Ina 5 x 3 x 2 fixed eflects (between groups) design experiment, with Dbsenvanons per cell, determine tne degrees Treeqom associaieg total number ol paricipants in t...

Fill in the ANOVA table. $$\begin{array}{lcccc} \text { Source of } & \text { Sum of } & \text { Degrees of } & \text { Mean } & \text { F-Test } \\ \text { Variation } & \text { Squares } & \text { Freedom } & \text { Squares } & \text { Statistic } \\ \hline \text { Treatment } & 2814 & 3 & & \\ \hline \text { Error } & 4915 & 36 & & \\ \hline \text { Total } & & & & \end{array}$$

Okay. So we know the general formulas are as follows. D mean squares. Yeah. Mhm. Mhm. For both error and treatment is simply the sum of squares comfortable. Mhm. Over the degrees of freedom. Mhm. Okay. Okay. Yeah. Okay. Okay. So this for both the air and treatment we also know the F test formula after statistic from a yeah there's simply T. M. S. T. Over the MSC for the treatment. So now using this these from this you can go ahead and fill at the table. So the mean squares For the treatment is 387 over to damn squares over the use of freedom. Which gives us 193.5. And the F test statistic will be 8,042 over 27. Which will give us to 97 .9. Enough DFC statistic you simply do 1935 Over to 97.9 To give us 0.650. And the total simply something of these two values respectively. To give us 8429 and 29.

So, as you can see here, we have three main sort of unit sells. Simple, cubic body centered and face centered for simple cubic systems. We have a total of eight Adams, seven one of each on each corner of the Cuban, then one at the centre. So if going, place them one, two, three, four thoughts five, six, seven, eight. So that's eight body center. It is a bit different. It's the same simple cubic. But this time you have a new Adam on the centre as well in the face off the center of the Cube. So again, that's Ryan. Write it so. One, two, three, four, five, six, seven, eight, nine. Let's live. Adams, finally, for face entered its the same thing, but instead you have an Adam on each corner and then anatomy on each face of the Cube. So this face this face this here below, to the side and back. It'LL be a total of fourteen. Arum's Let's try place them one, two, three, four, five, six, seven, eight, nine, ten You Evan, twelve thirteen. Then we have one left fourteen. So that's fourteen Adams. As for face center,

The pressure would want us to draw. It's, you know, say for simply will Big body sensei could be our fifth center. Could be a simple public. What? So you try it? I'm trying a cue. Hey. Okay, so you sit here for the simple kuh, Vic? Well, yeah, and that. So each of the corner as a horn here one year. Who for here? Yeah, from air half one here. Have or yeah, half. We're not done here. Yeah, well, not you. That's a simple Kubik. Have you seen these? Yeah. 12345123456 And we have eight in total. Let me draw body sense after a big what he sent. That could be It's seven. Lots of simple for big boys. Hey, need a difference? But me make it smaller. Yes, it came. So I have for that. So that's each of the corner. Like the simple Kubik. So 123456712345678 Then are the milieu of the bucks of the queue. We have another. That's let me use great corner for double the answer. My, we have a good actor making the accents that come. I can't draw something many things like a don't say a lot, but his center Yeah. So yeah, it's a sensor from here. Ah, is well Is this a battle? We are united Center. That's body said that Then the total war is the Spencer face inside. Could be. I'll try it, folks. Chums. Okay, so we are after that. Be at the age of the corner each of the corner where it Yeah, that's a That's a accidentally corner. Yeah, on the face off each side. We have one after. Let me his greatcoat. So this is one face. This is another face. Is this where we are? Yeah. Two. Three of anything. I want these face his face The Africa that feast We have his face. We have these Phase four empty his face. Fine. Then we have this face six faces. You have six cases. So that's h of this face, baby. These absence spaces at sitter This face is this one. Face this Well, we have one after. Yeah, like he's well at the same time off this week. So we have a warrant here for this face. Let me the first day off her face and they live into the war. Dark face we have. Oh, I don't know. Don't do this site we have here. Get three this scientifically for positive These we have war. Yeah, this site is side facing me. We have warm and it's signed away from me. We, uh I don't know. You will sit apart from the It's at some that we have right now. We are She's actually for this one. We are just eighth plus one atom at its center at its share. Back up, set up off the corner My foot Just simple. We're your teeth after each corner.

So in this problem letter A asks us to draw. The unit sells for these two different ah structures. And so the first one we have, Ah, black dots here, here, here and here. And then a white dot here and the unit cell is going to go like this. And then for number two, we have a very similar thing, except they're all black dots. And so again, the unit cell is going to go like this. And so for letter b thes air, both rombach lattices and for letter C, As you can see in the first one, we obviously have one white dot That's just ask how many dots are in each unit cell, and we also have one black dot and you may think that there's four black dots, but the unit cell goes from the center ah, out towards another center. And so, because of the shape of the unit cell, we're only getting one quarter of each of these black dots. So you take one quarter each of them and ad for those together and you get one total. And that's for number one. And for number two in a very similar way, we have to black dots. We have one in the center and then one quarter, two quarters, three quarters and won. So we have two black total, and that's our final answer.