 I'm back. Are you able to see what I am sharing? I'm not sure if I'm shared quickly. Back. We are back. I'm back. Yeah, we can see now. All right. Okay. So we left on question four. So now we are on question five. Question five is normal distribution. It says given a normally distributed population with the mean of seven and the standard deviation of three and 50 as the number of cases until the following questions. What is the proportion of participants with the Roscoe of greater than five? So it means bigger than. How did you answer this? Remember, you need to use the Z formula. Z of greater than X minus the mean divide by the standard deviation. How did you answer it? Z greater than the X is always given in the question. So our X is five minus the new is seven. Did you guys answer the question? Divide by three. No, I must put the equal sign. So the answer we get is Z of five minus seven. It's minus two over three divided by three. Minus two over three, which is Z of three. What is minus two over three? I got 0.667. Okay. Remember, you will need two decimals. So it will be 0. 0.67. 0.67. Now you need to go to the table. But before we go to the table as well. So let's go there. Remember, this is very useful. So we need to make sure that we know what we want to get. So our answer is negative. Before we go to, let's go back there. I'm going to draw it here. And then I'm going to erase it. So remember, our normal distribution, the answer is negative. Why am I having it as positive? It's minus. This answer should be a negative. It's Z of greater than minus 0.67. Yeah. Minus 0.7. The sign says greater than. So it means the sign tells us that we need to divide this and shade this area because it says greater than. So looking at the sign and the shaded area, therefore it means our answer will be in there. The larger portion. So we need to go to the larger portion and look for 0.67. Minus 0.7. We make this table bigger. Not that too big. 0.67. It is here. And the larger portion. That is the answer. So our answer for the proportion is 0.74857. So the proportion here, we can write S. 0.7. Greater than minus 0.67. 0.7 is equal to 0.74. 0.74857. 0.857. And that is how we will answer it. Because I'm going to run out of space, I'm going to delete this. Omega should leave it. No, I'm going to delete it. Even though it's going to take me forever. Delete. And number two. 5.2 says we need to find the percentage. So it means the proportion that we're going to find. We need to multiply that by 100. So let's go. We do the same thing. But yeah, it's greater than 15. So I'm not going to repeat the formula. You can repeat the formula if you want. I'm just going to substitute the values. Z of greater than 15 minus 7. So that will be Z of, what is 15 minus 7? 8 divided by 3. 8 divided by 3. Z divided by 3. 2.67. 2.67. So we're going to do the same. We're going to draw our normal distribution. And we're going to highlight. Our 2.67 is in the positive. Remember in the middle there is zero. So it means it's in the side. 2.7. So since it's 2.67 and the sign says greater than. So the shaded area will be the site to the right. So in this site, it is the smaller portion, isn't it? Because the larger portion is not shaded. So we go to the table. We look for 2.67. Once we are on the 2s and 2.67 each year. And the answer is 0.99621. Are we not looking for the smaller portion? Oh, sorry. I went to the wrong side. We are looking for the smaller portion. The portion which is not this, which is this. So we can say. The probability of finding that of greater than 2.67 is 0.00379. The pen is not writing with 0.379. Remember that. They said percentage. Multiply the answer by 100. And the answer that we have is equals to 0.87. I got 0.38. 0.38. Let's leave it at this mouse. We can just leave it at 2 decimals. We can say it's 0.38 percent. Okay, so the next one it says, what is the number of participants that goes between 5 and 19? So it means we're looking for those who's got between 5 and 15, not 19. Why am I saying 19? 15. So if we convert this, we already calculated the Z scores. So we know what Z scores are. So we know. I'm not going to repeat all those Z scores and do the calculations. We know the site it was 0.67 and the site is 0.0. It's 2.67. 2.67. We're looking for this part. So we can use mean to Z. Anyway, it's 2 marks. So we're looking for the number. So I can just go and find the proportion of the Z that lies between minus 0.67 and 2.67. Remember, we can use the mean to Z, add them together. Yeah, mean to Z for 0.67 and mean to Z for 2.67 and add them together. I'm going to start with this one. We know what those are. Sorry, mean to Z. That is the very one, which is 0.49621. Did you write that down? That is for 2.7. 2.67. Come back here. Just give it some time. It will pop up. I'm going to say plus 0.4. 9621. 9621. And we can go and look for 6.7 Z. It is 0.24857. 0.24857. 0.24857. Add them together. 0.74478. Slowly, 0.74478. Okay, we are done. We will be looking for the number. Multiply this value. We will be taking the overall number of cases that we have and our number of participants with the Roscoe between that and that will be and remember there is a number of participants so it should give all numbers as well. When you get to the answer, remember to limit as a whole number. So 0.74478. Multiply by 50. 