 and repeat. Oh, go see her. Where did you stop? Yes, please. Number 67. No, we started just briefly. I'm just going to say 32. Thank you. Thank you very long. Okay, briefly. I'm just going to give answers. Okay, type one era, it's alpha. So the only other thing that is alpha is level of significance. The null hypothesis is rejected if the p-value under H0 is smaller because we know that when p-value, this one we didn't explain, if it's less than alpha, we reject the null hypothesis. That's the rule. The power of a statistical test is the ability to detect the significance of the test. So the other one won't be correct because then this one says when we're looking at the p-value, when we get the power of statistical test, we want to detect if the result that we are getting is significant or not. So that is that. That's why we chose number two. Type two era, okay, is when. So we know that type two era will okay when the null hypothesis is rejected. When in fact it's supposed to be, oh, it's false, which means we're creating a type two era. A statistical test technique, we use the data from the sample to infer the result back to that population to make conclusions about the population. And that is why we chose number three. The others are talking about predictions and they extend those other things, not the statistical test in general. Choosing a larger value of level of significance, which is alpha would increase the likelihood of rejecting the H0 and will decrease the risk of creating a type one era. When doing a statistical testing, a researcher would calculate the effect size and we know that with the effect size, we want to check also the statistical significance of the test that you have. So you're going to check it in terms of whether is it small, that effect is small, medium or large. To sense the maximum risk, I chose the significance of one era and the sensitivity of the test is determined by the effect. Okay. Peter, okay, I'm not gonna read the whole sentence. Based on the statement, he has to determine whether the level of negative attitude of companies towards people with HIV is somewhat different from that of the workers in general. It does not say anything about the less than that one is bigger than or less than or more than or greater than or less than. So therefore, that won't be correct, that won't be correct. It says it is not equal. Okay. And we got there in two minutes. Peter finds that the workers in his company has a mean attitude score of 50, which of the statistical test procedure below would be most appropriate to use. Based on the information that we have, the population standard deviation is known. Therefore, we're going to use the Z test and because we're using only one company information from this one group, then we're going to be calculating the test for a simple sample made. And we are back on track 41 statistical hypothesis are statements about population parameters. Question 42 and 43 is based on the statement below. An educational psychologist compares two groups of learners from urban and rural areas on a language comprehension test. She manages to get a sample of 600 urban and 400 rural matched for gender and age to complete the test. She finds the mean language comprehension score for the first sample to be 32.5. And the mean for the second sample to be 30.7 for the rural and urban or from urban and rural respectively. Now question 42 is asking the educational psychologist decides to do a T test to compare the sample mean of the language comprehension of the learners with the sample mean of the rural learners. Which of the following is the appropriate tests to calculate? One is for one sample. If you see T for the mean bar, Tx means only one sample. That will represent one sample. D will represent two and two groups. Let's put it there. Not two groups, one group, but two variables. So it's the difference. So this will be two variables. The before and the after. Let me put it that way because it makes my life difficult when I talk about that. Yes, so D will refer to the before and the after. So that is the D and the C will refer to two groups. Two independent groups. So that should be the one because we're using the urban and the rural. There are two groups. A psychologist calculates the appropriate T test to compare the two means and the result. And the result is a T statistic value of 2.67. She determines that the significant level is one percent. The researcher is however concerned that the difference between the two groups means it's fairly small. And that the significant results may be consequence of the large sample size. What could she do to check whether the significant result is meaningful in use in a practical sense? She would calculate? Two. She will calculate the effect size. Which of the following level of significance indicated below gives the greatest risk of committing a type one error? Three. It must be one or two. Number two. Number one. So now we have three answers. Can I check the difference, Miss Boy? Yes, you can. Isn't it that like probabilities between zero and one? The level of significance, it will be either 0.01 or 0.05. So it will be between these two only, normally, as I have observed. No, you can have a level of significance of... At 10. At 10, yes. At 90 percent confidence interval, you can have at 89 percent, they are differentiated. Remember, a level of significance is how much error or margin of error that you will allow. So it's three. It indicates the maximum risk at the research. Yes. So 10 percent will be the... So if you choose the higher level of significance, it means you are allowing a higher percentage of disclassification of your results. Because that will say how the 5 percent you're saying, I'm allowing at least 5 percent, 1 percent. So you will choose it like this. In a medical environment, where we do not want to classify people as having cancer when they are not having a cancer, we want to have a level of significance of 1 percent. But in HR, you can even allow it to be 10 percent because we can classify people. It's not going to affect their health wise, but unless if we're saying people are at risk of doing something or falling into... Let me see which one would be worse. Work balance, like people falling into depression at work or having too much work or being overworked. Then you don't want to set your level of significance high because then if you set it 10 percent, most people will be classified as having a risk and then you will end up closing the shop. So you need to make sure that you set it low so that then it allows for that smaller. So 10 would be the maximum risk. So on this one, if there was... Which other one is missing on this? So this is 99. This is 90 and this is 95. So there is also like 80, which then 80 will be 20 percent. And then there are so many more than this that you can set. Sorry, three will be the right one. So when applying a statistical test, if the key value is smaller than the level of significance, then I'll hypothesis. What do we do in pv2? Project. If the pv is smaller than we reject. Then I'll hypothesis. No. And that is the rule. That's what they gave you there is just this rule. That you need to know. That should be in your mind all the time. The rule for pv. Yeah, it is confusing sometimes because it's too much content, but to master this rule is not easy. Yeah. I know you. So if the pv is small, it must go. Yeah, it must go. Because like this one, it's smaller, meaning when it's smaller, we reject. When it's larger, we do not. Yes. And actually the study guide says when the pv is equals to a smaller than the chosen level of significance, then you reject. So even if it equals to, I don't know if they would put it in that way, be mindful. Yeah, okay. Okay, so 46 consider the following statistical hypothesis. Mean of 50 or mean is greater than 