 Ms. Booyah, your mic is muted. Oh, yeah, I didn't notice that. So it means all along I've been talking to myself. Yes. So when last did you hear me talk? When you say that, you will come back. For almost 30 minutes, I've been talking to myself. Yeah. OK, apologies for that. Can you see my UNISA? Yes. OK, sorry. I was saying, here and now I don't even know where to start now, because I was talking to myself. I was saying on my UNISA under your module site, there are past exam papers that you can use also to practice. But I will take some of the questions, I will use this past exam papers as well. So that you can have the answers and the responses and we can practice on them. And sometimes, I think, sometimes your lecture will post in the additional resources, I think. It will post the mock exam paper, which will be last semester's exam paper. It will also contain some answer solutions. But I know that UNISA does not give, sometimes they don't give a solution on how to answer some questions. And I hope with this one, we will go into detail and put the stuff on how to answer. If it's a probability question, what is the formula that you use? How do you calculate it so that you are aware of how do you tackle a question as well? And what else is there? There is nothing more. And then there is my site, which is the e-Twitter site, which as you can see, I have so many things happening on my site. On my site, I also don't have official resources. I have additional resources. And that's all the material, like the presentations that I go through. I just summarized some of them. And I think you get this. Every time I uploaded them, you always received them. Then I know that I've created lots and lots of discussion forums, which I was hoping that we can have discussions as per each chapter. If you're struggling with one chapter, I know I've put some of the things on there. But this is just for you to discuss where you have issues with any of the questions. So you just use that. And I had also created the assignment once where you needed to discuss the assignment questions, but you're not using those. And then I, OK, the learning skills, I'm not going to go through that. Then remember the online sessions that we always have, the recordings, all of the recordings are here. If you expand them, some of them I've made them shorter. I've split them into two so that then you don't spend so much time on there. You can see all of them. And it also describes what is every video talking about we're discussing in that video. And these are the online sessions. And then I know that I'm repeating some of the things that we went through some time ago, but just to make you aware of what is out there as well. Then I also had some of the activities where it starts with the key concepts. And under every key concept, if I open one of this, there is the discussion. It's just a summary of what you went through. It's the same thing as it's on the slides and in every way. It's a repetition because we're repeating everything and everything again and again and again. And I can see there is someone already commented as well. Then there are additional videos. The first were videos that I did seriously last year when I was helping other students, I created shorter videos because we had 30 minute sessions. So I uploaded those videos, but they had, we didn't do all of the sessions because then the tutorial started and I stopped recording the 30 minutes videos and Unisa took over and started recording the videos and uploaded them on their slide. So I just shared those videos with you because there's actual videos, not long, 30 minutes each. And at the end of every video, there are questions, which also, these questions come from your past exam papers. I just put them here so that I can watch the videos. If you look at them, you can take them. And I was hoping when you take or when you answer the question, at the end of the question, you should be able to see who answered what or how many answers were there. Or maybe I should go to the other view, not this view. As you can see that question was not answered by anybody. If I go there and I get this and I say, what is the answer and I can choose, let me choose that one. I'm just doing it randomly. Choose that answer, what happens? And my answer is submitted and yeah, you get a response. If you look here, great. Yes, inferential statistic is a method used to infer the data. So all the questions that are here or that are on the line by doing, all of them have a response. And once you are done, you can also go in and check if any of the responses, people are responding the same way as you are responding to the question. So you should have all those capabilities from your side as well. But not only that, if I go back to the beginning as well, at the end of the sessions, I always kept the online sessions as well. So you can see there, I tried to answer this one just to see what kind of answer I get. And you can see there, it says no. Categorical data is the data that can be placed into categories because I wanted the response to show if you choose the wrong answer. You can see that this does not penalize you or anything. This is just for you to learn. For you to learn and understand every chapter or content that we go through instead. But then I noticed that nobody's answering these questions. So I stopped posting the questions. So I'm going to take all these questions again and I will create an online session which will look