37.23 rounded off to 37. Yeah, only 37. We have got between. Who has the score between 5 and 15? Who has it? The others falls outside of that. So that is for two marks. That's to do that. Okay. Can I ask? I didn't find the mean to that, but I added them. What do you call it? I call it the two values. The ones that I got for 2.67 on the 1.4. And I got the same number. Wouldn't it be wrong? You added? I added the value that I got for 0.67. No. And the value that I got for 2.67. Did you add or subtract because you needed to subtract? I added. Which value? I added then that then I got the same number that we got when it did mean to that. Yeah, I'm asking which number did you add? Oh, I added 0.00379 and 0. What was the other one? Oh, 0.7485. Yes. And then 0.379. Yes. Then I got 0.74478. You can get 0.74478 if you added both of them. You should have subtracted to get that. Because the other one is 0.74857. Already it's more than 0.774. Because if you say plus 0.00379. Then we get 0.7524. You're not going to get 0.74478. I don't know how I got it, but I didn't add the mean to that. But I got the same number that you got. Now I'm just trying to find out what I did. You subtracted the two numbers. Oh, yes, I subtracted. Yes, I did subtract. Yes, I think you're using the same method that I used in class. Yes. Yes. It will give you the same. So if you take the probability there minus the probability, you should get the same answer. But I don't know how your lecture marks. So please make sure that you use the mean. Try to use the mean to z. Otherwise you must show how you calculated the value so that then they are able to follow what you did to get to the answer. Okay. Don't lose marks. Okay, so question number six. Who have 10 golf balls in the basket? Four yellow, six white. You take out two balls from the basket. One by one without replacement. So it means the minute you took out the first one, you're not going to put it back. So it means the count from take becomes nine. The second time you go back in the bag. What is the probability that the first ball taken out is yellow and the second is white? We have 10 golf balls in the basket. So how did you calculate it? So I said the probability that the first ball is yellow is four divided by 10, which is not comma four. And so white is there now nine balls left. So for white is six divided by nine, which is equals to zero comma six, six, seven. That's what I got. Yeah, me too. I also got the same probability of first yellow would be four out of 10. Yes. And the probability of white. You said six out of nine. And what is four over 10? 0.4. And then six, seven, four. Six, seven, nine is 0.67. I think you need two because it says N. Because it says N. Oh, we're not supposed to multiply. Yes, we need to multiply. We can just say the answer would be and say probability could write this such probability of yellow and white would be four over 10 multiplied by six over nine. That's what we get. 0.264 multiplied by 0.7, which gives you 0.27. 0.7. 268 or 2.7 if you round off, yeah. Yes, let's leave it at three decibels. That is 6.1, 6.2. Your angle has five goals. Two are black, three are yellow. What is the probability that the first ball you take out will be black? The first black. What is the probability of first black? Two out of five. Two out of five goals. And that is how much? 0.4. 0.4. You and your uncle decided to throw all the balls you have into one basket. I was still referring to the first one. I don't know, but I think we're still referring to that. I think so. What is the probability that the first ball he takes out will be yellow? Oh, so it glows the first statement, which is 6.2, because they say they throw all the balls into one basket. Okay, but then I was this question confused me. These yellow balls that uncle has, are they his own or are they part of his mind? You and your uncle decided to throw all the balls you have into one basket. So your uncle has. Three yellow. That's my four yellow, makes it seven yellow. Yes, your uncle has five, but you have ten, remember? Very carefully. But then now there is what? So it means they are now seven yellow balls. You need to write this first. So now you need to add both of them because you and your uncle threw all your balls into one basket. So now you have ten plus five, which is our fifth. At the bottom, 15. So how many yellows are there? Seven. Four plus three is seven, so we can say. Yes, it's seven. Plus four is seven over 15, which means it's how much? Seven. Seven. Seven. There we go. One mark each. Remember, these are not the only questions they can ask. Remember, they can ask you also about how they. Which other one that they like. Like what they asked on the. Yes. Asking you. To calculate if you win a prize. Oh. And then. Those. This one was a bit tricky. Yeah. Yeah. Question seven. A. One. Whether there is a difference between the productivity of employees from two departments in an organization. You choose two groups. Consisting of 31 employees from each department, the productivity of employees. From each department is measured in terms of average unit produced. In a month in order to draw conclusion. You need to determine whether there is a significant difference between department a productivity score. And those of department B at. Level of significance is set at alpha of zero comma zero five. Okay. Formulate the appropriate. Not hypothesis in symbol. Are you. Not hypothesis. Not hypothesis. Mean A minus mean B is equal to zero. Is not equal. Not hypothesis. Mean A minus mean B is equal to zero. B. Is equal to zero. And that's all you can answer it. Come on. No hypothesis. I'm not. Yeah, wait, sorry. Let me fix my phone. No. Sorry. I can't do anything on this phone without opening those. Okay, so. Oh, you. If you don't put it this way. Or you can say H naught. Mean A is equal to mean B. That is in symbol. You're not hypothesis. Formulate the appropriate alternative hypothesis in waves. The productivity in department A is not the same as the productivity. Employers in department B. I said