 assignment questions or see similar questions that will help us answer some of those questions. I hope we will finish by after it will depend as well. We can finish by six or by half past five it will depend on the output key the questions are. Again also you need to have your tables ready because we're dealing with study unit 8 and 9 which is confidence interval and hypothesis testing so with confidence interval you need to know that you need to go find the critical value either on the z table or on the t table right the same with hypothesis testing you will need to know all the six steps of hypothesis testing but not only that you just need to know the basic properties of confidence interval as well as of hypothesis testing so let's look at the questions. A random sample of hundred results in a sum in a sample mean of hundred the population standard deviation is known to be 25 so if they tell you that the calculation standard deviation is known always remember that we're using set those are the things that you need to always mind yourself. What is the value of the standard error which then it means we need to find the population standard deviation divided by the square root of n so what did they give us our n is hundred the standard deviation is 25 so it just substitutes 25 divided by this square root of hundred. 2.5 which is option b. 2.5 like I said there will be those ones where I don't have all the full information there's nothing I can do about that one. This we can answer so question 3 asks the department of basic education earlier findings from the survey with your 90 learners which is n of 90 and average time travel or average travel time which means that is your mean from home to be at one of the school of interest assume that the population standard deviation of the learners population standard deviation so it means they have given you sigma so it is and it is known so we need to be using set construct a 95% confidence interval by now you should know what 95% confidence interval mean in terms of the critical value. What is your critical value if I don't get a response then it means I I'm going to assume that you don't know your critical values and these are the things that you need to have a summary of because we have been speaking about them even during the sessions to say the critical value are very important you need to know what the critical value for 95% is 99% is 90% is and so on so if you don't know how to find the critical value number 95% confidence interval is one minus alpha and your alpha will be one minus zero comma nine five which is zero comma zero five to find the critical value it's a set of alpha divided by two which is set of zero comma zero five divided by two which is set of zero comma zero two five you go to the table and the negative side you go look for inside this table you look for zero comma two five zero and then you go out to look for the critical values which are your z values which will be equals to one comma nine six that is your critical value so your z critical value is one comma nine six and then you need to remember the formula that you need to have already summarized some way you mean plus or minus your critical value of z over alpha times the standard error which is the population standard deviation and you can go and calculate substitute the values we have to use population parameters we use sample parameters so your mean is one one four plus or minus your z critical value of one comma nine six times your standard deviation of 72 divided by the square root of n of 19 and you can go and calculate one one four plus or minus which i can just a 1.96 i can calculate the standard the margin of error and the margin of error will be in case in the exam they ask you to calculate the margin of error you need to know what the margin of error is the margin of error will be 14.8753 14.875354 i think the correct answer will be c and then you just need to go and calculate the minus and the plus so on the minus sign we will have one one four negative i got 99.13 and positive i got 128.880 option c because there is nothing there i consider a t distribution with n with the nine degrees of freedom which one of the following statement is correct and now if you have your degrees of freedom and they give you your your alpha value the squish answers because now i'm giving you all the answers if i get the answers there which one of the following statement is incorrect now um these are things t value t value um is not associated with the critical values but it is probably it is the critical value that's what they are asking you so let's go find the critical value for your alpha value of 0 comma 1 okay that's correct and of 0 comma 0 5 it's also correct okay so on the oh sorry my bad let's go to the table you need to go to there you call this t table so you'll go to the t table and you're going to look for your degrees of freedom and your alpha field right and then choose whichever is correct and c d and e you need to go find or calculate your and find out which one is correct in terms of in terms of the confidence intervals but we need to be very careful when it comes to these questions as well not sure if there was other information given if not then because these are the things that i'm not sure what they're trying to get to with the between whether is this the critical value they say it lies between those two or they would have calculated the um the critical values for that but anyway so t of alpha and the degrees of freedom and this they say in the on the upper tail all right so if you think of it this is the negative side and this is the positive side on the positive side it is on the upper let's not use this let's call this the upper and the lower right let's explain you in this manner so if you went and found your critical value on the upper tail it should be a positive value if you find it on the lower tail it should be a negative value so yet the answer here is the t value associated with the lower tail of zero comma one three is one comma three eight three so go to the t table it is true it is on