50. Suppose that two tail p value is given at 0,045 I think we are repeating this and the level of significance is 0,05. The sample mean is found to be 55. What is the value of a one tail directional pv? I did a discussion around this. I'm not going to number one. No. Yes, we divide the two tail by two. You divide the two tail by two. So you will take that 0,035 and divide it by two, which will be option three. So you must always remember that if they give you a one tail and they ask you to find a two tail, what you will do? You will multiply the two tail by two. Yes. Remember what I just demonstrated? I said you will have two areas for the p value. So it means this is divided between those two, but it creates one p value for a two tail. For a one tail, we only look at if it's on the greater than. So this is greater than. So it means we're only going to take this p value that is on here. So that is 0,1753. A t test will be used to compare the means when. When do we use t test? Number one. When the population standard deviation is unknown. The p value depends on. The test is fixed. This is very tricky because I don't know what they try to calculate. And get it from the table. So it's very, it's very tricky with this. So this is why I'm saying this is very difficult to even try to understand. What do they mean by this? What do they mean by p value depends on? So it needs you to think hard because when you go find the p value. If we're doing a p value for z, then we need to calculate the z statistic. Remember, which is the t test. Then we take the z test and go to the table and go find the p value. But when we go find the value on the t table, we need to look at the alternative hypothesis site. Whether is it a one directional or is it a two non directional test? Because of that. Now they have one, two, three, which are all the things that I just explained here. So what does it depend on? I'm going to assume that it depends on number two, because if you don't have number two, you can't find the others. What is a test statistic? So it says the p value depends on. So you need to calculate the test statistic in order for you to find the p value. And that is if we're talking about the z. When we're talking about t, which we can actually manually calculate that and find it. We need to use a statistical tool to calculate the p value for us. But in order, in order for you to be able to find the p value. The z table comes after you have calculated your z test statistic, which is that the test statistic. Then you go to the table and find that is the step number two. Then when you go find the value on the table, you also need to remember what you said on the now, not on the null hypothesis, but on the alternative hypothesis. So also that, okay, that we should actually eliminate that is not even because only if we have the alternative. Because with the alternative, it tells you the value you find on the table or the value that you calculate. It will be a one p value and this will be two times the p value you find on the table if you use in the z. So it's between those two. But because the z table comes after the test statistic. So I'm going to say it depends on the test statistics. If you have calculated your test statistics, you can find the p value. Can I maybe just come in there? Yes. We have those z values from the z table. So we cannot have those if we did not have the z value. So there's something like that. So wouldn't that also be the case? Yeah. I'm saying it depends on what they try to achieve with that. Because the p value comes from the z table. If we're talking about the z tables. But in order for you to go find the p value on the z table, you need to have calculated the test statistic, which is the z score. Remember, you will have calculated that z. The mean minus the population mean divided by the standard error. Which is divided by the square root of n. And then once you have this value, you go to the z table to go find. How does size then come into effect here if we're talking about the size of the test statistic? The size will tell you. So this will be minus 3 points. Oh, let's not use minus 3 points something. Let's say it's one minus 1.4. Remember, when you go to the table, when you come to the table, what do you do? The same thing that we discussed earlier, which area are you choosing but based on your size, which is this, your z value. So the bigger the size will tell you in the larger portion, it will be the bigger probability. Oh, come on. How do I get rid of the blue thing? So that is the size. This size of your test statistics is reliant on your test statistic, your z. And remember also the size depending on as well whether it's positive or negative like we said. If it's greater than, we know that we say if you got negative, you go away in the negative side and it's the larger side. If it's negative and it was less than. Yeah, I don't know how to draw this thing now. Excuse me. So if it's negative and it's less than, you find it minus 1.4, you go to the smaller area. And those are the things. So it's the size of your test statistic that will determine where you are plus including the sign you get from your alternative hypothesis. So it's one of those. So I don't know. You can, I don't know. Do you choose? I don't know in the exam as well. The best thing about exams, they confuse us because we would find we know the facts, but the way they put the question. It's just meant to make us cook us. Yeah. And probably, yeah, you see, because they talk about the. So if, if they would, yeah, that's the other thing. I would have gone for number one. But you see number one is the after effect, because you cannot get to number one if you don't have. If you don't have the test statistic. If I have the z tables, I'll go to number one because I will have to pay value which will be dependent on that on the information on that table. No, but no, no, no, but the table, you cannot get to the table if you haven't calculated your test statistic. That value on the table, the p-values, all these p-values that you see there, all these probabilities, they are reliant on this value, which is your test statistic, which is the z. You cannot come here and choose any value that you see there and say, from this I can move there. But isn't this z here? You're rightfully saying this is dependent on that z and this what we're looking at here is the z table. This is the z table, but in order for you to find the p-value, it's dependent on you having calculated. Your z-value and coming here and saying this is my z-value is not dependent on the table. It cannot be dependent on the table. The table is the after effect, like for example. After effect indicates dependent. No. Leaving an effect on something. Okay. Let's assume then now we don't have a table, but we're using a statistical tool. We still need to calculate on the statistical tool. It will need to first calculate the z or the t test in order for it to go and generate your p-value. Your p-value can only be calculated or found after you have calculated. And you know what your test statistics looks like because you use your test statistic to go find your p-value. So it cannot be on the table. And it also cannot be on the z table only because even with the t test, we still have to find the p-value, although it's given to us. Yes, correct. Correct. So the only option on there that is correct because also even if we're not looking at the t table, also for the chi-square test, you can also find the p-value. So it cannot be only on this table. On the t test, on the f test, we find the p-values there on the chi-square test, we find the p-values there. So all of them depends on you calculating the test statistics. Ms. Boy, can I confuse things a bit? Yeah, confuse things. In session two of the study, we did the hypothesis testing and there were