there is a difference in the productivity of employees from two departments in the organization. There we go. You use that statement in your alternative hypothesis. Oh, okay. I noticed it. There is a difference and blah, blah, blah, blah. She's that statement. But now you cannot just say there is a difference in productivity. You need to say there. Yes, you can say that. Or you can say between the mean of department A scores and the mean of department B scores. Because we're talking about the means as well. So you can, you can say it that way. But even if you repeat the same statement as they have it there. But you will need to some way to have scores so that it makes difference or the mean score or something like that. Okay. 7.3. Assume that the data are normally distributed. Select the appropriate test statistic and calculate. What is statistic? So we have equal number of observations. So it should be easy. When we have equal number of observations. So we can use T. The T square. The T test. And if you go back to your formulas, if you don't know. Which formulas to use. These are the formulas. This one is the T test. For the differences. Where. And after. So it means when you give it. Sorry. When you are given. The same. Like the mean. Score before the test and after the test. You use that for independence. When you have equal sample. Sample sizes. And. Independence when you have. unequal. I don't know how to write unequal. How possible. Because I just finished writing equal. unequal. Sample sizes. So let's go back there. Do we have equal sample sizes? Yes. So which formula are you going to use? This formula. So did you write it down? Yes. Okay. So. Which is. The mean. For. A. Minus the mean. For B divide by the square. Of. I forgot now. I need to go into double check. Is it a square. A squared for a divide by. And a. Plus. B. Is it minus. Divide by sorry my bad. No, it's divide by divide by. Yes. So you can just substitute the values. 65. 64. Minus 63. 74. Divide. By. The square root. On. Remember they gave you a square. So you don't have to. If they just gave you S. You're just going to put the square on the. We just use the values. As they are. Five comma three. Divide by thirty one. Plus. Seven four. Divide by thirty one. What do you get. Seven four. Divide by thirty one. What do you get. The top is. Zero comma nine. Zero comma nine. And then the bottom isn't it because the. The denominators are the same. We just add the. Numerators. So it'll be seven comma two seven. Over thirty one. Which is. Sorry isn't it one point nine. At the top. Why not. Is no primary. It's not one point nine. Is it. Yes one point nine. Is that. Yeah, I know what One point nine. Oh yes one point eight nine. My best one point eight nine. One point eight nine. One one nine. when you're writing this module are you using iris or are you using the indigillator app? it's a two-day thing so yeah how does that work that it opens on the 34 hours yes yes they just give you more time to work through so you can do today and tomorrow make sure that you don't run out of time yes as they take into consideration the load shading in South Africa okay you don't complain I'm not complaining I was just thinking do I understand it correctly because everything else is a time pressure of three hours and one hour to upload and oh goodness yeah it's a last thing yeah yeah the bottom part those who calculated what do you get do you get 0.48 I have 11 I mean after you take away the square root as well and some digits if you have a case your calculator you can use the fraction the fraction thing in the calculator because it makes it easier I will send you guys my calculator on my phone some of you might have those who don't have it has a fraction calculation thingy that you can use to answer the question without doing step by step I'm going to do that so that we can compare our answers minus and the answer I get is 3.92 what do you get 3.92 you also get 3.92 okay so that is the answer to that question and it's for the remarks determine the degrees of freedom I've sent the calculator on the group you have sent the calculator on yeah the so they can download the calculator that the one you're talking about I have it on my phone as well okay thank you thank you somebody in there yeah either the the tv or the people in the background okay so let's move to the next question it says find the degrees of freedom so this belongs to that and this belongs to that so our degrees of freedom for this is n1 plus n2 minus 2 so freedom e plus nb minus 2 which is 81 plus 31 minus 2 which is equals to 62 right that is your degrees of freedom determine the critical value sorry can you just go back to your formula sheet where you're saying this one belongs with this one and this one seeing okay and also this one is saying degrees of freedom yes is okay thank you so two-tail test significant value of alpha of zero comma zero five so we go to the table look for t table which is this table we're looking for a two-tail of zero comma zero five and the degrees of freedom of so here is the degrees of freedom so since zero comma zero five is right here I'm going to highlight the column and your critical value let's go back for those who still don't remember they said critical value two-tail table uh two-tail test at five percent which is zero comma zero five two-tail test zero comma zero five degrees of freedom of 60 we calculated that where they both meet that is our critical value which is two point zero zero zero three t of zero comma zero five critical value is I forgot now two point two point zero zero zero three for one month interpret the results in terms of the rejection area so we know the critical