almost like this. So this is an online session. And you will also get an online, when you go write the exam, you will also get, you will receive a link that looks like this that says online session. And that will, oh, your online exam and that will be your exam. And you will be able to take that exam. So at this point, this is the submitted results, but you will not have this part. You will have the assessment. So if this is the assessment, I want to show you what it looks like. So you will begin the test. This is not timed. So your one will be timed, but it will come with questions. And then you will say, what will be the answer to this question? I'm just going to randomly select because this is a poison. I need to go to the table and answer the question. And then I am done doing that. You don't have to press save. You can just continue, continue this day. When you answer the question, it stores the answer on the database. You save if you want to go out and do something and then because you haven't submitted as yet. So that when you come back, you don't have to start from the beginning. You can continue from where you left off. You don't always have to press the save button. So if you're still busy with your assessment, then you can go on and say, or this one it is a discrete probability question. And then you say, or the answer maybe for the incorrect answer because I don't know which one is, I'm not calculating at this point. I'm just showing demonstrating to you how your exam will look like. And you will choose the correct answer that is related to that question. And you are done because this is the end. If I press next, you see that it's grayed out. I don't have that, but I can save. Or I just submit for grading. If you're still busy with your exam, let's say you are busy with your exam and you still have time, let's say you still have time. You want to go back and check your answers. You don't have to submit. You can save and go back. If the lecture allows you to have a button to go back. And if they didn't allow you to go back, then you can go back. The next step is to press submit for grading. And once you submit for grading, your exam will be submitted. So like now it will submit. Once it has submitted, you will receive this kind of information again in your inbox as well, in your email. You will receive a copy that tells you that your exam has finished. And you submit it and then that will be, and then you wait for your result. I'm not sure if you are able to see the submitted assessment on your side because I'm locked in as a facilitator or a tutor on this side and I'm able to see this. And what I will do every week is, as you can see there, the first one that was submitted on the 19th of September, there was one score. So it means one question was answered correctly and I'm able to come in here and see. And I will be able to see that, oh, but then they calculated it wrong and I will be able to see which one they got it right. And if the majority of people are getting the discrete probability correctly, then it means you don't have any problems with discrete probability. We don't have to dwell too much on that. And if the majority of you are getting the Poisson probability questions wrong, then it means it's a problem. We need to find more questions on Poisson probabilities and then we're going to practice more on those. You understand why I'm saying you need to take this assessment because then they will help me know which areas we need to concentrate on on a Friday and Saturday to discuss further so that we are all on the same page. And the other thing that will help me as well because I will be able to see the scores, I will be able to also see the distribution of your scores. It will not tell me who is who and who did what. I'm not even interested in the individuality of everybody. I'm interested in how do you perform as a group? That's all what I am interested in. So I'll be able to see that there were two students who submitted and how many points did they receive and what are the questions that they struggled with? So one response struggled with that one, one response selected. And I can see the different types of selections that you are making as well. And it will guide me to see that. Oh, those who submitted this question, this way it means they didn't do the greater than or equal they did the less than. So then it means it's a problem. We need to tackle the content to read. Oh, those people don't understand how to read the question probably correctly. So we need to help them because if it says, we'll get six calls. It means it is exactly, it is equal. So we go and focus on those nitty gritty things to help you understand how to answer every question that you might get in the exam. And it will be just like this. For all the questions that we will do in your assessment and if you look there, there are no names because my name should appear on every one of them. So I will not be seeing who is submitting what, I will just get the feedback of the entire group as well. And then I will use this to have those discussions. Okay. And that is all when it comes to to the online assessment that you need to know. The other thing that you need to know, I need to go back to your module site because I need to download the past exam paper that is there. I will have to download both of them. Okay, it's taking long. Let me just, for now, I'm just gonna download both of them. So now since you are writing online, the key