the one comma three but in terms of the critical values on the lower side it will be one minus one comma three eight three in the upper it will be one comma three eight three that's what this is so similar for a zero comma zero five you go keep on going to the left because i still remember my tables on the left which is one comma three three it will be one comma three is a three or eight eight three three eight three three on this on the lower side it would have been negative on the upper side it will be positive one comma eight three three so that will be correct and this will be incorrect because it's positive that's the two different in terms of the two questions for a 95 confidence interval you will need to go find your z over t alpha divided by two which will be a zero comma zero two five and the degrees of freedom of nine so let's go to zero comma zero two five and it is two comma two six two two it will be negative two comma two six two two and on this side it will be positive two comma two six two two so it is between the two values that is correct for a 98 percent it will be a 98 percent alpha divided by two which is zero comma two divided by two zero comma zero two divided by two is zero comma one right zero comma zero one so we go to zero comma zero one zero comma zero one and it is two comma eight two it will be negative two comma eight two and positive two comma eight two two comma eight there we go and for a 99 it will be t alpha of zero comma zero two divided zero comma zero one divided by two what is zero comma zero one divided by two it will be zero comma zero zero five all right three two zeros after comma so therefore go to zero comma zero zero five and your critical value will be on the lower side it will be negative three comma two four nine and on the positive it will be three comma two nine let's see three comma two five so which is four nine which is two five which means this is correct the only correct incorrect answer would be the one with the negative so we need to you need to always think about it in this way if they ask you for the lower side lower side is on the negative side upper side it's on the positive side so the incorrect answer here is number one moving on to the next question consider the following application exercise from a the previous assignment most school from school reported the decline of absence following from education department learner transport program and nutrition program in a sample of hundred and fifty schools so we have our end from june probably district municipality hundred and fourteen school reportage a decline that is our x in the number of learners absent construct a 95 percent confidence interval for the population proportion so some of these things are key words to let you know what you are calculating so we need to calculate our p which is x over n and from there we need to calculate p plus or minus z alpha divided by two remember for the proportion we always use z and multiply that with p one minus p divided by n with the standard error so calculate p what is p what did you get are you still there 0.96 0.76 0.76 0.76 0.76 then substitute into the formula 0.76 plus or minus we need to go find the critical value of 90 do you know what the critical value of 90 is this one is one of those special ones if you don't know now i don't know which one of the critical values is special for a 0.10 divided by two will give us the z value of 0 comma 0 5 which falls between two values remember that when we go to the z value 0 comma it falls between those two values because there are five point difference between them and the critical value will be a special one which will be one comma six four five remember that that is the only special critical value so which is one comma six four five for a 90 percent confidence interval one comma six four five because for the others the other one is two comma three three and the other one is two comma five eight but you need to know which one will be and 95 percent is always one comma nine six times zero comma seven six times one minus zero comma seven six divide right in the lower limit 0.703 zero comma seven zero three and in the upper limit 0.817 0.82 0.8 we can keep three decimals okay 0.817 0.817 let's see because the answers here are in three decimals don't get distracted look at the options if they are in three decimals keep your last answers as three decimals if they are two decimals keep them as three decimals so the answer here will be option b are we good or are we happy this we will do with the other assignment question because they didn't give all the all the information that you would need like how do we calculate the rest of the other statements i'm going to use the other question to do that or the other assignment questions okay suppose the calculated test statistic is a one-sided test this is very important we are in the hypothesis testing and that test statistic is given by minus 2.66 so they don't and they say in the lower tail so in the lower tail it will be on the less than side if they say in the upper tail remember upper tail will be on the upper side it's in the greater than so if they say in the lower tail it's a less than so it means in the hypothesis testing and the the thing was less than right suppose that the population standard deviation is no so it means we're using z what will be the p value that is the probability of z less than minus 2.66 that's in a in a way that we have understand the probability we can ask the question p value is your probability value so go find the probability on the table on the z table so we go to the negative side table and we look for minus 2.6 on the left and 6 at the top 0.66 so 2.6 on the left and 6 at the top where they both meet they meet at 0.0039 and the answer is 0.0039 which is option 3 that's as straight forward as that if it was in the upper tail area what would have done would have subtracted this value from 1 right in the upper tail in the upper tail we would have said 1 minus 0.0039 always remember that so there's everything that you've learned in the basic in the normal