value we have the test statistic interpret your results so it's a two-tail test you know I like to do like this and because it's a two-tail test shade the site and also shade the site and call this minus two point zero zero three and the site two point zero zero zero three so wherever the t the t test statistic that we calculated here we if it falls in the shaded area or remember I like to also mention that this is the this is the decision route yes it's just that this is just a diagram to help us make the decision yeah for a two-tail test so we go to say where does this value form if it falls in the shaded area we reject the null hypothesis because here you reject the null hypothesis so where does it fall three point nine falls in the rejection area so interpret your results what did you say when you interpreted your results I said three point nine two is greater than two point zero zero zero three so therefore reject the hypothesis the test of three point nine two it's greater than the critical value two point zero zero zero three the four we reject the null hypothesis I'm gonna call it H not but you can use the full weight we reject the null hypothesis that is all what you need to do because the next question says interpret your rejection in relation to the statement in your inner plane language and also state the certainty we have done this so if we are making the null hypothesis our null hypothesis said there are there is so is there's no difference high wow yes it is no difference if in those mean we reject that so therefore if we are rejecting that they fall means the alternative hypothesis statement is true so how do you interpret this in your plane language using this also in the uncertainty and remember the level is 95 so your level of is five percent so the certainty will be 95 in the whole sentence using the information we just stated so you can take the whole statement actually don't take that one use this one at the bottom use this statement in your answer plus also in a 95 percent they need high I don't know if also know how to split certainty here now why am I having all this ice say tea I'm not gonna write anymore you guys sort that out so you can write that in your plane language so you can say there is a 95 percent certainty that there is that there is a significant difference between department a productivity score and those of department b or you can say there is a significant difference between department a productivity score and those of department b with a 95 percent whichever way to choose to use use them as long as the statement will read with that and there is some sort of significance that you your state as well so it should be that statement the whole of it okay happiness yes okay then we move on to question eight and I know that person I'm not gonna repeat statement given the table with all the information um the lecture I have asked you to help answer the following question is there a significant difference in the student's attitude towards statistics at first second and third level I think this is similar to the almost the same question that we did previously so it should be easy to answer or you should have the answers to this question because it almost exactly the same the only difference probably would be that I can think of would be the values given yeah they changed the values they just changed the values but the questioning is almost exactly the same so what is 8.1 choose the inappropriate test statistics to this hypothesis question and calculate the test statistic present your answer in a summary table so remember you will need to go and calculate I'm gonna I need to give you all the formulas and then you do the calculation and complete the table I will come back because my kids are not sleeping and they should be sleeping by now so you need to first calculate your sst which is your sum of x squared minus the sum of x squared divide by n you need to calculate that and get it right and then you need to also calculate the ss group as as group which is your small n times the sum of and all these are formulas given on the here are all this this information is what you need to to get for 8 max so we need to calculate all of them so it is the sum of your summation of your x mean j which is for individual groups minus the overall mean which is I always like to put the x bar x bar on top the overall mean and I think we need square this I thought I know the formulas by heart unfortunately not that you need to calculate you need to calculate ss group then you need to calculate sse sse which is sst minus ss group which are those two values you subtract one from the other and then you also need to find your degrees of freedom I'm going to follow the same thing that we did the previous one so you need to find the degrees of freedom for total degrees of freedom for total you must look at the formula so which is capital letter n minus one you need to find the degrees of freedom for group which is your k minus one and you need to go and find your degrees of freedom for error which is k n minus one k n minus one and that is the small n and once you have all that information you need to go and calculate this line here then you will need to calculate your ms ms group if you haven't calculated them ms group by substituting ss group divided by the degrees of freedom for group and then you need to also calculate uh ms error mse or error which you will use sse divide by the degrees of freedom so you would use the value you find on the sse divide by degrees of freedom error and once you are done then you can calculate your f test statistic which is your ms group divide by your ms error and once you have that then you can