 So, we started looking at the first exercise on the hypothesis testing. So we're going to continue with that and go to question number eight. It's also a hypothesis testing question. If we look at the question, it says to test the hypothesis. The non-hypothesis says that the mean is equals to 100 and it is against the alternative, which states that the mean is greater than 100. So since, because this is greater than, it means we're doing a one-tailed test. And this also tells us, it also tells us that, it also tells us that we only have one regional projection, which will be on the right. My graph looks so weird. It tells us we have one region of rejection, which is on the, on the right because of that greater than. So if anything falls in this side, we're going to reject our hypothesis. Therefore, it tells us that we're going to have only one critical venue and based on the, based on the question that, or the statements that we are given, we need to also check because we know that we're doing hypothesis for the mean. Are we given the population standard deviation or are we given the sample standard deviation? So if you continue to read our question, our sampled mean, which is our n, our n is 100 and the observation found that the sample mean X bar is 106 and our standard deviation and they put the S. Therefore, our population standard deviation is unknown. Therefore it means also our critical value, it will use a T alpha because it's only one-sided tests. So it will be alpha and the degrees of freedom. So the question says, assume, assume a significant level of, of 1% calculate the test statistics. So also with this one, they are not asking us to find the critical video or anything else. They're asking us to calculate the test statistic. So we're going to use the T statistic, which is the mean minus the population mean divided by your standard deviation divided by the square root of n because this is my standard error and since we are given the sample standard deviation and then we just substitute the values into the formula, our mean is 106 minus our population mean is 100, it's always stated in your hypothesis testing divided by our standard deviation is 35 divided by the square root of n, our n is 100 divided by this 106 minus 100 equals 6 divided by 35 divided by the square root of 100 equals 3.5 and this is equals 6 divided by 3.5 equals 1.714 and the answer is in three, this is in four decimal places. So this will be 343 because the answer is 285714. Oh, I forgot, I was not supposed to do it for you, you are supposed to do it anyway. The next exercise you will do it yourself. And when you look at the answer, and the answer will be option number is, you must be very careful when you answer this question because if you look at them, they look almost exactly the same. They look almost exactly the same, it's just that for the others, they have swapped around the values of the ones and that's how you will answer that question because it's asked for the test statistic and this is our test. That was question number eight and if you look at it, there were only two questions for hypothesis testing. Now we move on into question number nine. With question number nine, if you look at it, they gave you the table and all that and this we can assume this is because square test question. The trustee of a company pension plan has solicited the opinions of the sample of company employees about the proposal vision of the plan. A breakdown of the responses is shown in the table below. We want to test if there is enough evidence to infer that the responses differ among the three groups of employees. This is the responses on a contingency table. Which option provides the observation in order to calculate the cash wave value? All they want you to do is to calculate the expected value of this table. How do we calculate the expected values? We calculate the expected value by saying the raw total multiplied by the column total divided by n which is the grand total. So what you have to do is to calculate the total of this table and calculate the total of the table. So I can rewrite that formula again at the bottom and I'll write it here. So the expected value or observation is given by the raw total multiplied by the column total divided by n or the grand total. So what you do is quickly calculate the total of this table. Again you create total and then you create total and we're going to use the total for calculate the expected and this is where your n will be. So calculate the total of the table. I'm going to give you time and then we're going to work out the total. So what is the total of blue color which will be 67 plus 73? It's 607 takes 2 plus 11, 110, 110, 110, which one, 67 plus 63? The top one? The top row? It's the 7 plus 32 plus 11. Oh, so this is 110, okay? Yes. And the against? 63 plus 18 plus 9? 90. 110 plus 90? It's 200? It's 200. So we also need to do for the columns? The first? 130. 32 plus 18? 50. 11 plus 9? 20. Now you have the totals. So you just need to calculate the expected value for 67 which will be the raw total which is 110 times the column total which is 180. I'm going to give you five minutes to do the calculation and then I will write them there and then we'll look at the options each one with the right one. We make this table bigger. Once we have calculated them we can go and look at which one is the correct one. So you said for each one? So let's say we want to calculate for 67. So the expected value for 67 you will say it is 110 multiplied by 130. Okay. Right by 200. And this gives you how much? So 110 times 130 is 14300. Divide by 200? Is 71.5. So then you can write there 71.5 and then you do for 32? Then you do the same for 32? 135. Then 2 will be 110 times 15. Now that's 5500 divided by 200. Yes. Which is 27.5 and that will be 27.5 and then do for 11? It's 110 times 20 which is 2200 divided by 200 which is 11. Is that yeah 110? Yes 11. Then do for 63? That's 90 times 130 which is 11700 divided by 200. Yes. 58.5. 58.5. Yes. Do for 18? It's 90 times 50 which is 4500 divided by 200 which is 22.5. 22.5. Yes. And the last one for 9? 