 exercise to do now. Easy and straightforward exercise doesn't. You don't have to do a lot of things this way. You just need to find out which of the statement is incorrect. So don't try and answer the whole expected values. Read the question. It says only the expected cell for youth and girls. So it means you need to be calculating the expected value for this. What you need to also realize with this table is there is no total. So you must calculate the total first for the table. Then calculate youth and girls expected value. So you will say the row total multiplied by column total divided by n. So which your n will be the grand total. And then option number two is asking you. What is the null hypothesis? You know what the null hypothesis always has to state. Is this the correct way of stating the null hypothesis? For the alternative, is this the correct way of stating the the alternative hypothesis? Remember you need to also do the degrees of freedom. Your degrees of freedom is number of rows minus one times number of columns minus one. Yes. So you need to answer that one. And then you need to do chi-square test distribution. Is it asymmetrical? Remember when we look at the table on the chi-square, it looks like this. So if you go to the graph that they drew for the chi-square table, does it look like a symmetric? Mine looks symmetrical in this way that I've drawn it. Let's change it. So this is how chi-square looks like. Is it asymmetrical? The tail goes to the left, to the right. Is it asymmetrical? This is a chi-square distribution. Is it a symmetrical distribution? And you need to say that. Okay. So that is your exercise. I will come back in one to do the feedback. Hey, I gave you more extra more minutes because I thought you might take longer. Did you calculate the totals? What is the total for girls? It's 78. 70? 78. Total for boys? 122. 122. And then the grand total will be 8 plus is 10. 38. 200. And then I'm not going to do the total for girls. I just want the total for youth. Total for youth? 38. It's 38. So to answer number one, row total times column total divided by n. What is the row total? 78. Our column total? 38 divided by 200. What do you get? 14.82. It's 14.82, which means this is correct. Number two, it says the null hypothesis states that gender and magazine preference are independent. Is this correct? Yes. It is correct because always in your null hypothesis, it should state that independent. Then for it means for the alternative, it will say the opposite. In this instance, it says alternative is dependent. Is this correct? Yes. Yes, because it's the opposite of independent. The degrees of freedom, how many rows do we have? Over two rows. We have two rows minus one and how many columns do we have? Four columns. Four minus one. Two minus one is one and four minus one is three. Three times one is three. Three. And for it means that is correct, which leaves us with the last one. The chi-square distribution is symmetric. It cannot be symmetric because it has an extending tail to the right, which makes this incorrect. A chi-square distribution, it is a positively skewed distribution, or it is skewed to the right. That is your chi-square. That's easy, right? To answer some of the chi-square questions. So now comes your assignment questions, which I can So this is a contingency table with fake news media and personality. Asking you to calculate the expected frequency for social media and politician. Asking you to calculate as well the expected frequency and traditional, the expected frequencies for traditional media and sports stars. They also asking you what is the observed frequency for traditional media and politician. Then, number four, they're asking you what is the null hypothesis. And number five, they're asking you are there two degrees of freedom. So you need to calculate the degrees of freedom for that one. So remember how to calculate the expected value, the row total times column total divided by n. Your degrees of freedom is given by row number of rows minus one and number of columns minus one. I'm going to give you five minutes for that question. But if you are done, please don't wait long. Just tell me done, done, done, done so that I can have an idea of how many people are done. So we can do, there are more questions as well. I am done. Are you still busy or are you just going to listen to what we are telling you? I think going forward, I'm going to ask individual to, we are six in this. So every time we have a question, all six of us who are here excluding me, okay, all six of you who are here in, let me not say us, all six of you who are here in this session, you will at least give me an answer for each one of the questions. So I hope you are ready. Whether it's right or wrong, remember we want to help you understand if you are lost. Masa, do you agree? Any guests, do you agree? I know that same always talk. I don't know about the others. I'm waiting for Masa and Rebecca and Mavitella to show me that they agree. Yes, we do. We don't have a choice here. Yes, Rebecca, yes. Masa, are you with us? Mavitella, are you with us? There we go. Yes, yeah, all of you, you are in. Okay, so let's do, we'll start with this one. There are five questions. So the other one will do the same. You are excused from answering this question. Okay, who wants to do with number one? The expected frequency for social media and politician? I'll do number one. Okay, let's give the ladies first. Let's do it that way. So since I can't see who's speaking, who wants to go? Was it you, Ne? Yes, ma'am. What was Rebecca? Oh, it was Rebecca. So Rebecca number one. Okay, the expected frequency. So I took the 3015 multiplied by the 1050. It's a social media and politician divided by 4,000. And I got 791.44. And therefore, number one is correct. Correct, yes. Okay, and Oscar, number two? Yes. I took the 985 times it by 665, the sports star, divided by 4,000. Then I got 163.75625, which are round off. It comes to 163.76. Which makes number two correct. That's it. Thank you. Who's taking number three? Masa, Ambitia and Ne. Masa, number three. What is the observed frequency for traditional media and politician? I got 258 points. Remember, the observed frequency is the value they give you. It's the value they give you in