other issue, remember today, we're not doing any too much work, we're doing administration, we're learning how the exam process will work and I'm picking all that. And then we can look at other things if you have other questions for the next two hours. We might not even spend the whole two hours online. So come on. Just gonna open one. Oh, come on. Okay, they will open. What I want to also mention is that it's opening. Is that since you are writing online, you will not be getting a hard copy exam paper. So if you are getting a hard copy exam paper, I will be saying there are limited formulas at the back of the exam paper. You need to make sure that you understand what those formulas are. Now is your chance to make sure that you have everything you need in front of you because you're writing online. It's as much as it's going to be an open book. It's not gonna be a closed book because then nobody's going to monitor what is in front of you. Not that I'm telling you to cheat, but all I'm saying is since it is online at your home, you have all the material, make sure that you at least have all your things that you will require. Like, I'm gonna go skip the whole format of the question. Go right at the end. Make sure that you have tables some way, way you are going to use them. Make sure that you have your formulas. So the tables are very important. You must make sure that you have the formulas and some of the formulas are here. On the past exam papers, they don't have all the formulas. So like, for example, here you can see that they have the formula for Q1. They don't have other formulas like Interquartile Range or Quartile 3. This is because every exam paper, they also put formulas that are relevant to that exam paper. Majority of exam papers do not have the Quartiles in there. So they never used to include Quartiles. If you look at the basic probabilities as well. Remember, there are so many questions. There are so many questions or formulas in the basic probabilities. But in the exam papers, they used to only give you two. But now, you have all of them in front of you. Make sure that you write them to say, by chapter, chapter by chapter, to know that these are the formulas that you're going to be using in this chapter, in this chapter, in this chapter. You must make sure that you make a list of them. So that they are there when you need them. You can refer to them and make notes to them. Because some of the questions, for example, like this one is to calculate the mean. But you know that what is the mean for the population is the same as calculating the mean for the population is the same as calculating the mean for the sample. And if they give you things like this, you know that this is the sample formulas. And these are your discrete probabilities. So you will need to know how to calculate on them. Or you're going to use the tables because you don't have to use the formulas. But sometimes that means for in the exam, in the assignment that they will ask you a question based on the formula to see if you know how to substitute the values onto the formula. And for normal distribution as well. And you will see that also the formulas on the past exam papers, they follow the logical order of your chapters or study units as well. What else don't they give you? So they give you most of the formulas in the past exam papers, but you will need to go and make your notes next to each one of them so that by the time you go write the exam, you have effect or a formula sheet somewhere where you can always check on it because you only have limited hours to go back and forth, back and forth from working on online. It's different than working on a piece of paper. Okay, so let's go back to the format of your exam. Two hours, we explained that, so this no longer applies because you're writing online, but for exam is also out of 100 months. And the order of your questions in your exam, so you're still going to write 25 questions. The order of your exam will follow the structure of your module. Remember, your module has 11 chapters. Your module has 11 chapters. With those 11 chapters, it means you're going to get at least two questions per chapter. Sometimes you will get three questions from one chapter because they are doing, if I take two questions per chapter is 22, then there is three left. So the distribution of those three might be, one might come from hypothesis testing, one might come from Chi square, not Chi square, but confidence interval and one might come from another basic probability, but you will never know. All you need to know is when you unpack your question and starting from question one, you will know that you are moving step by step through the study unit. So you will know that question one and question two might come from study unit one. So let's see if my logic is correct. So question number one, this is study unit one. So your question will look almost like this. Question two, study unit one. So you can see that there are two questions from there. Study unit one and two, I think one talks about, yes, study unit one and two, because two talks about visualization. This is study unit two visualization. Study unit two visualization. And sometimes with the visualization, especially when they give you the standard lift, it will include also study unit three. So you can see that already, question five, study unit three. And you can see that already I'm doing two questions per chapter. Study unit three, study unit three and study