distribution you still need to carry it when you answer questions in the hypothesis as well this one i'm gonna skip we'll use the other assignment for it okay so coming to the next question various literacy group recommended they're reading oh okay already have given you the answers and they didn't even look at the answers but it's fine they recommended the reading speed of 169 watts per minute for grade nine and a grade five is great five teachers convinced that the average reading speed for his class is more than which then helps us with the alternative recommended speed the sample size is 36 for grade five learners and the average reading speed is 175 and the standard deviation is 22 and we need to also take into consideration the information given so because they say here the sample of 36 grade five learners and the average is 175 with the standard deviation of 32 therefore it means everything is from the sample so we are given the mean or the mean of a sample it's x bar and we are given the standard deviation of a sample which is x therefore it means your population standard deviation is unknown and therefore it means anything that we're going to be doing we'll be using the t table because this is a t distribution question you are required to test the teacher's hypothesis testing at five percent level of significance so they give you your alpha value that you need to test that the average reading speed is more than the recommended speed and choose the correct statement below so our alternative states that the average reading speed is more than right that's what they say and we know that in terms of the population the speed was 176 so therefore our null hypothesis will read that the mean is equals to 167 because your null hypothesis always has an equal sign with a limit of which sign we use as long as it's an equal sign and it should be fine looking at the question and the statement most of this they are asking you to make a decision so therefore it means there are a couple of things that you would have done before you can answer this question so let's because this is the last statement it's your conclusion the first statement is state your null hypothesis and alternative the second is to identify the things that we are given I've already identified most of them I'm not going to worry about that the second one is to find the critical value or the third one is to find the critical value so let's go find the critical value so because the sign here it's greater than therefore it's a one-tail test so our critical value t of alpha and the degrees of freedom and our degrees of freedom is n minus one so we have t of zero comma zero five and n minus one where is our n our n is thirty six so it's thirty six minus one is thirty five so this is thirty six minus one which is thirty five so we need to go to the t table look under the degrees of freedom of thirty five and zero comma zero five at the top so let's go t table we're looking for thirty five we're looking for zero comma zero five and thirty five so it means we are on this color and one five eight nine six it's one point six eight nine six that is our critical value we will use that in making a decision because we know that our it's in the upper tail area so we can automatically create our original rejection which is one comma six eight nine six so we're going to use that in our rejection statement now the fourth statement is to find out which one are we using we're doing a t test so we're going to have to calculate our t distribution so which is the sample mean minus the population mean divided by your sample standard deviation divided by the square root of n which is our standard error so our sample mean is hundred and seventy five minus our population mean is always stated in the question in the hypothesis statement divided by the standard deviation was 22 divided by the square root of n which is 36 so due to calculation what do you get what is your t um 173.73 your t it cannot be 100 because if 175 minus 167 should be eight so you're telling me that 22 divided by the square root of 36 I got negative 3.226 no it cannot be negative 75 is bigger than 176 2.1 sorry Lizzy um is that uh it's 175 minus 187 or it's minus 167 oh minus 167 it's 167 my handwriting is that bad yeah it's ugly that's why we use computers so the answer is two point one eight one five one yeah oh mine it's it's it's it's two point one five one I also got two point one eight one eight one eight one eight one eight one eight one eight two yes yes so please check this is 22 divided by the square root of 36 so the answer should be two point one eight one eight okay oh gosh I must read out the values loud then so where does two point one eight fall on this distribution it falls under the rejection area because anything that falls in the shaded area we're going to reject the null hypothesis right so let's we're going to eliminate any statement that doesn't have reject on it so because two point one eight falls in the rejection area so we know that not enough information won't be the statement do not reject do not reject so we are left with two statements okay so um so we are left with two statements so the first one says we reject the null hypothesis and conclude that the grade five reading speed is more than 167 number two it says we reject the null hypothesis and conclude that the average reading speed is not significantly different from 167 which one a or b do you all agree with a the statement is a so you just need to make sure that if you you know all the six steps of hypothesis testing in the exam you can get questions like this or they can ask you questions where every option is one of the each hypothesis statement so you just need to know how to do the hypothesis testing okay so let's look at another question so this one we will use the assignment as well don't worry if I skip it most of the school nutrition uh decides uh reported the decline in the number of absences from the education transport lena transport and nutrition program in a sample of 200 school so your n is 200 from unsignature district 72 