four steps that you said that we need to take. Is that something different like the step one would be to state the null hypothesis? And then step two is what kind of test must I do? No, it will be different because on the hypothesis testing, all those six steps. So one is stating the null hypothesis and alternative hypothesis. Two is stating what you are given from the question, which will identify whether the population standard deviation is given, what is your end and so forth. Then step number three, we said we need to find the critical value, which is something totally different to the p-value. So the critical value is something outside the way we use the level of significance and only the level of significance for z. For t, we use the level of significance and the degrees of freedom. And then you go calculate your test statistic and then you make your decision. But in making a decision in relation to a p-value, you need to calculate your test statistic. Then take your test statistic and the p-value. And based on your alternative hypothesis, sign, it will tell you whether if you're doing a two-tail test, whether you're going to add the p-values together when you get them. If you're doing a one-tail direction, the value you see on the table and depending also whether is it the greater than or the less than side. If it's the less than side, the value you see on the table, if it's negative, that will be the value you use. If it's positive, then you say, but you take the larger side. But if it's on the larger side, you also say one minus the value you see on the larger side, which will be smaller and then you add them. So it's that complicated process. And that is why they don't want you to learn all that complicated process. But in order for you to find the p-value, you should have already calculated your test statistic. And the p-value cannot only be rely or dependent on the z table alone. Like somebody already also said, because also t, you can find the p-value on the t because that's what we did on what was this the t-test that they didn't say this is a t-value. But you can also find the t-test p-value. You can also go find the chi-squared p-value. You can also go find the f-distribution, which is for the other sessions that you don't do for the ANOVA and all that. You can go find the critical value for all that. Or the p-value, not the critical value, the p-value for it because based on those tables. So there are different tables that you can use to find the p-value. So the only thing that you need is the test statistic. See if I can delete all this. Maybe for later we can just check on page 78. Maybe we can do it as our own. Because it's talking about the null hypothesis and the value of the p-value. Page 78. That is on talking about study 32, 3.2. Before that, yeah. I think it's paragraph three. Yes, the p-value is okay. We're referring to this one. Yes, if you go down there you will see that it is extremely important. The probability of obtaining a value of 104 purely by chance due to random measurement errors. When the null hypothesis is true is referred to as the p-value. Maybe that is the case that they are looking for. And that is why I'm not sure in terms of when they say the p-value depends on the null hypothesis now. Do they mean the same thing? I think number two is the most confusing. The p-value is confusing. It's due to random measurement errors which is the size. So I think number two is the most correct answer compared to the three. I wanted to interpret. I hear you are on number two but this line where we are on page 78. It says this probability of obtaining the value. It sounds like the chance of obtaining the amount of 104. Please help me with English purely by chance. It looks like it doesn't talk about the p-value itself. It talks about this amount of value. Am I correct? I'm reading on English. Due to the random measurement errors. I would say number two is the most correct. It's confusing but if you had to compare the three I would still go with number two. I could be wrong. Even when you google it it talks about size. Number two is the most correct. I also saw this in the feedback of 2018. One of the papers but it had said the size of the p-value. I think it's the same thing. I think so too. I think it's number two because on page 84 it says that the test statistic is available with a non-probability distribution. We can use it to determine what the probability is of finding an effect of particular size which we refer to as the p-value. The p-value gives the probability of obtaining the sample and results under the H naught. If the p-value is small the probability is very small. The smaller the p-value the more likely the null hypothesis is false. That does not help for me. Ma'am can you read page 84? Where is page 84? Where it says type one and two errors of the power of the statistical test. Where? The first paragraph like the last three sentences on the first paragraph. Where it says the last part you can create a test statistic. That is an indication of how far the observed effect as reflected in the sample data deviates from what the null hypothesis tells us what to expect if it were true. The test statistic is available with a non-probability distribution. We can use it to determine what the probability is of finding an effect of a particular size which we refer to as the p-value. Thank you. Thank you for finding the answer. Thank you. This is it. See we just need to read. How are you going to read 385 pages before the tenth? There you go. Half the exam time is gone. So you must make as much notes as possible. Even including the page numbers because I think you said your exam is a take-home. So make sure that you put all these references and pages and some way where you can make notes of. All right. So we're done. Settled. So what is the answer? Number two. So the difference goes. I thought statistics is the most difficult one. You guys are writing the most difficult paper. The difference goal is like you doing pure stats. The difference goal which is D of your mean or X2 minus X1 is used to calculate the T test of difference in the case of one or two or both. One, two, three. Number two. Number two. Guys, you are disappointed. I would say number three. Number one. Number one. I'm going to talk about the differences. It should be dependent samples. It means the before and after. Remember the T. The T. Yes. The T. The T. The T. T is the comparison of the mean of independent. Thank you. And then the T. X is your the test for the unknown. Population. T test. One sample. One sample. Thank you. So you have three keys. Be careful of those keys. Yes. They talk something differently. Each of them. Which of the following terms. Population parameters. Sample statistics is not required when calculating a T test. Number three. Number three. The population parameter. Yes. Suppose you find that. The value of a T test calculated for your research results. When comparing two means is 3.0. And the appropriate P value. Is zero comma. Zero two. Which conclusion is appropriate. Okay. So what you need to do because they gave you the level of. Significant. Different level of significance. Let's do it this way. So take the first one, which is the P value. So the P value less than alpha. You reject the null hypothesis. That is. That is the rule. So now if you know this is a decision. Take each one of them. So let's take the P value there is zero comma. Zero two. What is my alpha there is zero comma. Zero one. Put the sign here. The sign will be. This is bigger than that. So it will be greater than. So therefore it means we not rejecting the null hypothesis. Yeah. So this one says. Do not. Reject. Null hypothesis. So you go to the next one. So the two that are left. Are the same. So you take your P value. Zero two. Your level of significance is zero