Wait, can you slow down? I'm writing this stuff down.


OK


Yeah, cause I just took an exam over this chapter and intro to hypothesis testing, and it was kind of difficult like the, the problem solving part because my exam is like, OK, we get 50 points on the multiple choice part and 50 points for problem solving, and there were two problem-solving questions both from this chapter. And so what happened was the teacher, um, she introduced the chapter two days before the


exam, so it was hard for me to grasp, like, the only thing I remember from this chapter is figuring out the upper and the lower limits of the confident intervals.


which is an easy task, like, but it's free, uh, easy because I just had to know my critical values and then multiplied by my um population standard deviation of the means, plus the meat sample meat, like the began.


Right, OK, well, this is what we're gonna be testing. So I'm writing the data here, so it tells us that we have 50 individuals.


So the X is 50.


No, N, N is 50.


Oh, the sample sizes 50.


50, and it tells us that the amine


X bar


Yeah


is 78.


Now, it tells us that


the significance level is 0.05. So I'm gonna write that down.


So


So population one was um people who were not tired and population too is people who are tired.


that's right


Thank you for coming back again. Achieve University's website thing.


OK


Yeah.


Population tools people who are extremely tired, right?


That's right


Because on the exam, I had problem figuring out which two pro which two populations were being compared.


Right


I was stuck on there


Yeah, there's more than one way to do this. We cannot compare the two means directly because they, they don't tell us how many people are in the first group, people who are not tired, they only give us the mean and the variance for the, the group of tired people, group number 2, we, we're given the value of n, which is 50


and um


and they tell us that their accuracy was 78.


So what we're gonna do, I'm gonna show you how to formulate the hypothesis.


Yeah


All right, so


we're gonna write the


so that's the second group, so that we start with what's called the null hypothesis.


No, but wait a second. My instructor, she starts with the research hypothesis.


like the 8 of 1, we call it H1.


OK. H sub 1. All right, we'll write that one first. I'll


OK.


Yeah, that's how I work my homework problems and stuff. So hopefully, I'm, I'm hoping that it doesn't bother you. Sorry, but.


No, that's fine


OK


So


naturally we think that people who are tired will not perform as well, so we're going to see if they perform just as well or if they're worse than the people who are not tired.


So what we're gonna do


we're gonna write the, this is the mean of the population


who is


tired. This is, we pronounce this new. You see this little symbol that I wrote.


I don't


I led it in that, that's, that's pronounced mute. That's the symbol for the mean of the second group, the tired people, and the research hypothesis is


Wait, how do I move this toolbox so I can see the information you have written, cause it's blocking the information you wrote.


oh, you can't see the book


I, I can't see the board, but the two parks in the middle is blocking the information you wrote for number 19, problem number 19.


OK, can you scroll up and down?


Oh, yes, I see, I see, sorry. I see.


OK. So we, we think that the, the research hypothesis is to see if the mean of the tired people will be less than the mean of the not tired people, so I'm going to write it like this.


Sou sub 2


less than mu sub one, that will be what you call the


uh research hypothesis. It's also called the alternative hypothesis.


Yeah, I know that too, but we call it research hypothesis and the no hypothesis.


OK


Now we, now what we need is what's called the null hypothesis.


like the opposite of the research hypothesis.


Exactly right


But we call it


Yeah


and uh


no, so the, that's called the null hypothesis, always has to have an equal sign.


So it's gonna be


mutual


no


We don't, we don't do that, sir. Sorry. We don't put an equal equal sign or anything. Like we don't even use the smaller dens sign. We don't use all of that.


Uh, that's for H1, smaller than, you see what I wrote for H sub 1.


Yeah, we don't, we didn't use that.


when we were starting this chapter.


You didn't use that one.


We just startedly stated, we just directly stated the research and the no hypothesis from the two populations being compared.


So maybe you wrote it like this.


In fact, I'm gonna write the number, the number is 82. That's, that's the um


I'm gonna write it like this, 82.


So is that OK


Yeah, like, like we actually stated the no and the research hypothesis. Instead of using less than or equal to or greater than or equal to based on the population mean. We didn't, we actually roast like stated it in words like people.


who


Oh, in work, OK. Well, we can do that. We can do that. I can write it in words.


OK


like people who are who are not tired, will


you know.


Yeah, we can do that. Let me, let me write it. OK, I'll write it here, then I'll move it. So H


H 0 and then H sub 1 we can say.


No, I want, I want you to do the H sub 1 first because that's how we do it. I don't want you to flip around because then I'll get confused in my head.


OK, so


the


I want to start with the research hypothesis.


yeah, OK. So the mean of the tired


pop.


population is less than 82.