90 times 20 divided by 200 which is 9. Now we have our expected values 71.5, 27.5 and 11.5. So now we just need to go and look at which table is the correct one. What happened to the table now? Oh there we go. Come back. So if we look at this. We need 71 and 825 at the bottom so this is not correct. Reduce it again. If we look at option B which says 71.5, 27.5, 11. 58.5, 22.5 it relates exactly the same as what we have on the table. This will be correct. Let's say if we look at the other values we can see that this one was rounded off. This one was rounded off not correctly because it should say 28 if they are rounding it off. And this will have been 59 if they are rounding it off but because we know that we're not rounding it off. Then that is not correct. And if we look at the next one as well. You can see that it also incorrect and the last one as well is incorrect. So the only one that is correct. Is only B. How do we know that we aren't rounding it off? You do not round off. So you will always get a decimal of 0.5. Okay. You always keep the decimals. Don't round it off. All right. So that is how we answer Kaizui questions. Going to the next question. On this question it says consider this output that we have. It's an Excel output where they have the observation values for row one and columns, row one, row two, column one, two and three. Which has the observed values for two variables. They calculated the total for that. And they also did calculate the Kaizui test or the test statistic of Kaizui, which is 0.331. They also calculated the degrees of freedom. And remember how we find the degrees of freedom. The number of rows minus one times the number of columns minus one. Not the row total but the number of rows. So here we have two rows. We have three columns. So you just calculated by using that. They also calculated the P value because that in Excel it will be able to calculate the P value of this Kaizui test. And they also gave us the critical value that we can use for this table. So based on this information that we are given. We need to see if the question is telling us the proof. And you need to know about the Kaizui test. It means if the Kaizui statistic, which is the test statistic, which is that if it's greater than our critical value. Sorry, my bad. I did correctly. If it is greater than Kaizui critical, which is this value, we reject the null hypothesis. That is the decision that we need to make. The other thing you need to always remember is for the P value. Remember P value rejection. So this is for the decision. And also another decision that you can make if the P value is less than alpha value, we reject the null hypothesis. Remember that. So in this instance, they didn't tell us what our alpha is at the moment, but they might tell us on the statement. We need to take that into consideration. And remember, those are your observed values. The values that you see here will be your observed values, your expected values. You will calculate them by using the formula we used previously. Now let's look at the statement each one of them. We can start at the bottom because I just want it's the easiest way to find the answer because then we will find the answer quickly without looking at the complex one. So we go to this one at the bottom, which makes it easy to eliminate if they are correct or not correct. So number one, number E, it says the observed frequency for row one and column three is 179. It means go to this table, look for row one and column three and see if the observed frequency is the same as what they are saying. Is that correct? No, it's one. And this is not correct. Oh, based on the information we're looking for the incorrect one. So automatically you will see that is the incorrect one and you will stop there. But that is not the purpose of why I wanted us to start at the bottom because it's easy to find the observed frequencies and the degrees of freedom. The others you need to think long and hard. But let's go to the next one, the observed frequency for row one and column three is 174. Row one, column one, column three, that is correct. The degrees of freedom, how do we find it? We find it by using row minus one and column minus one. How many number of rows do we have? We have one, two rows. So that will be two minus one. And the number of columns we have one, two, three, we will have three minus one. So this is one, two minus one is one and three minus one is two. And then the answer will be equals to two. And therefore this will be correct. On B, remember, we can use the decision of the p value at the alpha. Our p value we are given in there and they also give us the value of alpha, which is zero comma zero five. So if p value is less than alpha, we reject the null hypothesis. And remember with the null hypothesis, your null hypothesis would have stated that they are independent. Remember that they will state that it's independent and your alternative will state that they are dependent. So based on this information, we can see that our p value is greater than our null hypothesis. Therefore, we do not reject the two variables are dependent. So we do not reject the null hypothesis. Actually, this was made wrong as well. I think the sign should have been it should have been independent because we're not rejecting the null hypothesis because the two variables are independent. So from this example, they didn't do this question right. I didn't notice that as well when I was working through it. Oh, unless if it's me, I, I wrote this question wrong, but this should be independent for it to be correct because we're not rejecting the null hypothesis. Therefore, the two statements are independent since zero point. Before we even move on, I can just validate or check that question because I have the question paper for it. You can quickly check if it was my typing error or it was the typing of the question paper itself tutorials. It can be quick quick. Just now I'll check it for you. Paper question number might be that I am the one who typed the question wrong. Nope, it's like that on the exam paper that I used. So it's a six p value of zero comma zero eight