comma. Zero five. Put the sign. Zero comma. Zero two is less than zero comma. Zero five. So therefore this one says we reject. The null hypothesis. Isn't it. So now then go and answer the question. Number one. It says reject the null hypothesis. If the level of significance is zero comma. Zero one. That's not correct. Because we do not reject the null hypothesis at that. Number two. We need to be rejecting the null hypothesis. Let's not reject the null hypothesis. At alpha equals to zero comma. Zero one. That's not true. Number three reject the null hypothesis at alpha. It's the same as what you found. There. Four only number three is correct. So that's how you can. How you can make decision on this. So you will need to validate some. All of them. Based on the p-vane. And the decision. So if only you can remember the decision. Rule this. By now you should know it by heart. We have been talking about it. Since yesterday. I know the decision rule. But still this question. It's shopping me ding dong. I don't know. I don't know. No. It's because also they gave you two measures. Yeah. But also you need to remember the following. When you make a decision. In your hypothesis testing. Because in your module actually they made it easy. They only want you to make a decision. Based on the p-value and the level of significance. So. It means. Every way we have to make a decision. We always have to use. The rule. The decision rule. So you need to always compare your p-value. And your level of significance. Okay. Okay. Let's look at. 52. In which of the following cases. Can the score on two variables. Not be regarded as. Independent. Okay. The variable represent the scores. From people in a control group. And a treatment. Group. Where the members of the two groups. Was. Randomly selected from the same population. Before and after. Hmm. Being the variable represents. Scores from the same person. Measured before. And after the treatment. On the same test. Both. Both yes. Option B. B. B is dependent. Which of the following two scores. Of two variables. Not be regarded as. Independent. So now let's understand this. A and B. B. Is. What is B? Is B dependent or independent? Dependent. Because they are measuring the effects. Before and after. Dependent. Before and after. So this. A it says. The variables represent the scores. From persons in a control group. And the treatment. Groups. Where each member of the two groups. Was selected randomly from the same. Population. Applied. So number A. Is it. Independent or independent? Independent. Number one is independent. So what makes it independent? Can you show me here? Because. The two groups. The control group and the treatment group. Are two independent groups. Wow. Thank you. Those are two independent groups. And. The second one it says. From the same person. But they did A before and after. So you always need to look at those. Departition is something else. The option two is the one. That says B but not A. Wow. If English doesn't kill me through this course. I will say I have survived. Okay. So which one. Is A but not B. B but not A. Both. So he. B but not A. Is number two. Co-hand deep is a measure of. One. One. One. And large T. Test statistic. Implies that the P. Value will be large. Implies that the P. Value will be small. Is unrelated to the size of the P. Value. Number two. Number two. This is very good. With your module. I don't know. No clue. No clue at all. These people they are playing with us. So. Yeah. So. Implies that the P. Value will be large or the P. Value will be slow. It will be small. What do you mean by that? Right. The sample the smaller the. The. So the. You see you saying larger the sample. So larger the T. So. The T. The T. So. I think. Number three. To think about the T. Test. In the same idea and think about the graph. To see where. The value will. Will be on the graph. Right. Not necessarily. Not necessarily because let me. Draw the graph. what do you mean? This is the graph. Where is our t-test? So we calculated our t-test, let's assume that our t-test was, let's not even use minus. Let's say it was 7.3. We calculate our p-value, because it's very difficult to find the p-value. I can't even estimate. I can't even go to any table. That's the challenge with the question. That's why I'm not even sure what they're trying to ask here. What do they mean? We have too many challenging questions here. There is no question paper that we can't, we just like smooth right. Like we have to google search. Hi, no man. So let me see. I need to find some one of my notes. Oh gosh, it will be easy. It's not going to be easy. Ms. Boy, what is the t-test statistic? Is it the one that we differentiate with the z-test and the t-test of the known population and unknown population? Is it the same thing? Yes, the t-test is the value you calculate using that formula. But now what would make it large? That's how I'm trying to approach it. Yes, so let's take the one with the one sample, because that one is not that complicated. Because then it says the sample mean minus the population mean divided by the standard deviation over the square root of n. Please show up. So there. So if your sample size becomes larger, you see that's the challenge here, because this will just give you the larger t-test. It's not going to tell you the p-value. What happens to the p-value? And that's where my challenge is, because the p-value of a t-test, we cannot calculate it. We don't even know how it gets to be calculated. We are not able to calculate it. Can you say that? Can you say that? Excuse me, I have a thing on page 116 where it says remember however that the t-value is sensitive to sample size. For a larger sample, a smaller effect would be significant. Okay, so let's go there. 116. Below, go down. The last paragraph before the formula, based on the p-value. You mean that one? Yes. But this doesn't say much to answer our question. Our question says, let's go back. A larger t-test statistics implies what? Because that should be in relation to the p-value. A larger t-test statistic implies that the p-value is large or the p-value is small or is unrelated to the size of the p-value. Would it not be on the latest? No. What does it say here on where you have marked red on page 116? Yeah, this paragraph. What does it say? I see something smaller, a sample smaller effect would have a significant. Can we read it? I don't see the other part is cutting. I am trying to make sense of it. If we could hijack it. Way. This paragraph, what does it read in this boy? Because for me, I just see half of this. I see up to topic three and then the rest I don't see. The base on the p-value between the mean seems is end here and then I can say remember however that the t-value is sensitive to sample size. I don't know what it says going on. So it just says based on the p-value, the difference between the mean seemed quite impressive. Remember however that the t-value is sensitive to sample size. For a larger sample, a smaller effect will be significant. See topic three section 3.3.3. So I don't know if whatever is on page 120 is going to help us. Let's see. The first paragraph there. That's the first paragraph after the formula. Can I ask how are you getting this page? Are you searching the moon computer or you have to be a computer? So this t-value is larger than the p-value is bound to be. There we go. Hey, thank you. You see, we need people who can search PDF. There you go. So the t-value is so large that the p-value is bound to be very small. As in the case of the Z statistic, the t-values of the above three are seldom not significant. We computed it and found that it would be 0,000000. Most computer programs will report such as p-value to a four figures or decimal, which is 0,000. This p-value is clearly smaller than the level of significance. So that H0 must be rejected