unit three. So there are three questions. So study unit three might also come with three questions because it's bigger than the other study units. Then study unit three. So there are four questions from study unit three. Then study unit four, it's basic probabilities. You can see that you're going into different, and there are two questions from basic probabilities. Then we have discrete probabilities. There might be three questions, there might be two questions because in study unit five, remember, there is the basic probability of discrete probability, the basic concept of discrete probability. Then they will be, then there will be the, then there will be the binomial probability, then there will be the Poisson probability. And that is the structure. So you will see there is one question, second question, which is binomial, and that's the question which is Poisson. That is study unit five, study unit six, which is normal distribution. There might be two questions from day one, two. And we go into sampling distribution, which is study unit seven. Six is normal distribution. Study unit seven, sampling distribution. There should be two questions. And as you can see, it's question number one and question number two. And then study unit, confidence interval, study unit eight. There should be two or three questions from here. But because of the first one where they had three questions for basic probability and for the other one, they might have two questions. So let's see, because for confidence interval, yeah, we have three areas as well. Remember that we have where the population standard deviation is known, when it's unknown, and for the proportion. So one question, study unit eight, one, two questions, and three questions. So you can see there, three questions from study unit three. So study unit eight. Then we go to study unit nine, which is hypothesis testing. Also with hypothesis testing, they might give you three questions because it also has three different section where the population standard deviation is known when it's not known and when for the proportion. So let's see how many questions they ask here, but they might ask two because we're almost nearer to the end. One question, two, one question, two questions. So they only asking two questions here, but they can ask three, depending on how many questions they ask in other study units. Then we go into study unit 10, which is the second last. They might have only one question or two questions. They have two questions. And the last question, which we just did on Friday yesterday as well, the linear regression is your last question. They might also have two questions here and one question on halfway. And that concludes your exam. The structure of your exam follows your study unit. You cannot go any wrong. That is why when you write your formulas, make sure that you write them per study unit so that you know when you move into the end. In your mind, you must know that what are the things that makes move from, for example, like when you are in normal distribution, what are the things that makes you move from this question not being a normal distribution, but for it to be a sampling distribution. For example, these are confidence intervals. Let's go. Yeah. So here you're talking about normal distribution and we're asking about the probability of X greater than that. Then we move into questions that ask about standard M. You should know here and now, you're no longer talking about the normal distribution. And when they mention things like sampling distribution, you know that you are in charge of things like that. So make note for yourself some way because then you will be prepared for your exam as well. And if you have any question for now, feel free to ask. Do you have any question? Hello. Yes. When it comes to sampling distribution, I don't know how to do some calculations here. If you have your start guide, it's just time to page 153 of your start guide. It might take longer to upload, to download. Yeah, I was trying maybe to do some calculations here, but I don't get it right. But if you can show me how to do this calculation, I'll be very much happy because I'm stuck there. Okay. Just give it a sec. Let's go there. Set page. 153. Just the questions you are talking about. Go straight to 153. 153. 153 is you. Please. I thought 153 at the top will be the same. Okay, sorry. My bad. But like my start guide doesn't have 153. I can see it's 143, 144, 155. Going back again. There you come. 152. And, okay, so. Yeah, you see the first step is about the formula. Then I can't do the calculation on the second step. This is one of 0.46 minus. But I stuck here after multiply by. That's where I got stuck. So this is the solution to the question. Okay. So they, yeah, actually they're saying that the area between A and B is 0.9. So you need to understand that when they talk about the area between A and Z. So we're going to draw a graph. It's always nice to represent your information in this manner with the graph. I think they omitted to draw the graph here. So, oh, come on. I cannot write online. Okay. So, this is the probability. It will mean the area underneath the kef. The safe between A and B is 0.9. You need to go find the Z values of those. But since because, you might also remember this, because this is Z and this is B. It means you took one value and subtracted it from the other side. Remember that? Okay. But we need to go back to the question because some of the information