So that would be our research hypothesis.


Is that OK


So we wrote it in word now.


No, like you to add it from the like, I don't know how to describe it, but we like, we were people who are not tired or something, something. We were based on the population. That's how I write it


so


people who were not.


OK, well, tell, tell me how you want to write it.


or I can put it this way, the


the, the tired population.


has


um


mean


less than 82.


and 82 is the mean of the first population.


Is that, is that better


So I put it like people who are not tired are able to identify emotions correctly, then people, um, and then the more hypothesis would be that people who are extremely tired, will not be able to identify the emotions corre um correctly.


Yeah, you can, you can do that. It's saying the same thing. You're just using words to say the same thing.


Oh


because I've didn't write it the way you wrote it, so.


OK.


Like that would be, this is my first step


In the hypothesis testing.


Yes


I'll let you know, um, uh, once I write those two hypothesis, how I've written out.


OK


So I wrote for the research hypothesis, which is 8 of 1. I want people who are extremely tired, will not be able to identify emotions correctly. And then for the no hypothesis, I wrote people who are extremely tired, will be able to identify emotions correctly.


OK, yeah, sure. You can say it that way. That works.


And then step 2 is id is determining the characteristics of the um comparison distribution.


So that's, that's where we had to write all of our numbers down, right? Like the population mean


the standard deviation


Right


the, and the sampomine which is 78.


Where'd you see 38?


No, I said 78, sorry.


OK, yeah, 78 is the sample mean. 50 is the sample size.


Yeah


So we can write that. So the distribution, here's the distribution of group 2.


correct.


So I just write those numbers like the characteristics for it.


Mhm


That's nice


OK, I got them all down. This, the, the population mean is 82. The standard deviation is 20. The sample size is 50, and the same and the BM is 78.


The big M


Yeah, like the, it's called the samplemi.


OK.


the sample mean, OK, all right. Maybe one thing.


I began.


something you could calculate because we're gonna need it is this right now we only have the variants, which is 20.


Maybe we can calculate


the standard deviation.


Can you take


Oh, I thought that standard deviation was 20.


No, it says it's the variants. If you read the the problem.


Yeah.


Yeah


so to get the standard deviation, we have to take.


Oh, we are too. I know we are, I know what we have to do. We have to divide 2 by the square root of 50.


Uh, it wouldn't be 20, it would be, well, first of all, let's calculate the standard deviation first, which is square root of


and that is


for


First, let's go to figure out, um, figure out the critical value in step 3.


cause that comes in step 4.


oh OK


Step 3 is like you have to determine the cutoff score at which the no hypothesis should be rejected.


OK


All right


So to do that


point musically P um is less than 0.05. So,


I'm doing it


So this is a directional hypothesis, right? The research hypothesis is directional, right?


Yes, we, we set it up in a directional or also called one-sided test.


Yeah, one tilt test. So it would be um plus 1.64, right?


That's the critical value, right?


OK, let me check


Like positive 1.64.


right?


Cause it's 0.05, so


OK. 05.


Let's see. Is it uh


is it, uh, yeah, 0.05. I'm gonna get, I'm getting my calculator.


Oh, I just go with um


oh, I, we just go with 1.64.


OK. So, but it has to be negative.


Oh, OK.


I'm, I'm gonna show you on the board


I'm gonna draw the um


you have to draw the distribution at some point.


Yeah, yeah. I, I already drew it on. I'm on step 3 and I already drew it.


OK


I'm writing this stuff on paper.


And now we can go on to step 4. Are you ready?


Yes


So this is where we had to like calculate the disease score and stuff.


like the formula that we use stained glass, it was Z equals X minus the population need. Let me, let me go back to the.


It was, um, no, yeah, I think it was Z equals x minus the population mean divided by the standard deviation of the means.


OK, but we haven't calculated the standard deviation of the mean, yet we have started it, but we haven't finished.


Oh, we are in square root the 20 yet.


That's right. So the standard deviation of the population is 4.47, but the standard deviation of the sample meme


will be 4.47.


divided by the square root of 50.


That will be


our standard deviation to calculate the Z score.


Hm.


I'm doing that


OK.


4.44.47 divided by the square root of 50, right?


Right


See, I, I get stuck on this step, step 4 and step 2 because I don't really know like, because she said there was a difference on the in step 2 and step 4 of the hypothesis testing, then what we did in the intro chapter.


OK


Yeah, but I, I quite don't understand the difference here I like.


Do you see any difference like


Well, I'm not sure what your, your teacher said, uh, but everything you've, you've told me so far makes, makes perfect sense.


hm


So now


I got an answer of um 0.63.


