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12.1.7Queslon [ tpDwlemine (a) the 1 tect statistc; (b) the degrees of treedom (c) the aitcal value using a = 0 05, and (d) test the mponesi a te a = 0 05 levcl of...

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12.1.7Queslon [ tpDwlemine (a) the 1 tect statistc; (b) the degrees of treedom (c) the aitcal value using a = 0 05, and (d) test the mponesi a te a = 0 05 levcl of signiEcanceOutcoma Obsenved ErpectedHo P = Pa =Pc =Fo = nkadt 0a 0l the propotbors k dirrcni from I7c cthcn(0) The lest setkL D (Wypean erdanawd |

12.1.7 Queslon [ tp Dwlemine (a) the 1 tect statistc; (b) the degrees of treedom (c) the aitcal value using a = 0 05, and (d) test the mponesi a te a = 0 05 levcl of signiEcance Outcoma Obsenved Erpected Ho P = Pa =Pc =Fo = nkadt 0a 0l the propotbors k dirrcni from I7c cthcn (0) The lest setkL D (Wypean erdanawd |



Answers

10.60 For the hypothesis test involving $H_{a}: \mu_{B}-\mu_{A} \neq 0$ with df $=18$ and $star *=1.3$ : a. Find the $p$ -value. b. Find the critical values given $\alpha=0.05$

In this problem, we have to stake whether the observed value would lead to rejection off the null hypothesis. H not at the given significant level. For the given pairs off P values and significance levels Alfa First, the value is given 0.84 and Significance level is given 0.5 0.8 for is larger than 0.5 that this P value is greater than the significance level. We know if the value is greater than Alfa, that is, if the value is greater than the significance level. We do not reject the null hypothesis that is. Don't reject h not so this observed. The value would not lead to rejection off. H not act a significant level 0.5 the next P value is given 0.84 and the significance level is given 0.10 0.4 It's less than 0.10 that this p value is less than the significant level. We know that if the value is less than or equal toe the significance level, be rejecting null hypothesis. It's not that is this observed. The value would lead to the rejection off the null hypothesis. It's not the next P value given this 0.3 and the significance level given this 0.1 0.3 is less than 0.1 That this P value is less than the significance level. So reject h not that is this observed. The value 0.3 would lead to the rejection. Often that hypothesis it's not. And the significant level 0.1 The next we were you given is 0.39 and the significance level is 0.1 0.39 is greater than 0.1 that this P value is greater than the significance level Alfa. So we do not rejecting the hypothesis. It's not. Don't reject. It's not that this this absurd p value 0.39 would not lead to the rejection off the null hypothesis. It's not at the significance level 0.1

All right. So we're gonna doing some comparison P values on some significant levels. This is exactly same as the last video exception you. Oh, he's so so to start off with a look at the people. You off. No point no. 18 on the's left its level off. No point no one do ourselves a little graph. I talked about the importance of graphs last video. So this is gonna be my you thought you had to sit still on then we note that not quite no one is greater and not put no one. So we want at all for to be a little bit smaller. Yeah. And so in this case, we're failed to reject because that's not value here. Isn't inside the range off. It's not in the range of values that we were considered significant. Hell to Jack. No, already K equals no point No. Three, and Alfa equals point No. Five ourselves. Coop. So this is my people. You, it's it's tough. And then we know that not put not 33 is less than no point no. Five. So we put that there also. And then because, uh, stars in the critical region. Property value is less than that sickens level. We reject a shot. Okay, for P equals no point North 78 While I'm doing this just well, I don't have anything else interesting to say. I did a big summary off. How about those tests on the normal distribution on what the value is? What the significance Veliz in my answer to question 8.95 And I'd really recommend that if you'll show me to understand why this is happening, why this works, etcetera. So let's put our P value there with that stuff on. We know that not point, not 78 is greater than no point No. Five. Then we put up ahead. It's smaller when we find that this isn't significant. And so we failed to reject H nuts. That's because, um, the property is grated in the significance level. On last but not least, we have P It's no point no 64 Alfa equals no 0.10 last. We'll curve print. So we put our people you here. I've stuck on my values on the left, inside of the graphs for today, just out of habit. Well, it doesn't matter where when they're on the left of the right because he's describing areas, no actual values. Which is why I'll write that start here Rob than Pete. Because piece of the area, although I know it's local using that I then right Alfa And here that's because Alfa is sort of used to describe Yes, it is a bit confusing. I understand that. But these are describing areas, not points along this axes, and that's really important in this town. Eso no point, not 64 is less than no 640.10 So no 10 goes up here. Why couldn't And so this is within the critical region. Well, it's not labeled. Yeah, as they were going to reject. And again I was gonna put back to the rules that are super helpful. Remember if piers lesson like a reject occasional on if he is great that I don't do that don't reject age Not? Yeah,