like the probability of success should be given in the question and weigh the question. That should be the last questions. And there we go. So yeah. So yeah, they give you the question and they tell you that for this poll on personal finance it was 46%. That is your probability of success for that poll. So you will need to know that this is the pie value that you have. They also give you the sample size name. Now, since we go to the question, there's between. So, and because it's the proportion, you must also remember that this is the proportion. And they say the probability is 90% for the same sample percentage will be obtained for a symmetrical limit of the population percentage. So, to visualize it or to define it properly for it is since they're talking about the symmetrical limits, it means if it's in between, it means it should be, there should be the starting point and point for that area. It should be equal. It should be between those two points. And that is why they define the two points as A and B. We know that we have 46% which is our pie. And then we have, we're going, wait, wait, wait, wait, wait. So we know that we have our area of success, which is the pie. Then you also remember that now, because this talks about the limits. So if we are only given the population parameter, not the sample parameter because they are not doing that. So we will need to create the limit. So our limit will have the, let me do with the confidence interval. Remember that it has the plus and the minus side. So we use the population as our parameter or our point estimate. And we need to be using the critical value. Remember the critical value is the value you find on the table. It's your Z values on the table. So it means we're going to use that 90% which is our probability, the area. We're going to find it on the table and we'll find the Z values that corresponds to that Z big. And that will be the area that we're looking for. So what we do, we know three things now. We know N is 200. We know the probability of success is 46%. We know that our area is 90%. So we go to the table. You will go to the table and say for 90% your alpha is 0.1. But remember, because it has two sides, you will have to divide 0.1 by two. So that we get 0.05. 0.05. So let's see what is the answer there. 0.1 divide by two, 0.05. So we go to the table. You will go to the table. Actually, I shouldn't have left the way we were. I can use the past exam paper for that. So you go to the table. Let's use this one so that we don't scroll up and down. You look for the normal distribution which is the cumulative standardized normal distribution which has the positive and the negative side. Here we go. Inside the table, we must look for 0.05. So you come here, you look for 0.05. And remember, this is that one way to line between the two values which is 0.05. It can either fall here or it can fall there and we go out, we find that it's 1.6 and at the top we take 4 and 6. So it's 1.465 and that is what you have there. So that is the critical value. So you come back to the point estimate or to the class boundaries, you substitute. We know our probability of success was 0.6. Our critical value, we found it. It was 1.645, the square root of the probability of success times one minus the probability of success divided by n which is the standard error. Substitute the values 0.46 times one minus 0.46 divided by 200 and you find the test boundary. Yeah, I want to at this point, can you please show me how do you calculate this one? 0.46 minus 1.645. Yeah, I will show you on the calculator just now. Let me open the calculator. Okay, so you want to know how to calculate this whole thing? Yes, please. Okay, you do it step by step. It seems like my calculator is not responding to me now. What's wrong? Which calculator are you using? I'm using Casio, second edition. I think it's gonna open multiple versions now because I've been ticking and ticking on it. Okay, let's do it this way. So you're using Casio. Does it look exactly like mine? So a Casio calculator, does it look like this? Does it have a fraction? It doesn't have to be gray. It has to be black. Does it have a fraction? It's not gray. It does not have, you don't have the one that has a fraction in it. Okay, now it's fine. Every calculator has its own functions. So we're going to do this step by step. The first thing I will advise you to do is do not try and answer from this side and go that side. First solve what is inside the square root first by starting with the one in the bracket. I say one minus 0.46 which will give you the answer of 0.4, 0.54. Multiply that with what is outside the bracket which is multiplied by 0.46 and you will get the answer which is the one at the top. You have the answer will be 0.2484 divide it by 200. So you divide by 200 and get the answer by pressing the equal sign. Ignore what you see there because this is 0.00124 and some odd numbers there. This is the answer of everything that is underneath the square root. Now take the square root by pressing the square root button on your calculator. Since your calculator doesn't look like my one, look for the square root function. Press the square root and press the equal sign it will give you the answer of the square root. After you get this answer for the square root multiply it with 1.645. Multiply the answer that you got by 1.645 and press equal sign to get the answer and this will be the answer you can write it. You can write it down there. And then