OK, so let me calculate. So the


um


The standard DV um so the sta um, so the standard deviation of the means is 0.63.


right


OK. I'm gonna calculate. So this is called the


uh, this


the test statistics.


I don't know what happens, but in the exams, like I get nervous somehow and I get tricked up like I feel like it's trickier.


Mhm


because with if she allows corrections, but um it's not like


I don't know. I, I get stuck with this chapter for some reason, like I had problems understanding this chapters and understanding this chapter because we had to like learn it quickly, kind of.


Right


Yeah, she just, um, she just spent two days with it. We didn't even spend too much time, but the two problems solving questions were from this chapter, like it gave me the standard deviation and uh me or something in population, and then it


yeah, and with the, and then it gave me the significance level.


That's it


OK


And then um maybe the um, the big game, the sample me. I don't remember exactly what was on the exam, but it was tricky.


So tell me again what number did you get for the, uh, the Z score that for the test statistics.


What the standard deviation of the means?


No, you, you, you, you calculated the Z score, just, just a minute ago. You gave me the number.


There was 0.63 was the standard deviation of the needs, so.


OK, now we have to calculate the the Z score for the test statistics.


Sure


I calculated. I know. I, I know how to do it now. It's


and um the big game is also called the sample main is also like the eggs, right?


I'm asking you, is it the sampling is like a raw score?


No, uh, the, uh, we don't know the rascal. It's, it's similar to the Z score score, uh, but that's, that's what we're gonna be using. We're gonna be using it as a raw score and in our case it's 78.


Because in my formula, I wrote like X minus the population of the means divided by the standard deviation of the meter.


Yes, that's the general formula for the Z score. In our case, the X is similar to the 78. The mean is similar to the 82 and the standard deviation that we already calculated is it becomes our 0.63.


Mm


OK.


So in this case, our X would be 78, right?


Right.


OK. So


minutes 2.


divided by 0.63.


OK


It you


I got 6.35.


No, 6.35.


OK, that's fine


So that shows, that falls on the area of rejection, right?


Uh, very much so. We're, we're far, far to the left of the rejection area.


We would reject the no hypothesis.


It would reject the null hypothesis, and we would conclude that people who are tired are definitely they perform badly


compared to the people who are not tired


Oh yes


Yeah


I mean, I, I think I wanna do one more problem.


Because step 5 is just deciding whether to reject the no hypothesis because with hypothesis testing, um, all I understand is that we're always working to reject the Nohapais.


That's right


Well, reject or accept


um


or I would say reject or not reject. That's the way they say it.


Mm.


OK


Yeah, I would like to do one more problem, just to understand again, step 2 and step 4 of the hypothesis testing with the samples of the knee because like


I'm just


because um when I was doing the intro chapter, um, we had to use the same steps, but in step 2 and step 4, we had all the information we just had to compute this echo like um we were in chapter 4 in chapter 4, for instance, within divide the, um, we, we didn't like square root the variants.


to figure out um


the um


like


you know how we square rooted the train in this problem.


that we had to because the problem gave us the variance. The problem did not give us the standard deviation. It only gave us the variance, so we, we had to calculate the standard deviation of cells.


Yeah, but in chap


ter 4, it was all like all of the information was given to us, like,


I see


Yeah, this is step 2 and step 4 kind of more tricky for me, but I don't know.


I.


And the standard deviation, it's also called the standard error, right?


Um


I


which this chapter talks about, but we haven't like she didn't put anything about it on the test. I just studied it in case, like, we didn't talk about it in class, but I'm just asking you in general. It's also called the standard deviation, right?


OK, there's, there's a difference. If you have a population


and the population has a standard deviation.


then the standard error will be the standard deviation of the sample means. So to, to get, to get the standard error, you take the standard deviation and you divide by the square root of n. That is your standard error.


So in this problem, we figured out the standard error.


Yes, we calculated the standard error, which is 0.63 I think is what we got.


No, that was the standard deviation of the means.


Yes


I understand


That's, that's the standard error. We, if you look at our calculation, we started with the variants that was 20. If you take the square root of 20, that's 4.47. That is standard deviation.


Yes, I got, uh, I got that part.


of the population, but not the standard deviation of the meat. The 4.47 is the standard deviation of the population, then.


then we take that and we divide by the square root of n, that is the standard error of the sample meat.


Mm.


I put it as standard deviation of the means.


or you can call it that too. If you say standard deviation of the mean, the sample mean, that is.


Like I will, like what I wrote like SDM equals 0.0.63.


OK, yeah, you can write it like that.


OK. OK, I'm, I'm gonna put one more problem, just for more practice.


OK, we'll do one more problem.


Meal time, right?