percent reported a decline which is our p uh in the number of lenas absent the district manager is adamant that the population proportion which is our high uh of school that reported the decline in the number of absences is different from 78 percent formulate a null hypothesis and an alternative hypothesis so our null hypothesis if I can help you because it says different your null hypothesis will state that the mean is or the proportion is zero comma seven eight your alternative will say that the proportion is not different from zero comma seven eight that's your null hypothesis and alternative and then it says at five percent level of significance which is alpha which one of the following statement is incorrect so yeah all the steps of the hypothesis so we already stated the null hypothesis and alternative step number two state whatever you are given I've already stated that your p 72 your alpha is five percent we um yeah because it's proportion what type of a test that we're doing we're doing a search test so we need to calculate the proportion because the next one oh sorry the critical value or we don't have to calculate the critical value because we are going to use the p value as well but you can calculate the critical value uh the null hypothesis is rejected we can conclude that and the alternative hypothesis will state that so we can look at those statements separately or we can do the hypothesis so let's do the test let's calculate the test statistic so our test statistic because after calculating the test statistic we'll need the p value so the test statistic will be p minus the population proportion divided by your population proportion one minus population proportion divided by n so substitute the values our sample proportion is zero comma seven five or seven two let me rewrite that so that people don't blame my handwriting zero point seven two minus zero point seven eight divide by the square root of zero point seven eight times one minus zero point seven eight divide by two hundred so calculate the negative two point zero four i'm also looking at the answer it's not on seeing that the answer here is negative is it zero comma or two comma zero four two comma zero four but it's zero comma four eight right two comma zero five which is five right so now because uh we are dealing with there's a test so this is correct we looking for the incorrect statement that is correct let's go to ee says the alternative is that the population proportion is not equals to 78 we know that that is correct we stated it in the null hypothesis now let's go find the p value which is question b we need to find the p value so that we can make a decision because the decision says the decision rule if we're going to apply it says if your p value is less than alpha you're going to reject the null hypothesis so that is the rule it's not a final thing it's a rule that we will use to make a decision so in order for us to answer b c and d we need to find the p value so that we can use this rule to answer that so let's go find the question is asking for the incorrect i think this was an error on their statement but it's fine we're not looking for that much so let's go find the p value so the other thing you need to always remember with the p value is if your test is a two sided test and the z test is negative we're going to forget the value on the table and then we're going to add it together because the p value for a two sided test they are two sides so we're going to go and find this using the z value the probability so minus 2.05 on the table the z table on the negative side we're looking for minus 2.0 and then at the top we're looking for five where they both meet that is the p value the one p value so it's 0.0202 so 0.0202 and the side 0 sorry this area here i must not write it at the bottom i must write it at the top because this represents the the area so this area here is 0.0202 and this area here is 0.02 0.02 so we need to add both of them together so our p value will be equals to two times 0.0202 which is equals to 0.0404 or you can say 0.0202 plus 0.0202 so this is also correct in terms of our answer okay so now we need to base our decision on the p value so let's see our decision rule says if the p value is less than the alpha we reject the null hypothesis so let's see our p value is 0.0404 our alpha value is 0.05 so this value is less than therefore we reject the null hypothesis let's see we're going to reject the null hypothesis so the null hypothesis is rejected which is correct so if the null hypothesis is rejected therefore it means there is no difference so the population proportion is not different all right so we can conclude that the population proportion that reported a decline in the is significantly different from I think this question there is an error on this question because it cannot be that all of them but this is the incorrect one so this would have been because oh sorry it's different it's saying the same thing sorry my bad this is also correct because it's different from it is different it's not the same it is different from 0.08 because we are saying yeah we're saying it is the same the null hypothesis that we are rejecting that it is equals to 0.8 it's the opposite of the alternative which says it is different so we reject the null hypothesis and conclude that the population proportion is different is significantly different from 0.08 which is also correct so if all statements are correct then there is no incorrect statement is it minus or because option A says it's it's a positive number yes doesn't matter you know it does matter so yes so this is positive you are right this should be the incorrect statement it should be minus two comma and didn't pay attention to the minus we found that it's minus two comma zero five so this is positive the answer should be minus yes this is the incorrect one sorry my bad my bad okay so this is correct but the statistics is the incorrect one should be minus two oh gosh all right let's then look at those other missing questions how do we answer them so my we've done with the questions yes