draw your table I might not have enough space but you will need to draw your table uh oh yeah right what am I doing uh friend out of space I will come back and draw the table but if you're able to draw the table let me draw and uh just give me five minutes I will be back uh just need to check what these kids are doing okay are we are we done are we somewhere let's uh let's populate let's populate the values and we'll draw the table later on so sst sst is 915 minus 235 squared divide by 30 which is 55 235 I think I already used the wrong n I need to get it right and use the capital letter n divided by 30 and it's 225 they're not 325 squared it's 235 yeah 235 squared and the answer you got was um 195 minus 55 225 is that the answer you got no no no the answer is 74.17 yeah the answer is 74 yes 74.17 yeah okay and the ss group we use 10 and we say bracket I'm just doing a bigger bracket and we're going to say 6.5 minus 7.83 bracket plus 10 8 10 brackets where did you get 10 oh sorry 8 8 wait let me raise that and and write it again 8 minus 7.83 squared plus the last one 9 7.83 squared and what is the answer I'm interested in the final answer 31.67 31.67 and ss e will be sst which is 74.17 minus 81.67 what did you get 42.50 okay and degrees of freedoms this will be 32 minus 1 which is 29 I can just come here and calculate this one as well which is 31.67 divided by 29 and the answer you get is I got 15.83 15.384 15.834 834 so I can leave it as 15.83 and you can do ss degrees of freedom ah sorry you guys I'm sorry my bad you're not even saying you're substituting wrong that is ss total that won't be correct okay attention to the values used don't just accept it's 10 o'clock at night our brains freeze sometimes okay so let's get to the groups case how many groups do we have there's three groups three and three minus one which makes it equal to two so it means this divide by two and that will be 31.67 divide by two two is this 10.82 yeah three point eight three okay and then go to m s e we need the degrees of freedom so we know that this is three times small n is 10 minus one which is plus two nine times three 27 seven so we can then substitute our s s e is 43 and five zero divide by 27 and what do you get I got one point five seven seven one point size seven is now let's let's substitute 15.83 divide by 1.57 what do you get I'm just gonna draw the table here because I don't have another space to draw the table oh right no it's not gonna work it's not gonna work let's go find another spot in the meantime what is the answer to 10.09 happiness now let's draw the table I got 10.08 I also get 10.08 oh it's not anything it's so it's a whole point eight oh my god I'm gonna draw the table here okay so you will have your source these are freedom your s s s your m s and s your f which is your test statistic so since we calculated everything on there so I'm just gonna substitute the values f I'm not so if they want you to write the formulas so you can see m s g over for some reason now my pen is erasing why why why f m s g over m s e I'm not gonna write all the values I'm just gonna substitute 0.8 and your m s e is equals to otherwise you don't even have to repeat all these titles I was gonna ask you do you have to repeat the formulas in in the table not really look at what your example from your book the book just gives the values no formulas yeah just put the values so 31.67 31.67 this one is 15.83 15.83 and the other one is 1.57 1.57 so yeah you can say I don't know whether you use group or treatment it's group you can say that yeah and then they error and then they total and your degrees of freedoms there's 2 so 2 is 42.50 42.50 and then 2 and 27 2 and 27 and then this will be 29 and here you can also have the total you just add these two values 7 11 0.34 7 and then you can do the same you can add all of them I don't know whether you do add them but you can add them so that will be 0 13 6 7 and that is the table for 8 marks that's all what they want but you can show also all the calculations in case a table where it's worth one mark yes because in order for you to find the test statistics you need to calculate all this and then they also say present your answers in the summary table which is the summary table and all of it it's 8 points okay so 8.2 determine the critical value so in terms of the critical value we need to use the degrees of freedom for the and error yes so we can use degrees of freedom for one will be 2 and degrees of freedom for one for two will be 27 and we're going to use our another table which is the f table so f of 0.01 and the degrees of freedom so let's go look for the table and we need to pay attention 0.01 that's what they want so this will be your df1 and this will be your df2 so df1 is 2 and 27 so we're looking for 2 and 27 is that the critical value is and that is for one mark so you must also pay attention to your tables because it's split by degrees of freedom sorry by the level of significance okay so now 8.3 let's call this 8.1 that's a name 8.3 do you reject the null hypothesis if you look at this distribution it's left skewed it doesn't really matter whether we're doing a twitter test or not so the decision is if it falls this side of the portion of the graph we reject the null hypothesis and remember this we said it's 5.49 the origin of rejection anything this side we reject the null hypothesis so let's go to our critical value we found that it was 10.8 so it will be in the rejection area so what do you say you say f that i'm just going to use f statistic is equals to 10.08 which is greater than your f of 0.01 which is your critical value of 5.49 therefore we reject the null hypothesis f statistics is greater than