Yeah, I have time. I just have to step away for 2 minutes and I'm coming right back, but you can put the problem on the board or type it for me.


Oh, State College professor or something, or are you just doing this for like


I'm just doing this to help students.


oh


Many people on Achieve are like that.


So I'll be back in 2 minutes.


Yes, sir. Go ahead


19. A researcher is interested in whether people are able to identify emotions
correctly when they are extremely tired. It is known that, using a particular method
of measurement, the accuracy ratings of people in the general population (who are
not extremely tired) are normally distributed with a mean of 82 and a variance of 20.
In the present study, however, the researcher arranges to test 50 people who had no
sleep the previous night. The mean accuracy for these 50 individuals was 78. Using
the .05 level, what should the researcher conclude? (a) Carry out a Z test using the
five steps of hypothesis testing. (b) Make a drawing of the distributions involved.
(c) Explain your answer to someone who knows about hypothesis testing with a
sample of a single individual but who knows nothing about hypothesis testing with
a sample of more than one individual. (d) 4: Figure the 95%
confidence interval and explain your answer to someone who is familiar with the
general logic of hypothesis testing, the normal curve, Z scores, probability, and the
idea of a distribution of means, but who has not heard of confidence intervals.


Mm


OK, I'm back


Yes, sir. I'm back to.


Can you read the problem


OK. Did you type the problem? Let's see. Where is it?


OK, there it is. Uh


All right


But that's, that's the same problem, isn't it?


Yeah


No, I said a psychologist is interested in the it's number 20. A psychologist is interested in the conditions after that affect the number of dreams per month that people report in which they are alone. We were doing a problem number 19 was about um.


OK, I see, I see problem 20 now. OK.


OK, I, I'm reading it.


All right. Arranges to test with.


yeah, the two populations first.


OK, so 50 people who had no sleep the previous night.


The mean accuracy


for these 50 individuals who were 78 using the 0.05 level.


No, no, no. This, uh, the problem that I have, let me post it again.


OK


Oh, it's the same problem. Never mind. Let me try it again. I'm trying to put a different problem and it comes up as the same thief.


Sorry


19. A researcher is interested in whether people are able to identify emotions
correctly when they are extremely tired. It is known that, using a particular method
of measurement, the accuracy ratings of people in the general population (who are
not extremely tired) are normally distributed with a mean of 82 and a variance of 20.
In the present study, however, the researcher arranges to test 50 people who had no
sleep the previous night. The mean accuracy for these 50 individuals was 78. Using
the .05 level, what should the researcher conclude? (a) Carry out a Z test using the
five steps of hypothesis testing. (b) Make a drawing of the distributions involved.
(c) Explain your answer to someone who knows about hypothesis testing with a
sample of a single individual but who knows nothing about hypothesis testing with
a sample of more than one individual. (d) Part D: Figure the 95%
confidence interval and explain your answer to someone who is familiar with the
general logic of hypothesis testing, the normal curve, Z scores, probability, and the
idea of a distribution of means, but who has not heard of confidence intervals.


Oh my God. No, do you want me to read the problem since it's not allowing me to pace the next problem?


You cannot paste it in, in the chat.


No, it's not like it, it keeps pasting number 19, the one we just did. It doesn't like change.


Oh, I'll make sure you maybe try copying Problem 21st. Make sure it's copied


and then try pasting one last time.


No, it's not working. It's still no problem number 19.


I see. OK, well, read, read the problem to me.


OK. The problem says a psychologist is interested in the conditions that affect the number of dreams per month that people report in which they are alone. We will assume that based on extensive previous research, it is known that in the general population, the number of such dreams per month follows a normal curve with a mu of equals to 5 and uh variance of 4.


The researcher wants to test the prediction that the number of such dreams will be greater among people who have recently experienced a traumatic event.


Thus this psychologist studies 36 individuals who have recently experienced a traumatic event, having them having them keep a record of their dreams for a month. The mean number of long dreams is 88. Should you conclude that people who have recently had a traumatic experience, have a significantly different number of drinks in which they are alone. And A is to


carry out a Z test using the 5 steps of hypothesis testing, use the um 0.05 level. Make sure and B is to make the um um draw the distribution and then see is explaining the answer to someone who had never had statistics, and then there's the 95% confident interval.


All right. Well, let's start with, with our, with our data. So the in the general population


Yes


So first I just figure out the two populations, like the population in general and um


population one is population in general.


general population.


and population 2 would be


Do you want me to read the problem again?


No, no. The second population would be the people who have


had a traumatic experience.


I have.


traumatic.


OK


And then I'm gonna state my research and the know hypothesis now. I first step.


Mm.