and H1 must be accepted. And there we go. So let's see if we can answer the question. The question was asking. Elijah test statistic implies number two, a smaller p-value. We need to use Google so often. Okay. So I think I hope you are also making notes saying page some number, page 120 somewhere there so that you can remember because I'm not making notes of the page. Can I ask a question through you? Yes, you can. Fellow student, how do you search this? Do you use a computer or you have seen it in your studies? I'm wondering if this method could help me for the exams. You click on the magnifying glass it looks like and it brings up a find window. Oh, you're using the computer one because of the book one. It just makes me spin. Thank you. Yeah. So if you go on to the study guide, the digital one that you can download from the study material on the left corner next to the printer, there's a magnifying glass there, the fine text. And you click on it. So any, if you type in hypothesis or anything that you're searching, then it will highlight or bring you to that page. I see. I think when we, what, what do you give me, or give me an idea to take the very question paper, go on the digital one and whatever that you don't know, go and look for the study guide because if it's easy this way, then paging through the book, the book makes your head spin. Thank you so, so much. I like facilitating this session because you guys are very helpful. You're not quiet. You helping one another. Thank you very much as well. So we found the answer. It's number two. Moving on. If I can see six are based on this, a researcher is investigating the claim that playing a specific RD computer game will improve the eye and coordination of children who play it. To test this idea, a group of 40 great 11 learners are tested on eye and coordination test where a high score indicates better eye hand coordination. They then play the game for an hour after school every day over a period of two weeks. After two weeks, they do the same eye hand coordination test once more. The mean score for eye hand coordination after the treatment which is playing the game are compared to the mean score of eye hand coordination before treatment. What are we dependent or dependent? This is, it's a dependent. So dependent. We're still lost. It's the before and after. Yeah. Which is an appropriate alternative test for this analysis? I would say three. I would also say three. It's greater than the population before. Makes sense because of always after the treatment there should be improvement. It makes sense. Number three. He talks about improving the hand eye and coordination. That's the key word. Yeah. Greater than. I agree with number three. Let's hear number two. How are you supporting it? But you know what they've done? They've put the words funny. It's actually number two because no, no, no. It's actually they put after and before for number three. They first put after. No, that's right. That's right here. Sorry. Sorry. The question here is which is an appropriate alternative hypothesis? True. The alternative hypothesis needs to give kind of a direction. Not necessarily. Not necessarily. Why are you guys getting all these directions? Because the question, I don't see what you guys are seeing. I think the first one is one because after is smaller than before. So before is great. How do you know that after is smaller than before? Now that is an alternative hypothesis. Way in the sentences. Yeah. In the paragraph. The first sentence. The very first sentence. It says if the 3D computer game will improve the hand coordination of children who play it. So it means after treatment they explain that there needs to be an improvement, which is more. No. They could have even said there is a difference between when they, when they were, I told you you need to look for words like it's more than it's greater than it's increased, increased, improved. No, but improvement can improve. It gets better. It gets better more than. On land number three, it says where a high score indicates. Improved means it gets better. No, but that says a high score will, you can also get a high score even before. It doesn't mean it's better than the high score that you would get after. That is just additional information. But the critical statement is the critical point is the first sentence. It clearly says you want to test if there will be an improvement. That can, improvement can only be if there is a difference and the difference has to be more if you improve on something. I agree. It can't be because the paragraph does not speak about difference. It only speaks about improving and there's nothing about difference. Number two, it's number two also. It is number three. I don't know, you know what English confuses me. That's what I'm saying after if I pass or I survive, it's something else about this language. Look at the last sentence. It says the mean scores for high hand coordination after the treatment which is playing the game compared with the mean. You are confusing yourself. Sorry to interrupt, you are confusing yourself. The first thing to look at is what are they trying to do? They are looking at what they've done already. So you need to have a hypothesis where you will have the now and the alternative. Before you go to the last part of the paragraph, you need to define those first. Also what we're doing here actually is to define a hypothesis. Are you saying that? Exactly, you give the now and the alternative. So the now has to be equal? Yes, and in this case, the researcher wanted to find out if playing this game will improve. That has to be better than before. So now we're looking at the alternative. I agree with number three because I'm saying that. Improve, improve is better, more than, greater than. But now number three is likely to be, Ms. Boy, you had your view to say, where do you see all this? Okay, so, okay, okay. So now let's understand this. All of you are saying almost the right thing and the same thing. So the first thing that you need to check is what is the researcher wants to prove? And that's the main thing out of everything. The others will follow. So the researcher is investigating the claim that a 3D computer game will improve the I hand coordination of children who plays it. That's what the researcher is trying to prove. He's trying to check whether there will be an improvement. Yeah, he never said there is a, the ones who played before and after they will have that nothing about that. All what he wants to prove is to see whether there is an improvement after they have played the game. So what they did is they went and they tested 40, 11 graders that on the hand I coordination test where a high score indicates a better I hand coordination. This was even before they can play the game. They tested them. Then they play the game for an hour after school every day over a period of two weeks. After two weeks, they record the same I hand coordination test score. Then they want to check whether there is a difference between the mean score of I hand coordination after treatment to those before treatment. Now we need to ask ourselves, based on this information, our alternative hypothesis is there a way where the researcher said in his own way that after or playing will improve or playing is better than. It's for excuse me. The other. So, yes. So, you and they will improve this. I would vote. That's number two work because before. Even after there is no statement who says what we live and can we say it's not equal because we don't know the prediction there. Still back to differ, you know, the way improve is critical. I think number two is the best one now because now from the explanation it says there is no longer the same as they were before. There has been some change. So before is not the same as after. Yes. Whatever the case. Number