval. Where is that coming from? Don't worry, I will show you. Where is that coming from in a moment? The confidence interval divided by tolerable misstatement, which is tolerable misstatement. This one here, 575, as a percentage, which is mean divide by the population. And what's the population? The population is 19 million 350. So in the numerator, we have the confidence interval. So let's start with the confidence interval. Well, yes, let's start with the confidence interval. Let's start with the numerator. Let me ask you this. If you are selecting from a population and you want more confidence, so if you want your confidence to go up, let me ask you this, do you select more samples or less samples? And I hope you know that if you want more confidence, your sample size goes up, your sample size goes up. Now, how do you come up with this confidence interval? It's not giving in the problem. Well, on the CPA exam, they might give you the confidence interval or they might ask you to look it up. I'm going to show you how to look up the confidence interval. How do you look up the confidence interval? You look up the confidence interval from a table called the confidence interval table. That's basically what it is. And what do you need to select the confidence interval? You need the risk of incorrect acceptance and the number of misstatements expected. So in this problem, we are saying the risk of incorrect acceptance. Now we're going to start to define what we are giving. We are giving this as 10 percent and no misstatement. It means the misstatement is zero. So what does it mean 10 percent aria? Well, 10 percent aria, risk of incorrect acceptance. It's right here, this column here. This is 10 percent aria. It means if we are taking a 10 percent aria, it means we are 90 percent confident that what we're doing is correct. It means there's still a 10 percent chance we could make the incorrect decision. If you want to be 100 percent confidence, the risk of incorrect acceptance will be zero. If you want the risk of incorrect acceptance to be zero, there is no sampling. If you want your risk to be zero, you have to look at everything 100 percent. Here we are saying we are taking a chance 10 percent that we could be wrong. Okay. So let me ask you this. If you are taking a chance, so let's look at aria versus n versus the sample size. If you want to take less of a chance, so let's assume you want to take a 5 percent chance rather than 10 percent chance, what's going to happen to your sample size? If you want to take less chance, you have to look for more, so n will go up. So there is a negative relationship, negative relationship between aria and the sample size. So if you said, you know what, I want to take 20 percent chance. Well, if I have to take 20 percent chance, I can look at less. So notice if I increase this to 20, I have less sample size. So this is the aria. Aria is what chance am I making? The number of overstatement misstatement, the number of misstatement, but remember when we are doing dollar unit sampling, we're always looking for overstatement. That's why it says it should be number of misstatement. Notice here the number of misstatement are expected, no misstatement expected to be zero. So we're looking at 10 percent and number of misstatement is zero. Again, overstatement is listed here because you're always doing overstatement when you're doing M-U-S sampling. So simply put, if we are taking a 10 percent chance with the number of misstatements equal to zero, our factor is 2.31. And voila, we just find out our numerator, which is 2.31. This is the confidence factor. Now let me go back and show you. If you want to take more of a chance, more of a chance, more of a chance, notice your confidence interval goes down because you are taking more of a chance. If you're going to take less of a chance, your confidence interval goes up. Okay, notice, notice how the confidence interval is affecting this. Also, if you expect more misstatement, if you expect rather than one, you're expecting, rather than zero, you're expecting one misstatement. Well, if you're expecting one misstatement, your confidence interval will go up, will have to go up, the confidence interval will go up. So notice it goes from 2.31, you want more confidence now to 3.89 because you're expecting misstatement. So simply put, the confidence interval is 2.31. So basically we defined area and how does it relate to the end? So we're done with this, with this, with this word and with this word. We still have to find the denominator, which is the denominator is a computation between something called tolerable misstatement and the population. Well, let's talk about tolerable misstatement first, tolerable misstatement. What is tolerable misstatement? With how much, how many misstatements I can tolerate without rejecting the population? Here what we're saying is something like this. I, if this is zero, I can tolerate up to 575 misstatement. Okay, let me ask you this. If you can tolerate more, let's assume rather than 575, you can tolerate 700,000 tolerable misstatement. If I can tolerate more misstatements, I don't have to look for more, because even though I'm sampling, so simply put, if my tolerable misstatement goes up, if I'm willing to tolerate more misstatements, I don't have to get a lot of ends. Therefore, there's a negative relationship between tolerable misstatement as end sample size. Why? Because I can tolerate more. If I, if I cannot tolerate more, if I reduce this tolerable misstatement to 300,000, so if my tolerable misstatement goes down, I have to increase my sample size, also a negative relationship between those two. Okay, so now we have the tolerable misstatement and we're going to take the tolerable misstatement and divide it by the population. The population is 19,325. Generally speaking, if you have higher population, you need a higher end, but it's not proportionate. So if the population double, it doesn't mean you have to double your size, but generally speaking, you can say higher population would require a higher sample size. Now let's fit this whole thing together and see what is our sample size, because that's the question. But to find out the sample size, we had to go through all of this. So