So people who have


so it will be like people who have traumatic experienced um to um people who have traumatic experience will have, will have, um, will affect the conditions of their dream when they are alone, then um then the population in general.


Well, it, it's more specific than that. The what the psychologist wants to research is if people who have had


a traumatic experience will have


more than 5 dreams.


per night.


because the general population has 5 dreams every night.


on average. So


the research hypothesis is will people have had a traumatic experience, have more than that.


So it will be like people who have traumatic experiences will have more dreams than people in general.


Correct


So it's still going to be a directional


a directional


Yeah. Yeah.


because I think that's what you said. It's going to be a directional test.


So I put like people who have traumatic experiences will have more more dreams will have


more dreams when alone, then people in general.


Right, exactly


I'm still on that one, OK?


OK


Are you at home


Mm.


Uh yes


me too


OK. I'm on step 2. So for the no hypothesis, I put people who have traumatic experiences will not have um


more dreams when they are alone, then people in general.


Right


And then step to figuring out the characteristics.


So, the meal is 5, the variances


wait, let me see.


It's 4.


and it's 36.


And um the um the sample mean is 8.


which is also known as X, right?


Yes, for our purposes, yes.


And then, so we had to figure out, so it would be again um 1.64, right?


Positive.


No, here it's gonna be positive because we want to know if the population with the group with traumatic experiences will have more


than


5. So the, the direction is the opposite of last time, so it's going to be + 1.64.


OK


Just the PY


I.


Mm


If it was non-directional, it would be um positive and negative 1.96, right?


Um


Uh, let me see


I'll let me check


OK.


Like if we were to do 2 tilt tests.


Yes, you're correct. It would be a plus or minus.


Yeah


Right.


And then step 4 is um like when we had to compute the Z score now. So first, I have to um square root the 4.


which is equals


to scrambled up.


is true. So, and then 2 divided by the square root of 36, which is the end.


Right


That's right


It's 0.33.


That's the standard deviation of the means, which is like also the standard error.


The standard error, that's correct.


OK


I call it the standard deviation of the means. SDM


OK, now we can compute the Z score. So it's um


8 minus


5 divided by 0.33.


I'm getting the Z score of 9.09.


So we will reject the no hypothesis then?


Definitely


Like it falls in the um in the share shared, shared region.


Yes, it, it falls very far


into the shaded regions, so definitely we reject the null hypothesis. In other words


uh


in other words, it, it's very reasonable that people who had a traumatic experience will have more dreams than the general population.


So it's very deep in the rejection region.


Yeah


Oh yeah, because the rejection region starts at z equal to 1.64. We're at 9.0 something.


OK. So we inject the hypothesis.


Cause I try to understand this chapter from my classmates, but they couldn't really explain it to me like they were kind of like one lady was kind of like um she was like, sometimes the questions you ask, they don't make sense. They're really like frustrating.


Oh, you mean, you mean somebody on Up Chief said that?


No, no, no, not here. Like somebody in my one of my classmates.


OK


or one of your classmates, OK.


Oh


Here is, I just started yesterday. I just knew about this yesterday from the um from someone.


Yeah. I just knew about this yesterday.


OK, well, I hope it makes sense for you today.


Yeah.


Would you like to do one more?


Uh, I think that's, that's all I'm gonna do for now. We've been at it now for


for an hour and a quarter already, but you know what you can do, you can make another request on Achieve and and other coach will help you.


Hm.


they have limited time like


like you have, that's all I can do. That's all you can do today with me, like you have a limited time or?


Well, uh, how long is your next problem? Is it a similar problem?


OK, we can do.


OK.


Oh no, we gotta figure out the confidence interval. And we got a, um, how do I explain to a person who has never had statistics, and we had to figure out the 95% confident interval. We're, we're not done yet.


So it, it's the same, this same problem, right?


Yeah, which I know how to do, but like I need help with explaining to someone who has never taken statistics.


Like I just explained all of my uh my steps.


You, I can, I can show you how to calculate a confidence interval if you like.


Oh


No, I know that. I know that, sir. I know how to do that. I'm asking you like a question where it says Part C, where it says explain your answer to a person who has never had a stats course.


OK


So is it to explain the answer where you did the hypothesis test, or is it to explain the, the answer you got for the confidence interval.


Uh


like explain in general, this is before um this is before the confident into like explain in general what I have done so far.


OK. All right.


So


So I'm gonna just say


like, I'm gonna just take all of my, um, the 5 steps of hypothesis.


yes


Mm


OK. That's all I have to do for the explanation part to someone who has never had statistic.


Um, you probably need to explain in more simple terms. Let me see how you would say that. Give me a, give me a minute or two to see how you would say that to someone who doesn't understand hypothesis testing.