two is correct. For me, number two makes sense. I say that if I let's just analyze what Miss Boy said. She said we have to realize what the what the intention of the researcher is. The intention of the researcher here is to investigate the claim that, you know, if after playing, there will be an improvement. So then the null hypothesis would be equals to meaning, you know, will be equals to if there is an improvement afterwards, which is what she or he will be trying to investigate. Improvement can only mean better than before. It has to be better than before. I agree, but it's not specified if there was any improvement. They left us hanging there. No. Remember, that's what you're going to test before you have to identify your hypothesis. Results comes later. Which is the point of departure. Identify. Exactly. But also there's a claim specific to the computer game will will improve 100 percent. Yes. OK. Let me summarize what you guys are saying. Based on the discussion that you have. It's true that the null hypothesis will have equal. But what matters the most is what goes in the alternative. So if we agree that it says will improve means that after will be bigger than or will be more than the before. So it means there I hand coordination of. Of the children will be better after. So what we're saying is before is less than after. In summer. That's what we say before is less than after. So after which is the same as after is more than before before is less than after or after is bigger than before. And that is what all the statements here there are. So if we say that is not applicable because of that will improve meaning then the after will be bigger than before then number one alternative would not be not equal. This one says we're saying after. So number one says after is less than before. That's what if you choose after. So you must be very careful because you're saying after is less than before. So you're telling me that after they play the game there is no improvement. I don't choose number one. So then in terms of that it says they will improve. So we're going to assume that it improves. So when it improves then number three is correct. Don't think that is correct. The reason why I say that is the researchers hypothesis is saying that it will improve. And the question is which is an alternative hypothesis to the analysis. Are we not supposed to be stating which answer is reflecting the alternative hypothesis to that which is stated on this scenario which would be question number one. Yes. Yes. Number one because we have to come to the conclusion. Not necessary because what okay here is the other thing that we also need to take into consideration when we when we put the researchers statement. So if our research statement is greater than or equal it will be in your null in your null hypothesis and the alternative will be. So if we say the researcher is saying it's greater than or equal if that is the case then the alternative will be less than. It will say it's not going to improve. But if we say the researcher is saying their thing is greater than we cannot put that in your null hypothesis but you can put it in your alternative hypothesis because then because in your null hypothesis you can only put any sign that does not have an equal sign. So which will be the less than or the greater than. In your null hypothesis we are saying. If they if they say it's the same but they improve which is greater than. They are not the same they will be more than it will be greater than we only can put it in the alternative because in the null hypothesis we cannot put the less than or the greater than. Not even because your null hypothesis so let me see do we still you know this one doesn't deal with the null hypothesis so your null hypothesis always has an equal sign. So in your null hypothesis we always have a greater than or equal less than or equal. So we can still put this as the researchers wants to prove that it's more than if improve is more than yes this go into your into your alternative hypothesis and when you do your decision that's where most of the time you find that you go into have a type one or a type two era rejecting the false null hypothesis when something like that you will be committing a type two era because this won't be a true null hypothesis that is on the null hypothesis statement because we take in the null hypothesis statement we putting it in your alternative beyond me I'm sorry I don't understand okay because for me I wouldn't yeah also for me I wouldn't even say that I wouldn't even say that the researcher wants to prove to test that this will improve the i-coordination as greater than or less than it's still whether there are any differences between the two because we're going to compare whether before or after are they different. I want to suggest something if you look at the next question would that not help you to determine the question 55 to do if you can figure out if the question or if the hypothesis is a one-tailed t-taste or two-tailed that would help. That's the thing because the minute you choose one tail here and you say that is your one tail test therefore when you come here option one and option two you will choose one tail because it's between those two if you choose not equal it will be a two tail because number three is incorrect so on which statement you choose in number 55 you are going to choose also yeah the incorrect statement 56 would be number one and number 55 would be three no 56 won't be wait 50 what 56 is number one 56 is number one because you've got two groups before and after so you're saying 50 I'm very confused 55 is three 56 and 56 is one okay so that is for those who chose number three those who choose number one your 55 is number one and your 56 will be will still remain number one those who choose number two your 55 will be number two and your 56 will be number two so the only thing that is very confusing yeah is that improve what does improve mean man I don't know so I I I I can tell you that there will be things that guys that I don't even know what I think let's let's make it simple but I think because because it says because it says improve it means it's greater than if you didn't want if you didn't want to for it to be greater than you would have said to find if playing the computer game has an effect exactly I want to get coordination then then would know the effect would either be less than or it would be greater than if I have 50 percent on my on my test now for me to improve I have to get more than 50 percent wow that's the meaning of the waiting room all right wow okay so I'm going to leave it to you guys give me an answer 55 I was thinking with three and 56 it's one it's one one okay so you need to go and read more in terms of those um well very tricky I prefer things to be straightforward this is very tricky I need people to be clear with me tell me that it's greater than or less than or don't confuse me with all English which of the following assumptions are sufficient for a two sample t test even if the sample size are relatively small they're okay so the assumption are sufficient for a two sample t test so the sample standard deviation must be equal but the distribution must be unknown the data from the sample comes from a population that are normally distributed so that the standard deviation need not be considered the data from both samples comes from a population that are normally distributed and the sample standard deviations are equal number three so the t the sample selected from one sample has no effect on the other the samples are randomly selected and are independently drawn the population variances should be unknown what else am I missing that needs to make that statement correct the sample standard deviations must be equal the word unknown makes me to say there's two the t test