your critical value therefore reject the null hypothesis that will give you one mark to state the sentence like that 8.4 interpret your results remember we interpret it based on the information the information that is there a significant difference remember you said there is no difference we are rejecting the null hypothesis therefore it means to say in the easy difference so same as what we did previously also remember with satinity and because it's 0.01 what is our satinity the percentage 99 percent we're going to say with 99 percent satinity there is no there is a significant difference no attitude there is a significant difference there is a significant difference in the attitude of students towards statistics at first second and third year level this can be confused with 99 percent satent oh yes yes yes yes and that will give you two marks as long as you can mention 99 and you can refer back to that statement you get two marks for that right I think we are almost at the end which is chi square test so they've given you the contingency table with gender and yes no and not sure so it's a two by three table and I think it's almost similar to the one that you had previously as well that we went through so they also calculated your chi square test statistic which they found that it was 51.39 make a contingency table to represent the given information and clearly indicate your observed and your expected remember I said you can also from here you can also say identify your observed and you're expected in a bracket or you can create a table on the side similar to the same and but you will need to have totals first before you do that because you need totals so let's first calculate the totals so you need to calculate totals so you will have totals and you will have totals they so this is 45 this is 40 and 15 and 15 and going aside this is 50 and this is 50 and the total will be 100 so remember in order for you to calculate the expected value so let's say we want to calculate the expected value for five we say the row total which is 50 multiply by the column total which is 45 and remember this is only the remarks but you have to do do it that way divide under it i'm gonna get you the values just now 22.5 i will write them just now and just okay so for five it's 22.5 and this is 22.5 the middle one is 20 and 20 and this will be 20 and this will be 20 so you can put this in brackets in brackets and I think this is 7.5 so that will be your observed and you're expected in brackets okay because they say clearly indicate your observed and your expected value so once you redraw this table just say some I think you can write it here say observed and expected in brackets you can just do it like that then they will understand what you have done it's only the remarks anywhere okay so once that is done the next one says find the degrees of freedom so the degrees of freedom here is your number of rows minus one times the number of columns minus one don't count the headers don't count the totals so how many rows these are the rows two there are only two of them two minus one and how many columns and these are columns and there are three columns minus one which is two minus one is two it cannot be two it's one and three minus two I'm already giving you the answer which is equals to two and that is for one mark the next one the critical value so our chi squared critical value it's zero comma zero one and your degrees of freedom of two and the degrees of freedom of two so we go to the table so every time you hear critical value always remember to go to the table so we're using zero comma zero one so that is zero comma zero one and two and your critical value is two comma it's nine comma two one two one zero four and do we reject the null hypothesis also remember this if it falls here this is in rule we reject the null hypothesis so we know that this origin of rejection is 9.21 what did we get the test statistic is 51.39 so since the chi square test statistic is equals to 51.39 which is greater than the critical value of 9.2104 we the null hypothesis and the last bit interpret your results and with how much satin it the same anyone who wants to try it for the last time because this is the end how would you answer it let me try okay okay sorry go ahead no you can go Karen it's fine um I would say there is a significant difference between South African men and women in terms of compliance with a lockdown regulations and that this can be said with 99 certainty here we go thank you and all the best with your exams any question oh no just a huge thank you yeah so what I would have done without you in my pocket mon I can now brain at this point trust me it's not really when are you writing uh 30 to the rest yeah the people who will be released at God's six in the Tuesday in the evening yeah on Tuesday yes Tuesday to Wednesday if your exam is almost the same as the two papers that we just went through I don't see any problem just to remember all these things that's so easy with you you see like you make everything too easy seems so easy and you're looking at a paper I mean I I tried to do this paper and in four hours I had only done half you see most of these things that you do in this paper they are in your study guide probably I've done the whole study guide trust me still you when you open a question paper it feels like it's different I don't know it's just me yeah it's like that level of confidence you don't even know where to start it's like oh no stop what formula is this so I've taken out my on my formula should I've written what they are and what chapter they're from that way I don't know it sort of makes it a bit easy but still I we needed this trust me