Like they never take stats before, like someone who has never taken statistics before.


right? You would explain it this way.


You would say that


if


the people who had a traumatic experience had


the same number of dreams.


as the general population.


then you would expect


that the Z score that you calculated.


uh, would be


less than 1.64


95% of the time.


But because you got the Z score that is so much higher.


it's almost certain that the people with the traumatic experience have more dreams.


That's how you could explain it to someone who doesn't understand testing.


Mm. Can you write it down somewhere because you put it in the text chat box, but it keeps going up, so it's kind of hard to see.


OK, I'll try to write it, um.


so.


Yeah, if the people


I thought the checks, the chat box didn't let me scroll up or something.


Yes, you can scroll up and down the chat.


And then call um calculating the CI 4 95% it's just I had to put in the minus 1.64 and plus 1.64 times the um


times the 0.33 plus the um


hm


let's see, plus the 8, which is the sample.


Right


I can write it on the board if you like.


You can go ahead and do that, but I, I know the formula for that. It's the plus minus disease um the um the Z score on the distribute like the cut-up score on the distribution, um, times the standard deviation of the means, plus the sample mean, plus the N.


Right.


Let's see


So then, um, like going back to my, um, like the research hypothesis and no hypothesis, I would have said like people who have traumatic experiences will have the same number of dreams when they're alone, then then the population in general.


Uh, that's not the research hypothesis. That's the null hypothesis.


what you just said


No, in my research hypothesis, I say like people who are traumatic experiences will have more dreams when they are alone than people in general, and the no hypothesis is people who have traumatic experiences will not have more dreams when they're alone, than people in general.


OK, that's correct. That's correct. If that's what you said, then that's correct.


They said you want to do for today?


Uh, yes, well, that completes your, your, your problem


Mm


So I, I will stop here but uh feel free, you can make as many requests as you like, you know.


Because I, I haven't eaten lunch yet, it's, I'm about 2 hours late already.


Oh, so sorry.


Oh, no, no problem. I enjoy doing it.


I loved, uh, cause I love how he made it so simple for me to understand, like, now I understand, um, like the whole chapter like basically.


OK, that's awesome.


Yeah


and for the for um


and for the for number one again, like I forget to write down, uh, you said it, uh, it varies based on the same, it varies among the population based on the sample mean, right?


For number one,


Yes, so let me, let me answer that. Yeah, for number one


uh, the 7


The berries based on the sample meme. It varies, but among the population based on the sample mean.


right, you can say that yes


There is among the population.


based on the um


la


based on the sample


based on


Oh


I


Yeah, I haven't eaten lunch too yet.


OK, well, it's time for us to eat then.


Yeah. We expect


that disease for


and disease don't live here. I'm still writing something down.


But


uh


this is


Mm


OK, you can leave, sir. Thank you.


OK, you're welcome. Have a good day.


You too


Hello! I’d like to get some practice by solving the problems on this PDF. You might notice a bit of overwriting on it, but I still want to work through it. Here’s the link to the PDF: https://example.com/document.pdf


Starting with problem 2 of Obj. 14!


Hi Sarah! I can see it, Ill copy it over so we can look at it together.


Ok


I need help with solving it kinda


Yep #2


Sarah


ok so basically we want to factor out the same monomial out of the two parts


ok


oh find the gcf fo both?


yes


75/2 won't work


think of it in two parts


so the gcf will be


and -25


can you factor something out of y^2 - 25


almost


for the first part we can factor out y^2 that is right


there


yep that looks right


Ok now


the next one


so i distrbute


the 2t with that problem


and move everything to the left so you have 0 on the right


so combine everything


combine like terms?


yes


kk


i have t^2+13t-2=0


can you double check the t^2 term


oh its 5t^2


can you type out you're working out on the board


i'll be able to help better that way


can you start from where the question starts after you distibute and show me how you moved things over


k


Can u write bc i write big


and ill write how i solved it


sure ill write the expression after the distribution


can you show me what the expression looks like after adding t^2 from both sides


yeah so its t^2


is this correct


well since we have -t^2 on the right, we have to add t^2 to both sides to get 0


you subtracted t^2 which changes the equation


wait wiat


you said we combine


yes i missed saying a step, first we move balance out the equation by moving the terms to the left


ill walk you through it


ok


when we add t^2 to both sides do you see how that turns to 0 on the right side?


so we don't combine like terms?


we will once everything is on the left


after adding t^2 to both sides we get:


does that make sense? now we do it for 3t and -3


what should we add on the left to get rid of 03?


sorry -3?