is greater than greater than zero point zero five the two variables are dependent. So it was a mistake that they did from the question paper, but you know that some of these exam papers they have errors. Okay, so this should have been an independent one to make it incorrect. And the value of our critical value is less than the critical the critical value of five point nine the null hypothesis is independent so we cannot reject. So since this we are not rejecting, we should also not reject this the statement should also stay the same as independence. So as you can see with this one, which is true because if it was greater than the test statistic of zero comma zero one is less than our critical value which is five comma nine nine six. Therefore, we do not reject the null hypothesis and we can state that this is independent as far as this one also should have said it is independent. The only incorrect answer would have been option number. Any question. And when we went before you ask question when you go to the exam you might not also know these things because you will never know what your lecture has put in as a correct answer or option which is incorrect like we saw with the assignment as well. We correct answer was marked as incorrect, whereas it should have been a correct one so it depends on what the lecture has submitted as an answer in the options when they submit to the examination department. Any question. So, so what I wanted to ask is so with the first option with option A. The, the car squared stats would that be seen as the, is it almost like the t value or. No, this is our case squared state, which is your sum of your observed minus your expected squared divided by your expected. Remember that. That is your case squared state. That is the way that they calculated. So, so is that how is how is the basically what I'm trying to get to is on what basis to be rejected is that because that's a value effectively that's calculated. How do you. By using the decision with the critical value remember you will go and find the critical value. Let's do it this way. All this. So our kind square test, we're going to calculate it using. You calculated using the sum of your observed minus your expected. Remember that. Yes, go and find the critical value, which is the kind square critical value, which is. Where is alpha and the degrees of freedom. Alpha and the degrees of freedom. Let's say our alpha in this instance was zero comma zero five like they have them. So then you go to kind square spec and you go find alpha zero comma zero five and the degrees of freedom is true. And this you find that it is five comma nine nine two. And this you calculated it using that formula based on this calculated the expected value and solve it and you find that it's zero comma. Now, you know, based on the kind square test, but if you don't know how the kind square test looks like you can go to the table and go look for the kind square test. So if I go critical values of time, there is a table. This is the table that has the critical values of time so you can see that the rejection area is always going to be on one side. So you go here you look for two and you look for zero comma zero five, which is that value. Zero comma zero five that way that is your critical value. So that we assume that you got that value. Come here. You make a decision. We know that this area, which is our area of rejection original rejection. Our kind square test. It's five comma nine nine nine nine two based on this information that they give us on the table we saw that it's nine nine five one nine nine one. You take this value, you look where does it fall if falls on the site. Therefore it falls in there. You not reject the null hypothesis and we know that in the null hypothesis is independent. So you can say that we are not going to reject the null hypothesis. Okay. Happy. Thank you. Thank you. Okay, so that was kind square test. So with kind square test, they gave us two questions in that exam paper and the exam paper that I'm working with. Actually, I got it from the SDA 1510 I use the one outside of your module. And if you look at the this is the value that I used. So if you look at it, it was the major in 2018 exam paper. So we move into 24 of that exam paper. So it's 1510 and 1610 your content are almost exactly the same. The exam paper that you are writing is different. But also this year they might ask you the 1510 last year exam paper and the 1510 they might get the 1610 last year exam paper. They can interchange that because it's different lectures. And yeah, in different kinds of but the data like some of the questions might be repeated in both of the exam papers. So yeah, you can get questions that were asked in the 1510 in your 1610 as well. Okay, so this question paper question number 11 which will have been question 24 in that exam paper shows that the study was carried to determine let me put it bigger. To determine the adverse effect of the fertilizer on the maize, much fertilizer, which is our X value, which is our independent variable. And on the maize field, which is our Y independent, our Y dependent variable. A random sample of six farms were chosen in how they and their maize yield were recorded after the field has been over fertilized. And these are the results. Now since they are giving you a table like this, so you can use your state mode to capture the data. Remember that so all all. Cut late has have different ways of capturing the information so make sure that you go to your state mode. And capture the information go out on this one go to share my screen. My entire screen not just a not just the PDF. So I don't know what kind of calculators you have. If I can get an indication of what kind of calculators you have. Then we can work through this because at the end we need to be calculating the Y intercept the Y intercept regression line and the correlation of coefficient. So it means we need to know how to capture the data from your state mode. Are you using case your calculators or was that sharp scientific calculator. Casio using cash. Casio. Okay, I'll use my effects case