Everyone today we're gonna be looking at a set of P values and significant levels on deciding what decision will occur. So for this, I'm Indra grafter everyone, because during graphs, is so important. I used to really hate my teacher when he would tell me drug rattle the time because I was so bad at drawing them as I'm sure you're about to see. But actually, they're so helpful and visualizing your work can really help deepen your understanding off what's going on. So the first question we have a p value of no point, not 14 on a significant level of no point not to. So let's do our cut. So property is so this. The's always here are really areas. So poverty is is the area under the curve? So if we say okay, so we've got this probability here on is on. So that will be What's that called said? Wonder if hate, but right, so that's as its value. And then the poverty at all you is below that. And what we find here is that no point not to is is bigger than not point. Not one for and so the Alfa We'll be here just a bit bigger. I said that's a great accountability. That And so because this thistle here, the P value does that value is inside of the range of what we would consider rare enough to be noticeable. To be sufficient evidence, we're gonna reject patient. Okay, My questions. You just turn themselves off. No. Right. So second, what we have the P is no 0.118 on offer is not point no. Five. Just wanted during this. Just gonna talk a little bit. So you should never have a negative probability each have elected people. You should never have a negative Lipkins level because their areas, like I said, having a negatives that's the value. Absolutely fine does not matter. But having a negative area is really not. You know, it's kind of breaking maths a little bit, and so it's not great. So again, very soon, I think good drama people. You first. And then we find that no 0.118 is great then no 0.5. So this is offer, and this is always for hate chicken, That's that. So we find that. Okay, so that start isn't rare enough that we would consider it to be weird. So we failed to reject patient already two holes ago. So we have P is equal to no point, no for eight Alfa, is it too? No, point No. Five. And you find that? Um, no, but not by was a very common significance level and no, entirely sure why. But it's certainly one that came up a lot when I was able my times. And so we do record. Are you having a pretty good success rate with kids today? Quite pleased. That's true RPI value. And I'm sort alternating left and right here because it doesn't matter. It's an area we don't have any context is toe which side of the graph that should be on. So we have. It goes that star. And then we see up here that no point not for a is less than not. Point No. Five. And so, But it is just a little bit more this area here on and that's Alfa. And so, even though the poverty since that stars only just inside of the range for the scripted double, that mean it's significant and so we can reject be sure last but not least P equals no points, not 64 Al Foot equals no point. Once here, if you want a little bit of ah, stronger explanation as to what's going on in these questions and why this is important. I did a nice, long, so foundational explanation off what's going on in my answer to question 8.95 eso I drive already back then that I tried very hard to explain all the parts of why we do this and why it's important about P values to different levels. So, yeah, so let's put up the value on here. So this is eyes that stuff and that's no point No. Six on. We know that not put one is growth and not 10.64 So we put Al for here and we say, Well, that's significant. So let's reject not And so all of this is really just going to show the rule that we talked about last video and the video before, which says the when P is less than or equal to Alfa. We reject on one P. It's greater than Alfa. We did it


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