ok i think i get it


so basically everything becomes positive


not necessairily, the goal of this step is to get 0 on the right so that you can solve it the way you usually do by factoring


if like terms are on both sides its just more confusing to solve


do you want me to show you the next step? that gets us closer to getting 0 on the right?


let me know where i can help


nvm I understand it


answer is t=-4/3,-1


now $4


yep nice job


oops sorry another look made me see that both t's should be positive, double check your signs


ill start looking at #4


kk


can you show me what your first step in doing problem #4 would be


yes


x= -7,4


to balance the equation and get 0 on the right we need to subtract 28 from both sides


yep you got it!


next one


honestly a lot of these problems are not from the notes that we've done w my teacher in class


so it feels like im re learning new material


that's ok im happy to help, sometime exampled don't translate that well but the same concepts apply


where do you get stuck with this one?


the 2Y2


remember how in the first one we had 2 parts and we collected the same factor from each part?


this is similar


mhm


ok


since -y = -2y Sarah we can replace it with that


sorry -3y +2y


do you agree its the same equation?


yes


ok now we have the two parts, what would you factor out of 2y^2 + 2y


nice, good job!


is there anything obvious you would factor out straight away?


woudl i combine it


can you show me what you mean?


nvm


did you notice that both 36 x^2 are both squares of certain numbers?


wait i get it


gcf is 4


great!


are you sure you need me here :P


actually


one sec


Ok so I want to show you the difference of the notes


of obj 14


which is way diff and i have a test coming up and she gave us this practice sheet today so idrk


can you copy it here


ok, so what i see is the objective is the same but in what you just shared there are certain things that don't appear, like perfect squares and how to deal with Sarah etc


exactly


i emailed my teacher about it ill wait for her response but last night i was working on the problems from the notes w a past coach


basically same format of the problem just w diff numbers


i left off at page 2 problem 9


so i want to work on thatinstead of ths


bc its just like i'm learnin new things


I see what you are concerned about


it can be overwhelming but from what im seeing you're doing quite well


For the test its two questions per objective usually they're easy so idk


you also use the concepts from the current share on what we did today


I think it was based off of the notes too


some more practice might help make you more confident


Khan Academy has free videos on how to deal with those and practice questions


those problems are harder i don'tt hink she'd put those on the test since she gives us smaller #s etc an ones from the notes


yes just practice until you feel comfortable and look out for small mistakes when taking the test


Do you still have time


to work on the notes isntead


sure i can stay 15 more minutes


ok i just need u to do diff numbers but same format etc for problem 8 page 2


ok let me take a look


kk


try this one


K


those numbers won't work


won't match when factoring


let me try it here


oh nvm


i used wrong #s


ok ill wait for you to try it again :)


perfect


i think you make mistakes with signs, make sure you watch out for that on the tesy


want another one?


yes #9


i said problem 9


problem 9 is diff than this


24x^2 -4x-4 right?


yes


its the same i just put one term to the right


i want you to make sure you get it right, whenever you move things to the right you have a tendency to mix up the sign


i want to*


to the left*


yep now similar to problem #4 you want to factor out the biggest constant


k


gcf is 6?


yep


yep with the 6 on the outside of the polynomial


the 6 can be cancelled out e.g. 6x=0 is the same as x=0


when its cancelled you have exactly what you wrote


kk


ok so now do the ac mthod


I'm sorry I have to leave now :')


It was really nice working with you. I'll hand you off to another coach. Hope you ace your test!


hello


hii


im doing corrections today


ok


i think is right


i js changed it rn


which part do you want me to check


which graph do you think goes along with #4?


C


Sorry, no


whattt


wait im loooking on the wromg paper


its B


#4 is not B either


ohhh


Alex


For one thing, at what value of x does the graph change for #4?


and x+2


I am asking at what value of x the function goes from using 3x-2 to using x +2 ?


ohhh 1


Right, but in C, the graph shifts at x =-1, right?


yes


and and B the graph shifts at x =0


so B and C cannot be rigth for #4


so it would only lwave us with E


leave


E is not the only possibility


d too


What would be the y intercetp for #4?


No. the y intercept occurs when x =0


ohh


so we get A


in #4, when x=0.which equation should you use the top or the bottom?


bc of the y intercept


too


top


right, and what is the y intercept for 3x-2?


Right, so we already narrowed it down to D and E


which one has a y intercept of -2?


i nean


A


noo


E


what is the y intercept on graph E?


nvm its d bc of -2


y intercept


Yes, it's D


Jamie i have to erase the back of this rq


what do you need for this?


all of it for 9 and 10


You should figure out some points for x <0,   0<x<2,  and x >2


do you know what I mean?


-1, 1,0?


