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An ANOVA tabie is given. Find the missing value for the F-statistic. Round to the nearest whole number,Deoteer 0 sum 0 Mean Soutee freedem Sauatet squate statiate _...

Question

An ANOVA tabie is given. Find the missing value for the F-statistic. Round to the nearest whole number,Deoteer 0 sum 0 Mean Soutee freedem Sauatet squate statiate _Value Groups 22.0351 11.0181 0. 14188 Enor 67 0750 #7Toul894144

An ANOVA tabie is given. Find the missing value for the F-statistic. Round to the nearest whole number, Deoteer 0 sum 0 Mean Soutee freedem Sauatet squate statiate _Value Groups 22.0351 11.0181 0. 14188 Enor 67 0750 #7 Toul 894144



Answers

Fill in the ANOVA table. $$\begin{array}{lcccc} \text { Source of } & \text { Sum of } & \text { Degrees of } & \text { Mean } & \text { F-Test } \\ \text { Variation } & \text { Squares } & \text { Freedom } & \text { Squares } & \text { Statistic } \\ \hline \text { Treatment } & 387 & 2 & & \\ \hline \text { Error } & 8042 & 27 & & \\ \hline \text { Total } & & & & \end{array}$$

So, you know, the formula for main squares for both treatment and error Is simply mean squares is equal to the sum of squares over 80° of freedom. And similarly, we know the formula for the EFTA statistic isn't the Mst over the MSC. It's now using these formulas, we can start and filling out the values for this table. So for the treatment the main squares is simply going to be 2,814 over three. Just 9 38. And for the air it will be 4915. Okay, Over 36. Just 1 36.53. So 1 36.5 and 9 30 eight. Not for the after statistic, simply going to be 9 38. Over 1 36.53. Yeah. Which will give us 6.87. Yeah, I'm pretty total. Can simply sum up the Values respectively 7th 7 and 29 and 39.

So we are given in a nova table that has some missing pieces in it, and then we're going to solve for the values that are missing. So in our unova table, I'm gonna write out, okay, We are given our source degrees of freedom, Sum of squares, and then we have or Meena Squares over here. So our first source was a factor air and total. And we're giving the degrees of freedom of three. We are void in the middle here for the error, and then we have a total of 20. The sum of squares. We have 40 where the error is 40.4 and then we have a total of 1 64.2 and the mean of squares is blank. So we need to find all of those missing values. So there's four that we're going to go through and solved before. So the degrees of freedom, some of our sum of squares and the meaning of squares Okay, so we're gonna first look at the error degrees of freedom. So the rule here is the degrees of freedom for the error. I would simply be the degrees of freedom total minus the degrees of freedom factor. So good way to remember that is whatever you have up here for, the 1st 2 needs to equal the total, right, So you could do 20 minus three to get her answer of 17. So to double check yourself, you would just do 17 plus three. And if that equals 20 you're good to go. So we've already found the degrees of freedom by doing again. The 20 minus the three, which equals seven teams can write that off for your reference. Then we need to find the sum of squares. So the son of squares factor is going to be added to sum of squares error to get the sum of squares total kind of the same concept there. So we would actually have you could rework that to what we have. So it would be the sum of squares. Factor equals the total minus the error. Because again we have the total. We have the error. So you would do the 1 64 point Teoh minus of 40.4, and that's going to give you 1 23.8 So up here, 1 20 three 1 23.8 again to double check yourself. If 1 23.8 plus 40.4 equals 1 64.2 you're good to go. So then, finally, we need to find the mean sum of squares for both of factor and the air. So for the mean square we have the mean square of the factor equals the sum of squares factor over the degrees of freedom factor. So that's how we're gonna solve. So we go back up to the chart, We would see the 1 23.8 which we found divided by the three. And that's going to give you 41 point 266 so we can write that up there for the error, so it should Bay 41 41.266 So then we're gonna go back down here and do the same thing for the error now. So I m s or the mean of squares. Error equals the sum of squares air divided by degrees of freedom air. So pulling out those it would be that 40.4 divided by the 17. Would you give us 2.376 so we'll plug that back in up here needs need to be reversal. Bear with me while I reversed that. So we hade the factors should be up here. So we're screwing that up to the 41.266 And then what we just saw it for for the Erawan would be two point 376 Okay? And then to calculate for the second part here, we would need to find what f would be. So they're asking us f and then f so we would have the equation of I mean of squares factor over the means of squares. Hair defined r f. So that would be 41.266 divided by the 2.376 And that would give us 17.368 So that would be our f. Okay, So we were able to find all of those missing pieces in the missing values that we had for our table. And then we were also able to calculate for F based off of all those calculations making I think up here, we would just need to add for our mean of square. So will be the 41 point 266 plus 22.376 of your total would be 43.642 So that's us filling in everything we have there. Okay, But they were only asking us to find the four less. Here, here, here, here. So those are the four to fill out the, you know, the table that we solved for. And then we were also able to go find F based off of those and F A B 17.3.


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