is what we I don't know I don't even understand that question I think I chose one because of the t test and that unknown on the option and known I think is the mean for t test if I'm not mistaken not for standard deviation so I be I guess it's gonna be two or three the population means is unknown for the t test number three please help miss boy I'm I'm also going with number three no I'm also going with number three but this equal standard deviations is throwing me off I miss boy want to kind of quote you you know one on on on one of the presentation that you made on the formulas a clear distinction between the z test and the t test is that the word known the descriptive statistics are known and on the other one some of the descriptive statistics are unknown so when I just see this word alone and yes that is that no that is true no that is true what if I can go back to that as well so for the t test this the population standard deviation needs to be unknown what only the population standard deviation and your distribution can be from a population that is normally distributed so this is correct in terms of what they are saying there what I'm not sure about is the following because statement number one is it's unclear because yeah it says the sample standard deviation must be equal but the distribution must be unknown so which is very confusing as as what throws me off is the standard deviations must be equal why I'm saying that is if I have two samples one can have a standard deviation of 1.5 and the other one can have a standard deviation of 0.2 but the for some when we do as a test we can also assume that the population and I think it's on the notes as well that I've shared because for a two the the two means of independent samples what I know is either the populations standard deviation are unknown and they are assumed to be equal only the populations standard deviation here I'm referring to the other thing is they they need to come from an independent population where it means that the sample that was selected from one sample should have no effect on the other sample number two the assumption of those independent tests would be the sample should be drawn from that population independently the population should be normally distributed and if it's not normally distributed the sample size should be bigger than that the variance should be unknown but assumed to be equal that is on the population side now on your questions it says the data from the sample comes from a population that is normally distributed and the sample standard deviation are equal and that's why I say it's throwing me off there because it talks about the sample not the population so what does your text your study guides say on the two test sample two sample t test what does it say what are the assumptions that they give you because then that will help you answer that question testing the differences between two minutes before we come first the difference between independent and dependent and there we go so the sample has no effect there we go that's what I just said the two sample comes from the population and has no obvious relationship that's one so this is dependent what other thing are they talking about the implication of this is that you know that is not what we're looking for so the test where do they talk about the assumptions the two samples come from the same population we've dealt with that don't they give you assumptions I haven't seen that anyway here wait a minute on the questions on page 135 125 it says the assam number seven on page 125 the assumptions underlying the t test are one equal distributions are normal variances two unknown standard deviations and three normal population distributions with equal variances and the right answer is number three but I don't know if this is not really the same as what they're asking yes our question here you see this is normal population distribution with equal variances so which means equal population variances not the sample variances because if you look at this let's assume that this or because this is uh is it the pre and the no these are two groups these are independent you can see that we have two different standard deviations they are not the same you understand the independent or dependent this is independent okay even if it's not independent even if it's not independent because the mean difference between the scores will be different as well so the sample and that is why I'm saying in terms of the sample they yeah if they could have just removed this I would be fine with number three as an answer I still have my own reservation on that because it says the sample standard deviation are equal they don't have to be equal but the population standard deviation should be assumed to be equal so if they because we don't even know but we need to assume that they are equal not the sample because we're going to be using the sample to test to calculate and usually the the test won't be the same so for group one we'll have a different like you have here group one has a different standard deviation which is the same as different variance because the standard deviation is the square root of your variance which is different this value is different from that value so that's why sometimes it's very confusing I guess maybe I need to read go through your study guide and understand it further probably two years from now I will master your psych 304 but not now I it's very confusing really it's a lot of a lot of a lot of facts thrown into one sentence you know yes because also number two says a standard deviation so from the population so that the standard deviation need not be considered so in terms of in terms of that so we can say the standard deviations are unknown uh not the yeah so it can be that the population standard deviations are unknown and not that they are not considered so it's very tricky to answer your module are we going to pass this module then yes you're going to pass with flying colors where is the party going to be yeah you're going to pass with 1890 you'll give them a memoranda you'll never know a researcher has to select the appropriate t-test to compare two minutes in each of the situation described below in which of the cases would a t-test for independent group be the best option so tc is independent groups so evaluating the effectiveness of pain relievers by measuring how much the pain relief after taking a medication in a sample of patients two evaluating the development of babies groups between age two and age three of for the sample of girls three evaluating the differences in level of self esteem between student athletes and non-athletes a researcher has to select an appropriate test to compare two means in which of the following describes below in which of the cases would a t-test for independent groups be the best option i'll go with number three because of evaluating the difference yes number yes yes number three difference and because also they are using two independent groups which are the student athletes and the non-athletes yes and this one it says they are just evaluating the development so it's not the difference and the first one is measuring the pain before and after so this will be a dependent so yeah number three thank you when would a statistician choose to do a t-test rather than a z test to compare a sample mean for a given population you are a statistician ma'am you can tell us number three number three population standard deviation is unknown you need to read the the question so um the statistician will choose a t-test when the population standard deviation is unknown a researcher wants to determine whether the level of academic accomplishment that a student has reached is in any way related to the way in which the student approaches a problem to do this she plans to relate to relate the exam mark of the