you so I don't know the kind of one that you have. Open my case your one, which might look exactly the same as your ones and this is the case show that we have been using all along. That is our data. So now we need to put our calculator to state mode we press the mode. And then you select wait say set on your calculator. My one is on three and you select the ABC and remember the ABC we need to write it down so that we can always remember why is equals to a plus the X. And then we can remember that our Y is equals to our B zero plus our B one X where this is our intercept. And this is our. No, so everywhere where we're going to answer the question in the exam. Because what is the intercept we know which way we're going to be pressing our A for intercept and our B for snow. So now we select two for the line for a plus B X so we press two. And then we want to capture the data by first putting in the X values. So we say to equal. So two equal so I must go up. It's for four equal to equal eight equal. And remember to put all the values in order so that when you put the other values as well they are aligned. So I've captured all six values. Go to the top by moving to the left with my arrow and going up up up up until I get to nine number one. And then I can put 22 equal 20 equal 19 equal 17 equal 16 equal. And now I've captured all the values. The first question since we can use that for process of eliminating the questions. Once we are done we can press the AC button. And now we can put. We can we want to calculate the correlation so we remember to press the state button by pressing the shift. And then press button number one for that. And we're going to press five for a. And we have our AB and an R and X hat and Y hat. We are looking for R because coefficient of correlation is R. So R corresponds to three. So we just press three and then press three. And we press equal. And that is our coefficient of correlation. Going back to our question we're looking for the incorrect one so we know that this is correct. And then we look at B. B says a strong negative relationship exists between the amount, the yield and the amount of fertilizers. Do you agree? Is there a strong negative relationship? Yes. Yes there is a strong negative relationship. B is asking you to find the correlation. Sorry, B is asking you to find the Y intercept. Remember our Y intercept? In this instance it will be A. And it also asks you to find B which is our slope. So going back you go shift and then you go stat. You go five for reg. And there are your A and a B. We start with A first which is on one. And then you press equal. And that gives you 22.8746 which means this is correct. And then we want to calculate B. So you do the same. Oh sorry, my bad. I think I've closed. Did I close it? They didn't close, they're still here. Okay, so we want to get to the B. So we go shift. We press one. We press five for reg. And we're going to select two for B which is our slope. And we press equal sign. And that gives us 0,571. Because the number to the right is five. So we can add one and that is one, three. And that is correct. So now it means C is also correct. Question number D it says. The slope for this problem applies that for every one unit increase in X score there will be a decrease in the value of your Y. Is that true or is that false? I'll say true. Because it is a negative slope and since it's a negative slope it says for every value when X increases there will be a decrease in the value of our Y. And that is correct. And remember we're looking for the incorrect one. So the last one it says our regression line is given by Y is equals to B1X minus B0. The way they wrote it I'm going to be writing the formula there is an X next to the value. So therefore it means this is our B1 or which is our BX. Like we know that our formula B goes with an X. And this says plus A. So if we go back to our values that we calculated. What is our A? A should be 2.79. So since this is not A that is not correct and since this is not B that is not correct. Therefore the incorrect option is equals to that. So you will need to be very careful when you answer the questions like this in the exam as well. Because they can just trick you by this by swapping the values around and if you're not paying attention you might select another value to say oh but I don't know which one is incorrect. Maybe let me just piggy piggy my Melanie and then choose the incorrect one. Which was not or which is not the truth. So how many simple this one is simple linear regression. Oh yes this is linear regression. Didn't I mention that in the beginning or sorry. So this is linear regression. And this is the second last question so we can go to the last question. And your last question which is question number 12 is also linear regression. As you can see they also follow the same format like from your structure of your module. And with this question if I can make it bigger so that you can see the question clearly. The estimation of the relationship for this annual bonus Y in thousands and the years of experience is given by this equation. The question of determination is 0.49. If you notice on this question as well before I can move on. It looks almost exactly the same as the other questions that we have been doing with the asset self assessment question. So you might find that this question we dealt with in one of the questions in one of the session that we dealt with when we were doing the self assessment because like I said most of the question comes from the past exam papers and it can be from the 1510 module or from the 1610 module. So the question of determination is 0.49. Which this is our R squared. The objective is to estimate the annual bonus of a person with five years of experience. So if this is the objective for five years of experience so it means where we see X we can put five there. And with that we can substitute into the formula and calculate what the value of our Y will be. And do that calculated and want to have calculated it. Once we have calculated it then we can look at how we answer all the questions based from question number 