notice, what I want you to notice is I ignored the number of inventory, because this is a dollar unit sampling. I don't care about how many units I have for now when I compute my sample. So TM is 575,000 as a percentage of the population. The population is 19,325. Let's compute this, this denominator 575 divided by 19,325,000, and that's 0.297. I'm going to make it 0.3. So 0.3%, 0.03 is my denominator. Now I'm going to take 2.31 divided by 0.03 equal to 77. Simply put, I have to sample 77 units, 77 of those 31, 3,140. This is the number of unit I want to sample. So basically, we answered the first question, but it's very important to understand how each one of those factors, the population, tolerable misstatement, area in the number of misstatements affect N, because simply on the exam, they could always, I could ask you 15 different questions about those five factors and how did they affect N. Once you understand them, you'll be able to answer all my 15 questions. So make sure you understand how it works. Once again, you can go to my YouTube if you're interested to learn more, I mean to my website to learn more about this topic. So we find out the sample size is 77. That's fine. That's if you're asking about that. Now, assuming, assuming, here's what we're being asked next, assuming a random starting point of 123,608. What does that mean? It means we selected, we went to Excel and we asked Excel to generate a random number, which is basically we asked one of our teammate, select a number between 100 and 200,000. And they came up with this number. So simply put, we selected a random starting point. Even Excel, if you go to Excel, there is a random function, random, and you could just ask them random between two numbers, like it's something like this. It's random and you open parentheses and you put one and a thousand. And it will give you a number between one and a thousand here between one and whatever the number is. But the point is it's randomly selected, identified the cumulative dollar amount associated with the first five samples. So simply put they're asking us. You, you selected the show me the five, the first five account you're going to be selecting from those 3,124. So how do we do this? How do we do this? So the random starting point is 123,608. Well, what we do at this point, we have all these accounts. We have what you have to understand is we have those inventory account and we have them in total of 19,325. So we have item one, item two, item three, item four, item five, item six, all the way to 3,140. And those are, and those are they have each one of them has a dollar amount. So the first one is 100. The second one, 200. The third one is 400. I'm just giving those dollar amounts. So here's what's going to happen. The cumulative, the first one is 100. The second one, the cumulative 100 plus 200 equal to 300. The third one, this is the cumulative column, 400 plus 300 equal to 700. And let's assume the fourth one is a thousand, the fourth unit. So that's the cumulative is 1400, so on and so forth. So you guys got the point. So we that we have the cumulative and this is how we compute the cumulative, although, although we are not given the cumulative here, but the point is how do you, how do you select those units? So here's what you do. The first one, let's assume let's add zeros to these numbers. The cumulative were 100,000, 300,000, 700,000, 1.7 million. So those are all add zeros to them. Okay. So to make it more realistic. So if you are being asked, assume a random starting point of 123,000, 608. So we find the random point. So the random point is 123,608. Then how do you find the second random dollar selected? So this is the starting point. So 123,000, 608, it's in between 100,000 and 300,000. Therefore, we would select item number two. Now, how do we select the following item? Because we need to select five items. Here's what we do. We'll take the total population, 19,325,000, and we'll divide this number by the sample size of 77. So let's do that. So if we take 19,325,000 divided by 77, and that's going to give us 250,097 dollars, 250,097 just surrounded, 97 dollars. What does that mean? This is called the sampling interval. This is called the sampling interval. So how do we use the sampling interval? Here's what's going to happen. So this is the first item. How do we select the second item? We're going to take 123,608 and we're going to add to it the sampling interval of 250,097 dollars. So the second item will be 374,582. Now, 3074,582 falls between 300 and 400,000. Therefore, we'll select item three. Then the third item will be 374,582 plus 250,097. And that's going to give us 625,556. It falls between two and three. We already selected three. So basically third is not really useful. The fourth item, 625, 550 plus 250 plus the interval. And that's going to give us 800, 76,530. 876,530 is in between those two. We select the fourth item. I mean, here it seems they are I'm selecting every item that that's because the numbers are just made up those numbers. So it doesn't have to be correct. And the fifth item is 876,530 plus 250,097 dollars, which is equal to 1,127,504. Again, I would look for that interval and I would select the number. So this is how you would select the five items. This is how you would select the five items. So this is how you would select the five items. So we learn how to compute N, which is the sample size. We learn how to find out the five items. This these questions again, I can ask you so many different questions about about about this question. So make sure you understand how to find the sample, what each item means and how to find a particular item from this. In the next session, what I would do is I would assume a sample of 100 units was obtained and this were the results and I will compute the bound the overstatement bound. Remember, it's always overstating when we're when we're using M.U.S. and draw the audit conclusion. As always, I would like to remind you to like my recording, share it, visit my website for additional lectures about this topic and auditing. If you want to improve your CPA exam preparation score, check out my website, study hard and stay safe, especially if we are living through the through the coronavirus.