Let's firs find f(x) at the two breakpoints.


wdym


the graphs change at x =0 and x =2


wait can u write it on the board


what is f(-1)?


yes, you use x+1 for x =-1, so what is f(-1)?


And what does that equal?


OK, plot that point


what


wait so will it he closed


be


the point will it be opened or closed


it's just a point, it's not a point where the graph dhanges


oh ok so closed


yes


go ahead and graph it.


I will upload a better graph.


Chris u


for x =0, because it is a point where it shifts we can use both the top and and middle equations.  One will be an open point and one a closed point.


if x =0, what does that equal using the top equation?


it would be -x+1


being 0,1


Using x + 1 that would be (0,1)


ohh


so this one will be opened?


using -x+1, that would also be 1


so we can use a closed circle


oh okau so 0 we use x+1?


You need to use both, so that you can see how far the top equation goes.


Now find f(1)), because 1 is between 0 and 2


hello?


closed


ok, plot that point


OK, now f(2))


Do you know what I mean when I write f(2)?


im confused


so are we on the same orobkem


uhh no


OK, you need to know what that notation means.


f(2)) is asking "what is the value of the function when you plug in 2 for x"


ohhh


so we write f(2) in the bix for X


and then do -(2)+1


I don't know what"bix" means


box


so then we get 2,-1


Yes.


that gets a closed circle, right?


Now we move onto graphing the bottom equation.


The bottom equation starts at x =2, but it doesn't include 2, so that point will get an open circle.


If we use x =2 in the bottom equation, what do we get?


ohh okay


im a lil confused rn


what we are doing is graphing three lines


the top line is y =x+1 but only is valid for x <0


the middle line is y=-x+1 but we only graph it between x =0 and x =2


ohh whats our other points


that were using?


are we still using 2 for x


or what


The middle line stops at x =2 and the bottom lime starts at x=2, so you need to figure out f(2) for both of them


using the middle equation f(2) = -1


that gives us the point (2,-1) and gets a close circle


wait Pat write it onmthe board


the bottom equation starts at x=2


i think im confusinh myself


using x =2 in the bottom equation gives us 2- 1 =1


ohh ok


so the bottom line starts at (2,1)


anf  its open


ookkk


but that gets an  open circle because it is x>2 for the bottom equation


what would f(4) equal?


4-1=3 so  4,3


can you plot that on the graph?


would it be open


or closed


The question of whether a dot is open or closed is only for vaues of x where the graph shifts


so closed


(4,3) is just a regular dot


all dots on a line are closed, except possibly at an endpoint.


Now you can just draw the line for x>2


so will it be a straight like theu it


But your line cannot go lower than x =2.  Your line starts at x =2


the lines cannot overlap


would we add arrow or no!


yes, that's it, and you could add an arrow because it goes on to infinity in both directions


like that?


yes. that's it/


okk


Look at the graph.  For values of x <0.we have graphed the line y =x+1


for valus of x between 0 and 2, we have graphed the line y=-x+1


and for values of x >2, we have graphed the line y=x-1


does that make sense now?


wait can u write it on the board


write what on the board?


wait


so we idk


im confused


The graph is on the board


are we still on 9?


I believe we are finished with it.  You have the graph for it.


ohh okk


so we on 10 now


for 10 they want you to tell them what mistake the person made


yes


can you see the error? think about that.


the second function is wrong


why do say that?


what is the second function?


so the graph should have a closed circle at x=-1 and a open cricle for the first and second part


the graph isnt showing


like the correct


points


You are right that the errors are with open and closed circles.


(-1,2) should be open


and (2,-2) should also be open


ok?


Hello?


yesss


mb i was writing it down


Do you think you get the basic idea of piecewise functions now?


yes but i have 4 more to do


i think im messing up w the grpahs


Sorry, but I need to go now. But you can post another request


have a good rest of the day.


You too


thank u sm for ur time


Hello


Hello!


Could I get some help with this question?


Jamie


Do you have an idea of what you should do first?


Multiply the 3 to the 6


That is sort of right.


what you are actually doing is multiply both sides by 3, right?


Yes sorry


Whenever you have denominators in your problem, you should think of multiplying both sides to "clear" the denominators.


What's next here?


That’s where I got stuck


what do they want you to solve for?


They want me to solve for b


right, so that means you would like to end up with b= on the left.


but there is something else on the left besides the b, right?


That so


That sounds right


what is on the left besides b?


any thoughts about how we could "get rid of" the 11a?


We subtract it on both sides?


yes!


give that a try.


Exellent!


Would that be my answer?


Let's check and see if that works. We will plug in 7a for b in the original equation


it works, so it must be the correct answer


Oh that makes so much more sense!


Thank you!


you are very welcome


Have a lovely day!


you too!