8. So this should be 0.9333 plus 2.1143 times 5. Because I made this very small I can see why I'm writing. Just calculate this value so that we can find out what the Y head is. Are we done? Have you calculated it? Do you have the answer? Don't try and answer the question. I just want you to calculate and then we'll go through the question ourselves. I will explain some of the things on how to interpret it afterwards before we answer any of the questions. Did you calculate it? Yes. Okay how much? So 5 times 2.1143 is 10.5715. And then plus 0.9333 that's 11.5048. Okay so now you need to also take into consideration that they say the bonus is in thousands. So it means we need to multiply this value by a thousand. Then we get to the answer. So what do you do? You multiply that value with a thousand and what do you get? 11504, 11000, 504.80. Okay so and that is your predicted value. That's how you will predict a new value of your bonus based on five years of experience. That's why. Number two, you need to be able to know how to interpret the question as well because yeah not only about the five-year experience but they want you to also know how to interpret the equation of a straight line. Remember the y-intercept we interpreted by saying if x is equal to zero so if there will be no years of experience the minimum expected balance will have been 0.9333. That is if there are there is no years of experience a person will end 933 in bonus. Number two, you need to be able to explain your slope. The slope says for everyone you need to increase in the values of your years of experience there will be an increase in your bonus of 2. An additional, not that, an additional 2.143 which will be 2.143 additional increase because that is the slope so it means your bonus will increase by depending on how many number of experience you will have for every additional unit that you increase your number of years of experience there will be an increase on your bonus of 2.143 that's slope. The other thing they gave you was the coefficient of determination where they said it is 0.49 which means there is a 49% total variation in the values of y that is explained by the values of x and we are able to also calculate the coefficient of correlation of correlation from that by taking the square root of r squared which means the square root of 0.49 so you need to calculate that and say how much and this will be 0.70 and taking into consideration what is in front in terms of the slope the slope is positive so our regression will also be positive so based on this information that I just provided you and talk about we need to start answering the question. We are looking for the incorrect statement so if you are listening to me you will know which statement is incorrect so we'll start with A. Is A correct? Yes you've got a constant of 93. Yes we have a constant of 93. Would you repeat the question? Yes. Sam is trying to show his answer I think he said last time that he can't speak so he's trying to show us his answer by video. Okay. Oh, okay. Let's bring this also into the mix. I'll close the calculator and bring the camera in so that we can see Sam as part of the discussion. Sorry, I need to minimize. Oh, come on. Let me minimize this one first. Come on, work with me. You will be part of the discussion Sam, don't worry. We are including because we're doing the last question anyway. Okay, so we are able to see you there. So B is correct. Yes. Okay, and is C correct? Sam is also saying yes it's correct. Yes, because for every 5A experience that we calculated that we said there will be an increase in the bonus 11,000 or end. Number D it says there is a positive correlation coefficient between the annual bonus and experience. Is this positive? Since we calculated it, we can also look at the sign in front of the slope. Is it positive or negative? Yes, Sam, it is positive. Correct. Which makes the last question the incorrect one. Which is the option that we are looking for because if that was positive, the last one it says the coefficient of correlation will be negative 0,70 and we calculated it, it's positive 0,70. And we're done with one exam paper. Any questions? This was the last exam paper or the last question from this exam paper. Do you have any questions? I will post the timed assessment that you can take at any time, any place and then when you are ready to have a discussion on that we can schedule a session online and we have that discussion, but I want to make sure that everybody has taken that assessment so that we can work through the areas where you found them more difficult. So I will post it hopefully by tomorrow or earliest Monday morning you should have it available. That will be a timed one so you can go through it but you will also be able to submit it as multiple times as possible. So you can go through that the first time, the second time, the third time but it will be timed as if like you are writing an exam so it means you will have to make sure that the first time around you give yourself two hours a day to complete it or maybe I should not do it timed. I should not make this one, I'm not sure because we have limited number of days as well because you're writing on the 16 and you are still busy with other things so we only have three weeks. I need to make sure that I accommodate all these things or take all these things into consideration when I do that, whether I should make it timed or not. I will see, maybe I will not make it timed but the one week before you go write the exam I will make that one time in two hours time but for this other one that I will post it will have all the questions like it will be a past exam paper from question one up until question 25 as if you are writing the exam and you can submit it as multiple times as you can. I will also provide feedback for every submission that you do and if you haven't noticed with this one some of the questions I also in the feedback I do give detail, maybe I should go to the I downloaded it somewhere I should find it on my download sorry, I mean the document maybe I should go to download I have it downloaded since I