the table. It's your joint value for politician and traditional media, where they both meet, that's the value. Which one is that? It's 350, yes, it's correct. You're saying it's 350. Yes. There we go. Ambitia, number four? Ambitia, I don't know your full name. I can only call you by the name I see on the screen. Okay, Ne, you want to go for that number four? Okay, the null hypothesis, it can't be dependent, it's independent, so that one's wrong. That one is incorrect. And we were looking for the incorrect answer. But just for interest sake, the degrees of freedom is equal to two. Our number of rows have two minus one. And our number of columns, one, two, three, they are with three. Therefore, that would have been correct as well. So, there is one person in this group who went silent on us. Okay, continuing. Also, I'm going to give you five more minutes as well. They're asking you to confirm if any of this statement is correct in terms of the critical values. We didn't do this question. I will deal with that just now when we do the answer as well. But for now, what you are expected to do is see if the critical value, so you go and find critical value of zero comma one zero and the degrees of freedom. So what is your degrees of freedom from here? We calculated the degrees of freedom before, which we found that was two. So you're going to go and find the critical value for each one of this statement in order for you to find out which one is incorrect. When you are done, say you are done so that you know that you have expected all of this. Five more minutes. So, I'm done. Okay, are we all done? I had only one person saying done the rest. Are you guys done? Talk to me. I'm not done. Still struggling with the table. Are you still busy? Are you guys still busy? I am. Done, ma'am. Okay, I'm going to help that lady who said they are struggling with the table. So we're going to show you how to do the critical value for number one. So it says it's 10 percent and we need the degrees of freedom. Remember, you're going to ignore that part. So our alpha is zero comma one zero. So which is that one? Our degrees of freedom is two. So for all of them, the degrees of freedom will always be two. So you just need to alternate for every one of them. So for that two will be four comma six zero six. You see how to use the table. Okay, sorry ma'am. So how do we determine the two? How do we get two? The two-week. We got it because we also calculated it from the previous question. Remember, the previous question was asking there are two degrees of freedom. This is a continuation and how you calculated degrees of freedom. You found the two. So you just use the degrees of freedom and alpha for every one of them. Okay, I got you. Thank you. Okay, while you got me right there, what is for number two? At five percent, that will be at zero comma zero five. So you need to find your car square at zero comma zero five and then the degrees of freedom of two. So you need to look for zero comma zero five. Okay. So in two, so it will be that five point nine nine one. So that means option number two is also correct. Correct is. Option two is correct. And who wants to check option three, which is two point five. What is two point five? Two point five is zero point two five. Zero point zero two five. Option three is correct ma'am. Option three will be correct. And then option four, which is zero point zero one. That one's also correct ma'am. She is nine point two one zero. So all of them are following one another. Is that one? So which leaves us with one final question, which says, which says as the level of, as the level of significance increase or decreases, the critical values decreases. So if we look at all these values, so our level of significance, which is that if it decreases, so if it moves from zero comma one to zero comma zero one, it's decreasing. That's the, that's also the critical value decrease or increase. It increased. The critical value increases because the answer you can see from the table here, it shows we started with the four point six zero six zero five. We ended up with nine point two one zero. So it increased from four to nine. So that means this will be option number five will be the incorrect option. So I think now we're going to almost the last bit of the questions, which will be the last one. So this one you can do on your own. You will need to go and calculate the chi-square test. So it means the first thing you need to do here is to go and calculate the expected value for every value that is on there. For one thousand eight hundred seven hundred five one five four eight five three five zero and one five zero. You will need to go and calculate the expected value for all of them. So you calculate the expected value and once you have calculated the expected value you can calculate the chi-square, oh sorry I must make this a presentation mode so that I can write. So you will need to calculate the expected value, which is the row total multiplied by column column total divided by your n. And when you're done you can then calculate your chi-square test. You will do that. Then once you've done that you can answer the following question, which is almost the same it's related. So you go into, you go into answer whether you are rejecting the null hypothesis or the alternative hypothesis. So another thing is you need to look at the statement because with the statement they say we reject the null hypothesis, we do not reject the null hypothesis, media, platform and personality are independent. What else they didn't give you with this question is the information about the alpha. I am sure I took everything, everything else. So if I go to the question, sorry because I think I didn't copy everything from the question, but you will look at your assignment question and answer that. Let's see. So the question was just question 20 just as you consider the below statement, we reject the null hypothesis, we don't reject the null hypothesis, media, platform and this, but you need more information than that. So if they didn't give you enough information to reject, I don't know how you're going to find that you are going to reject the null hypothesis unless if you're going to use all the test statistics or the critical values that they gave