we are at the end right at the end okay some of the questions I said we will pick them up from here I can start from the bottom and then we go up okay so this is the same as what we just went through I'm not gonna bother too much so let's look at this one says in a sample of 100 the sample proportion of 0 comma 3 to consider the following hypothesis and calculate the p value and I think we have done that but no we didn't choose the correct answer from the list of option this is similar to the question that was cut of this one no the other one I think it was in the null in the hypothesis this one where they were asking you to find the p value right so if we need to go find the p value the very important thing there is the sign in your alternative so this is a mistake here there should be an alternative so we need to go find the p value and because we're dealing with proportions so we need to calculate first this that value p minus the population proportion divided by the square root of your population proportion one minus population proportion divided by n our population proportion is 0.4 our sample proportion which is our p is 0.32 so 0.32 minus 0.4 divided by the square root of 0.4 times one minus 0.4 divided by n of 100 so what do you get minus 1.632 okay so we keep two decimals so it's minus 1.63 right so we need to go back to the sign it is a lower table it's less than so the value we find on the table that is the p value that we are looking for so let's go minus 1.63 go to the z table look for minus 1.63 where they meet that is your p value which is 0 comma 0 5 1 option c so in your assignment they would have given you your sample depending and your population proportion as well i'm not sure if because on this question it was cut off cut off but probably it would have been a no it would have been another question because depending on your n and your sample proportion you would have calculated your p values differently okay so what other question or the one with the plus or minus the question would have read like this consider a two sided test with five percent level of significance and the degrees of freedom of 25 right so our alpha is five percent our degrees of freedom the f is 25 and they want you to find and yeah our population standard deviation is unknown therefore it means automatically when they talk about degrees of freedom we should know that we're talking about t so because it's a two sided test we have to divide our alpha by two and the degrees of freedom so it will be t of 0 comma 0 5 divide by 2 and the degrees of freedom of 25 if they didn't give you the degrees of freedom they would have given you n and you can calculate your degrees of freedom by saying n minus 1 so here they gave you the degrees of freedom so there's no need to take this and subtract from 1 right so this you need to find 0 comma 0 2 5 and 25 so we go to the t table t table and we look for 0 comma 0 2 5 and you look for 25 2.0 5 9 5 2.0 5 9 5 2.0 now I forgot 0 5 9 5 so if we round it off to two decimal it will be 2.0 6 and it will be option a okay but other questions we cut off that we couldn't do it was this one are we probably do have a full question and here is the question in a sample of 36 the sample mean is 83 it is also known that the population standard deviation is 16 you are required to use this information to test the following hypothesis so the mean is the null hypothesis says that the mean is less than 80 the alternative says the mean is greater than 80 so it's a one-sided test and it is in the upper take okay so um we are given the population standard deviation so then it means we're going to be using z and we can answer all these questions step by step so the test statistic less than 80 so your test statistic for z will be your sample mean minus your population mean divided by the population standard deviation divided by the square root of n so that is our sample mean is 83 minus our population mean is always dated in the hypothesis which is 80 divided by the population standard deviation which is 16 divided by the square of 36 this is 36 not 38 so let's have late i get 1.125 yes 1.125 let's keep it to 2 decimals 1.131 oh sorry this is 3 decimals sorry my bad let's keep it all of the decimals but it's fine we can answer the question I just wanted to keep it to 2 decimals because the next question is to go find the p-value and with the p-value we need 2 decimals but we can see that this is the incorrect statement right so this is not correct um anyway let's continue with all the other statements the p-value we need to go find the p-value so remember that it's greater than so therefore to find the p-value here we're going to say 1 minus the value we find on the table and the value we're going to find the p-value on the table based on 1.13 so you go to 1 comma in the positive side 1 comma 13 so they both meet which is 0 comma 8 7 8 7 0 8 0 comma 8 7 8 and the answer is 0 comma 1 2 19 so our p-value is not right that's what if there's something wrong then 1 comma 1 30 that's what we got right 1 comma 1 30 unless they use a different p-value never did this so this should be 0 comma 1 2 0 comma 1 2 9 2 that's what you said yes and there was something wrong with the question okay at 10 percent level of significance the rule is to reject the null hypothesis so we will they know it will not be they reject the null hypothesis if the test statistic is greater than 1.186 so yeah they assumed that you would have calculated the critical value so the critical value here will be of 10 percent because it's a one-sided so it will be 0 comma 1 10 percent will be 0 comma 1 0 and then you will go inside the table and look for 0 comma 1 0 comma 1 0 comma 1 0 it will be 1.28 and it will be 1.28 and because it's on the apartheid then we would say 1.28 would be on the apartheid on this side and therefore it will fall 1.285 if that is the z value it will we will reject the null hypothesis so you reject the null hypothesis therefore hence the statement is also correct because it says at 10 percent the rule is to reject the null hypothesis if the test