can't see it now let me go to I'm just going to show you I'm going to exit some of the answers I think I will do them the same way as should be able to provide I will send you the document this document as well sorry I forgot to put the numbers I will email it when I send the weekly communication this week you will notice this is just for all the feedback so I didn't do question by question feedback all I did was the feedback at the end so explaining why you selected that is incorrect and how you can answer it correctly and also it has all the details so I have tried to go down into much detail when I provide feedback on the incorrect one and this is what I will do for all the assessment that I will post and if you go at the end somewhere you can see there I'm also trying to show you how to do some of the calculations as well I can see that this question was repeating that is the one that we did which was repeating and on this one as well there I'm showing you how to calculate this feedback on how to calculate that and how you can find which one is the correct one and not the correct one and then also here you will see there is some feedback and for the correlation I'm not sure if I'm doing any feedback other than just providing the statement to say why is it incorrect maybe I will send this and what else can I send to you I must also do the same with the previous one that we did for study unit 1 to study unit 12 so that you can have all the answers as well and then then I will post the other online assessment for you to do at your own time and when you are ready we can have a discussion about that we can schedule again another online session but for this weekend next week I'm canceling all the online discussions so that everybody can work on their own and catch up so that we have fruitful discussions where you can also give input and also discuss how things are difficult or not because at the moment you don't know what we have done what's difficult when you are doing it alone because you've never tried it on your own yeah so I'll just give you some time for two weeks one question before we go ma'am the question is that part of the hypothesis question is it included as part of the hypothesis yes it's also part of the hypothesis remember it has also the seven steps or six steps that you can do stating the null hypothesis and the alternative hypothesis stating what you are giving calculating the critical value calculating the test statistic making the decision and continue so it's still a hypothesis test and depending on the type of questions they will ask so I will try and see if I will look at the types of exam papers that I have and try and mix them to see if they are asking different format of questions for example maybe if I can go to one of the past exam paper under the download I can go to 10 and just open this one some of the questions we use them in the activities during our online sessions as well so they should give you some guidance in terms of the type of questions that you will get in the exam so if I go to the bottom one so for example like this one is a test question and they are asking you to find the critical value and they give you the level of significance so you go to the table using the degrees of freedom and this alpha they go to the table like you will go here and say alpha is 0,10 what will be the degrees of freedom if you ask one and you find that answer that is the critical question that they are asking then the other questions they might look like this as you can see here they have all seven steps all six steps what is your alternative, what is your degrees of freedom what is your critical value, how you make a decision so different questions in the exam you just need to know your content as well and maybe also if I look at the regression questions but with the regression questions like we've done most of the exercises from the regression question so if I look at this they only have one question on the regression question which is this it asks if x is independent y is dependent what is your slope based on this information so your slope will be the one next to the x and then it says is there a relationship between x and y this is regression regression is a test to see whether there is a relationship between the two variables and it says if x is equals to zero y will be that so if x is equals to zero y will be that and they are looking for the incorrect statement the questions are easy you just need to apply your mind as you can see but they ask them in different formats yeah that's something that's simpler than your ones these ones are easier and if I look at that same October November 2018 question paper as you can see is exactly the same as 2019 exam paper you see that the football football are different if I look at this it says the degrees of freedom is 3 the critical value is 7.18 if I look at this actually it's exactly the same but yeah they are looking for the incorrect one and yeah they are looking for the correct one so yeah but they are exactly almost the same so if I go to the second one remember this on this one they were asked to find at 10% so if I go down at 10% and in 2018 they were asked at 1% but the same type of exercise including also with the last question on your regression line which here they are asking you which one is the incorrect one and in 2019 they were asked what is the incorrect one as well so but different regression line is it different it's the same they just changed one of the variables one of the values so you just need to make sure that you go through the exercises or the activities in order to prepare because the questions are almost exactly the same it's just that they ask them in different ways maybe next time they might use the same question but instead of saying A and B they might say male and female and on number one and two they might put Mary and John something like that or chicken licking and KFC something like that but the concepts are still the same all right thank you very much thank you very much thank you very much thank you yes yes enjoy your weekend thank you bye Sam bye Sam bye Sam