you, which is 10, 5, 2.1 and 1 to see if all of them, when you calculate the test statistic, do you reject the null hypothesis or not? So based on that information, you can come here and say, are you rejecting the null hypothesis and not rejecting the null hypothesis and you will need to state which one of those statements are correct or incorrect and those will be the last questions. Any question, any question. If there are no questions, it is 10 2. Thank you. I have this one last exercise to you. Let's see if you can do it in five minutes. So I'm giving you up until to do this last exercise and then 52 will recap and conclude. Come on guys. How many of you have done only one person? Okay. Do you want to give us the answer? And then we recap and conclude. Chi square test was calculated and that is and that was the answer for that chi square test. It was 18.50. Assuming that there is a five degrees freedom of five degrees of freedom, which one of the statement is incorrect. So it means you're going to also do the same as what we did with the previous one. Go and look at the table for your critical value. So the first one you're going to look at the critical value for 1%. So if the critical value for 1% is it equal to that or for 5% is it equal to that or for 10% is it equal to that? And once you have found those critical values for those, then you can determine especially for 1% whether are you rejecting the null hypothesis or for 5% are you rejecting the null hypothesis. So you need to find the incorrect one. You are done. So it means you went and found the critical values. So what is the critical value for 1%? 15.086 is right. So this is correct. And for 5%? 11.071 is correct. So that is correct. For 10%? 9.236 is correct. So that is correct. So now since we know all this, so we're going to say for 1%, if this is our region of rejection created by the critical value of 15.086, where is 13.05? 13.05 falls inside the air and it falls in the do not reject area. And the statement here it says HO can be rejected at 1.5. Therefore, this is the incorrect statement. If we look at number 5, it says our critical value is 11.079. So if we put 11.09 here, 11.071 here, our 18.5 will fall somewhere inside a rejection area. And therefore, H0 will be rejected at that point. So which makes statement number 4 the incorrect one. So you need to know how to find the critical value and how to use your critical value and your cost statistics to make a decision. And with that, it concludes what we did today. So today we discussed how to apply the cost square for independence. Remember, in your module, you only do cost square for independence where we use the contingency table. If in the contingency table, they didn't calculate their total to quickly calculate the total because then the possibilities are you will be required to use the total to calculate the expected value. And we use those expected values to calculate the test statistics because the test statistic is your observed minus the sum of your observed minus your expected square divided by your expected. To find the critical, to find the critical value, we use alpha because we only have one side of the rejection area. So we just use alpha and the degrees of freedom. And remember, our degrees of freedom is number of rows minus one times number of columns minus one. And when you have your critical value, then you are able to clearly define where your region of rejection will be. And you will use the test statistic and your critical value to make your decision. And that's all what we've done today with cost square testing. So by the end of today's session, you are able to complete your assignment three and submit it. Please make sure that you submit it when in advance because if you wait for the you wait for Friday, things might happen. So please go through your assignment. If you have any issues, remember you have the WhatsApp group to discuss. You have my UNISA to go through and discuss. Otherwise, thank you for coming. I will see you on Friday when we do linear regression. Then after that, every Saturday and every Friday, we're going to do exam preparation. Therefore, it means the majority of things that we're going to be doing on Fridays and Saturdays, I will post them on my UNISA as online assessment. We are going to go through those online assessments when we do the exam preparations. I will try and find as many questions as possible from the past exam paper and post them as online assessment. So every week before you come to class, you will have to go through that online assessment. Not this coming Friday, but from coming on, not the coming Saturday, the coming Saturday, we will do the exam prep like in recap. So we'll go through what we have covered so far, refresh our minds, look at how the composition of the past exam papers looked like, how you're going to write your exam, we're going to iron out all those things. Then the following weeks, proceeding to that one, we are going to do the assessment. Every week is assessment. So it means every Friday, when you come to class, you should have already completed the online assessment. We're going to do those activities in class. We're going to get the answers because I realized that on my UNICEF doesn't give you the answers when you answer the online assessments, but we're going to go through them in class. So it means by the time we finish with all exam preparations, you would have answered all the past exam papers that I could get access to. Then you would have answered most of the questions. In case UNICEF decides to repeat one of the past exam papers, you would have answered all of them. So it should not be a problem and it will give you time to practice and practice and practice. So every week, there will be an assessment linked to the activities that we're going to be doing on every Friday and every Saturday. There will only be one assessment for that week. And then the following week, we cover the other assessments. And then the following week, we cover the other assessments. So every week, it will be an assessment day. And with that, thank you guys for coming. And I will post the recording online tomorrow. Actually, because today I'm very busy. Thanks for the question. Thank you. Thank you so much. Thanks. Thank you.