group of undergrad student to their results on the test that indicates a problem solving style what is the independent variable in this problem solving style number one yes option three it's the x definitely number one is it number one a researcher wants to determine whether the level of the level of academic accomplishment that the student has reached in any way is related to the way in which the student approaches a problem solving so that will be the independent variable oh wait a minute i think it's three three is the dependent it means the level of academic accomplishment depends on the problem solving how does it solve the problem it will result in better academic accomplishment or lower academic accomplishment i think like the level of accomplishment academic is one that determines the problem so according to the handset shows option three no you are correct in in in your explanation but the answer is number one so here what it says here if if academic accomplishment is related to problem solving that means if your problem solving increases or decreases how is that academic accomplishment behaving relative to that so you only vary your your your problem solving that will be your your independent variable yes so in a way you told you you told me something new today you said to me that there is something called the construct and a construct is where you operationalize some things and then you create a variable so in this instance she wants to look at or we ever is she or he or okay i must not oh she okay she wants to use the exam and the test mark so that she can see how they answer or perform on the how does it improve the level of academic accomplishment because the master they got there tells them or will give her an indication of the problem solving thing so the problem solving is your independent is your input into checking your level of academic accomplishment so you yes yes i also agree now you know all right okay so let's go there Pearson product moment correlation can take any value between minus one and one minus one and one r can take any value between minus one and one probability can take only zero and one what is the correlation coefficient between the following variable x and y looking at the data i would say uh three one one positive one one yes number one one is number one so if this is five minus five i'm going to just make up notice there so if this is minus five and this one also is minus five then it's our dot will be there and if is this seven and seven our dot will be there minus one our dot will be there zero and if i draw this you can see that this is a positive relationship so i will assume this arm is one because it's on a perfect straight line i only use those few because i can just assume make an assumptions there so there's be a positive one so that will be option number one one if it was in an opposite they took these values and made them opposite it would have looked somehow like an opposite direction would be negative we did discuss something like this area as the sample size n increases what happens a smaller value of the psn correlation coefficient will reach significant a larger value of psn correlation coefficient is required before the results can be significant there are no implications on the level on the significance of the value of the psn correlation coefficient i found this answer on page i'll tell you now um 139 let's study so it says if you increase the sample size to 100 a smaller result r will be equal to 1.60 would be significant at the same level where about on the page is it um it was it's the um third paragraph from the bottom up the consequences of this is that for a large sample a relative modest correlation can run out to be significant okay so it says as a sample size n increases what happens to r so the question be the larger n a smaller result of r would be significant so it would be one i agree it is also agree it's one question 64 high square test is is used to compare number one one that's your key weight cross tabulated you don't talk about any other cross tabulated on the other one so this one's talk about the extended continuous we know that it should be categorical and this talk about the mean value we know that it should be a categorical so only number one is correct if there is no relationship at all between the scores what would be the most likely value zero that would be zero so based on question 66 and 67 a psychologist reads an article in which the author claims that playing computer games oh gosh it seemed like we're repeating she decides to test this by asking sample of children to report on the number of computer games they play per month measuring aggression level of each child with an appropriate psychometric test she expects to find that a positive correlation will exist in her sample between the level of aggression and the number of computer games played if she should draw a graph of the relationship between the aggression and the number of computer game which the scatterplot below will give the most probable representation of the data if the expected relationship exists number one because she said it's positive so it should be great graph a graph a if only all the questions were like this one yay what would be the most appropriate test to use because the hypothesis implied by this scenario above here number three number three number three base your answers to the question of 68 and 69 on the following a researcher wants to establish whether the type of employment category is filled by employees of a particular company is all is at all influenced by the agenda he collects a data from a sample of hundred employees where each employee is categorized as manager middle manager number two which of the following is the appropriate test the relationship exists between two and number three it's a chi-square it's in clever so it means when you write your test you must start bottom up because it's like the ones at the bottom are easy so that you don't run out of time so uh the contingency anything on chi-square is easier yeah the contingency table below and we want what would be the expected frequency for rural males and that's the question calculate the expected frequency of rural males so they have calculated the totals all right total times column total over grand total yes we just take that multiply by that divide by that so it's six multiply by six divide by 18 row total times column total divide by the grand total wow is equals to two two two two and that's because i aimed for a dot look yeah we're done no it was as expected as you you go back to 54 quickly for me please i i am 64 64 i missed that one okay one okay thank you you okay i will i will post this one on what Okay, so guys, this concludes my engagement with you. Guys, so because I with you guys, I wish you all the best with your exam. But remember, I'm not going to do every message during the week. But I will try my level best to look at the chat and then also do the activities. If you want, I can leave, I can give you or no, you can use the same link. You can come to the session, the same link to do your 2020 together alone, tomorrow or whenever. You can still go into my link. I won't mind you using it. Maybe I can also come in and spy on you guys while you are working, but I'm not promising anything. But if you want to continue working together as a group like this online, somebody sharing the exam paper and you always do it. You can do that. Hopefully there won't be any arguments. Hopefully there won't be any arguments. You need to keep it clean. You need to work together. And if you don't agree, don't move on. But yeah, because I've got other things that I need to completely do tomorrow because today I sacrificed my afternoon session. But all the best guys, I wish you all the best and thank you very much. Thank you. Thank you.