go and say 0.46 minus this whole number. So you can write this number down 0.057973 one, two, three, five, one. You have to write all of it. In order for you to be able to get to this number we only round off when we get to the final answer. So now you take 0.46 you say 0.46 and then you subtract that whole number you wrote down somewhere you say 0.057973213212 Then there is a delete button on your calculator as well. You can delete if you made a mistake. Three, one, two, three, five, one. And you press equal and you can see that the answer is there. And I can see that they rounded off quickly as well because they have 0.21. The answer should be 0.20 and 0.4020. They rounded off two quickly to three decimals or four decimals. I'll take the four decimals from what I have. I'll say 0.46 if I say minus 0.057977 Let's see what they get. No, they still not getting the same answer. So they rounded off somewhere quickly to three decimals. Let's see, 0.46 minus 0.058 equal. So they rounded off to four decimals, something like that. So they rounded quickly because if you keep all the values you should get 0.42020. Something where they do in the calculation they rounded off quickly. If you're using a case show like this one. So yeah, I'm also giving those who are using the case show like this one, you can do this whole thing at once. I say 0.46 minus your calculator knows the Bodma's rule. It will do the correct one. If you're going to do this and you do them manually and start by doing 0.46 minus 1.46 you will get it all the wrong. Well, you need to do it in order if you're doing it manually. Six, four, five and say multiply by and this is the square root, you say square root. And because this is a fraction you can use the fraction mode and my thing is instead mode I need to convert this to a normal mode. So I must start from the beginning, 0.46 minus 1.6645, multiply by the root. I put the practical root and at the top is 0.46. Open bracket. Open bracket. 1 minus 0.46 and you go scroll down and put 200 there. And when I press equal, it will give me the same answer as we got from the best time when we would need my work. Any other question? We are almost done. I'm not clear because you will show me how to read with the Casio calculator here. So I didn't, I'm not yet clear. Can you read for me please? Which one? The manual one. Remember, you are not using a Casio. I was showing those who are using a Casio now. So I showed you the first time you do it separately. Like since you are not using a Casio calculator you will have to do first the one inside the bracket. I'm using Casio. I'm using a Casio. If you said the Casio does not look like my one. I asked you if your Casio has the fraction button like this. Has a blockies. Does it have blockies? It will be blank. It will be Casio FX287851782. FZ82 or something. What kind of a Casio are you using? Does it have this button that looks like this? Like a fraction button. If it does not, then you cannot use the fraction button like I am using. You will do it manually by first doing what is inside the bracket then multiplying by the 0.46 outside, dividing by 200, taking the square root, multiplying it with the critical value and writing out the answer. When you are done then you can say 0.46 minus the answer that you got the previous time. If your calculator does not look like my one right now, you just need to do it manually, step by step. Then remembering the both must say brackets first, powers or exponents or roots needs to be taken care of. Multiplication comes before addition and subtraction. So you will have to do the multiplication first before you go to addition or any other subtraction. Okay. Any other question? I hope you are clear. Otherwise, if you're not, then can we take this? You can request a welcome video chat and I can show you on your calculator as well. Yeah, it's better than this maybe. Yes. Because I don't see your calculator, I don't know how it looks and I really want to help you to know so that you can understand how to use your calculator that you have in front of you. It's very important. Any other question? If there are no questions, then we are done for today. So we can have a lovely weekend. I will see you. I will send a notification. I will also post on the WhatsApp group. I will send an announcement when the online assessment is available. I will do it tonight and tomorrow. I will try and publish it on Monday so that you have enough time during the week to go through some of the questions so that by Friday and Saturday we have enough information for us to do the exercises in class. Please don't forget to also chat with me for your calculator so that you can also be able to answer some of the questions because then they will include some calculations. I will also include the chapter 3 or study unit 3 which requires you to do the mean, the standard deviation, the coefficient of variation. Make sure that you learn those steps on how to use your calculator. Let's go to the session where we did study unit 3 and look at those videos again on how to use your cashier, your shop calculator to answer those questions so that some of those questions you can practice using your calculator. Okay. All right. And with that, that's today's session. Thank you very much, guys. Remember, if you have any other questions as well, feel free to post them on WhatsApp or on my Unisa. Thank you, ma'am. Thank you, ma'am. Enjoy the rest of the class. Thank you, ma'am. Thank you, ma'am.