statistic is equal or greater than 1.28 which is correct at this point we have the only correct answer and oh yeah you know why this is probably the p-value that they found there they used 1.28 which is 1.29 if you go there you might find that this will be the p-value but we can double check that later at 10 percent significant the null hypothesis is not rejected uh in terms of in terms of the true statement that we have here in front of us so if our p-value is less than so our p-value is 10 percent sorry our alpha is 10 percent so it's 0 comma 1 0 and our p-value is 0 comma 1 2 or 1 3 we can call it 1 3 so it's bigger than the the level of significance therefore we do not reject the null hypothesis so this statement also is correct so we do not reject the null hypothesis and this is an apartheid area which is correct so let's double check number b because i'm going to i'm i'm 100 percent sure that p-value they used 1.28 so let's see if we use 1.28 so we'll need to go to 1.29 1.2 1.2 oh sorry on the positive side 1 point let's remove all this 1.2 1.29 is 0 comma 8 9 9 7 1 minus 0 comma 8 9 9 7 if you take that 1 minus 0.8 9 9 7 equals no it's also not because then that is 103 i don't know how they got the used 0.08 they're not 9 oh sorry so that would be 9 0 but it's still not gonna work 9 0 1 5 we use that it's 9 0 1 5 what do you get yeah it's still not correct list it's 0 comma 0 9 8 5 yeah i don't know probably there wasn't a letter on this question as well because their answer is option a and we know that that is also not correct unless if we didn't calculate the right but not so many people in the same room can get the question wrong so 83 minus 80 divided by the our standard deviation is 16 hasn't changed and our n is 36 the square root of 36 and 1.125 i don't know why they would have gotten 1.28 at any so that they said this was their incorrect answer we left with seven minutes um which other question so this one we did do and i'm gonna answer the other questions that we did answer would be the one way we calculate okay let's see if we can calculate one of this so we can use this one as another example doesn't matter whether you see the the waves so construct a 99% confidence interval for the population mean income you are given the sample size of 50 and the income of 3 500 on average so that it would be our sample mean with the standard deviation so this will be the sample standard deviation s and we need to construct a 99% you need to be able to know and read the question and understand what is it that you are given in the question whether are you giving the population standard deviation or are you giving the sample standard deviation because that is very important it will help you know which one are you calculating so in this instance we need to find the mean plus or minus t alpha divided by 2 and the degrees of freedom as divided by this we need to go find the critical value so the critical value t alpha of 99% which means is 0 comma 0 1 divided by 2 and n minus 1 and our n is 50 minus 1 so therefore our critical value we will find t of 0 comma 0 5 sorry my bad at this point 0 1 divide by 2 it's 0 comma 0 0 5 0 comma 5 it's 0 5 and 49 so we need to go to the TV and values of t and look at the last column and 49 which will be on the next page 49 which is 2 comma 6 8 2 comma 6 8 so we will substitute into the formula 3500 plus or minus 2 comma 6 8 times our standard deviation of a thousand divided by the square root of 50 and you can find your lower limit and your upper limit 3 8 7 9 comma 0 0 yeah it's option in yeah the lower limit is 3 1 2 0 option in 3 3 1 2 0.99 and the upper limit 3 8 7 9 0 1 8 9 so which is 0 so it's option 8 okay so we left with two minutes but you should be able to double check something because I think there was another one way we skipped okay so this is almost similar so you should be able to answer any of this confidence interval it's only this one way I don't have a full question to know how they would have asked you otherwise you can practice with other questions but I won't post there so you need to always know so in case they ask you to calculate a margin of error you need to be able to know that always your margin of error will be the failure after the plus or minus on any equations oh no that's it I'll find you right by two and population standard deviation over the square root of n this is your margin of error if you calculate in the mean plus or minus your t alpha and the degrees of freedom with s divided by the square root of n this is your margin of error right so if they ask you questions like that you should be able to know each one because you don't calculate and for the for the proportion it will also be the same because it will be only this is your your margin of error so depending on the question so for example this one they're asking you to find the margin of error at 99% and they give you the sample the sample mean and the population standard deviation so therefore you're going to use this form you know this one right so that I might do going to use number one first one so therefore your margin of error to answer this question will just be your z alpha divided by two so we can't really hear you can you mute someone I don't know who is unmute look at themselves you will use that so for a 99% confidence interval you will need to always remember that your z of 0 comma 0 1 divided by 2 which is z of 0 comma 0 0 5 you will go to the table or you need to always remember that it is the same as 0 comma 0 so the negative side to 0 comma 0 0 5 is 2.3 2.58 let's see 0.005 it will be 2.58 so that will be 2.58 so you will say 2.58 multiplied by your population standard deviation is 15 divided by the square root 3.87 b okay b and e have the same value and so there was an error on this one so they are the same the answer was 3.87 so and that completes the revision for aside minutes okay are there any questions relating to content of study unit six seven eight and nine up to where we are right now is there something that you still I'm sure of if none then I'm going to stop the recording right here