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The dala show Ihc bu) chps peI minule dtlerent femperalulesFind Ihc regresston aquahon_ letling Ihe first variablu bc nuecnd lemparuluiu IC HlD wnen ctprw al the ta...

Question

The dala show Ihc bu) chps peI minule dtlerent femperalulesFind Ihc regresston aquahon_ letling Ihe first variablu bc nuecnd lemparuluiu IC HlD wnen ctprw al the taie 890 chirps pCr minute snnitcance Chupsin Lmin 1025 1129 Vcnparate (") 92 8 Uemeldhnn Viotna culicunl vuluur oltho Pearson correlation cootlic IM (independent (x) anlable Find Ihe bestYal i$ dia tovrossion eqlalion? #D: (Roun Holnt cugmn plmcu Whal r Iho bost prodicIou vollo?IMMARARI#FD (Round I0 onu dcink plucuaatt

The dala show Ihc bu) chps peI minule dtlerent femperalulesFind Ihc regresston aquahon_ letling Ihe first variablu bc nuecnd lemparuluiu IC HlD wnen ctprw al the taie 890 chirps pCr minute snnitcance Chupsin Lmin 1025 1129 Vcnparate (") 92 8 Uemeldhnn Viotna culicunl vuluur oltho Pearson correlation cootlic IM ( independent (x) anlable Find Ihe best Yal i$ dia tovrossion eqlalion? #D: (Roun Holnt cugmn plmcu Whal r Iho bost prodicIou vollo? IMMARARI #FD (Round I0 onu dcink plucu aatt



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Repeat Exercises $10.141-10.146$ of Section IO.5. There, you applied the paired t-test to solve each problem. Now solve each problem by applying the paired Wilcoxon signed-rank test. Sleep. In $1908,$ W. S. Gosset published "The Probable Error of a Mean" (Biometrika, Vol. $6,$ pp. $1-25$ ). In this pioneceing paper, published under the pseudonym "Student," he introduced what later became known as Student's $t$ -distribution. Gosset used the following data set, which gives the additional sleep in hours obtained by 10 patients who used laevohysocyamine hydrobromide. $$\begin{array}{ccccc} \hline 1.9 & 0.8 & 1.1 & 0.1 & -0.1 \\ 4.4 & 5.5 & 1.6 & 4.6 & 3.4 \\ \hline \end{array}$$ a. At the $5 \%$ significance level, do the data provide sufficient evidence to conclude that laevohysocyamine hydrobromide is effective in increasing sleep? b. Repeat part (a) at the $1 \%$ significance level.

Looking at a data set giving those values for altitude and the speed of sound. We want to create a scatter plot which I've done in Excel 1st. And the scatter plot looks something similar to this. It appears to be very linear for these first few points. And then we plateau at the end here with the same values. So we want to now know what this correlation coefficient is and we can calculate that in Excel if you're doing it in the same way I am with the function where equals C O R R E L. And then in parentheses we have our X values and are Y values. And what this yields for us is a correlation coefficient equal to -09722. Because that's very close to negative one. We can say that we have a very strong negative linear correlation within the status set. So interpreting this, I think it helps to draw trend line in here and it looks something similar to that if we take into account these plateau at the end, so interpreting that what we see is that as these X values are increasing, so as altitude increases the speed of sound is tending to decrease. So interpreting this, we say exactly what I just did. We see that as altitude increases there appears to be a tendency for the speed of sound to decrease. Now I should stress here that this does not imply any bit of causality. Correlation is just an explanation of a relationship and the direction. So the strength and direction of relationship between two sets of variables. So we're seeing just this tendency for the speed of sound to decrease as altitude increases.

Here we're going to continue working with correlation. Were given some data on the maximum weight somebody can squat in one repetition and the amount of time it takes a professional soccer player to sprint 10 m. I believe we'd like to do first, in part is create a scatter plot. So I've just imported this data into Excel, created a scatter plot there and it looks something like this. All right. And then if we were to draw a trend line through this, which I typically like to do because I think it gives a better idea of the direction in which the dad is moving. So it looks something like that. Then we go ahead and we can calculate this correlation coefficient and Excel in Excel, it's calculated with a function equal to c o r r e l multiplied or for inside parentheses. Then we have that value of our exes. And then the Y values as well. That gives us a correlation coefficient which is equal to negative 0.9766. So that's pretty close to negative one, which is telling us that we have a pretty near perfect or you could say very strong as well if you'd like a near perfect negative linear correlation within this data set and interpreting this. What we see is that as our X values are increasing. So as those maximum weights are increasing, we're starting to see our Y values decrease. Which is that amount of time it takes to sprint. So we can say here that as our maximum weight, I'm just going to um w increases there's a tendency for that time it takes to sprint. That distance is going to decrease. I should stress too that this is just a tendency between these. There's no actual causation implied with correlation. It's just telling us that the time it takes to sprint tends to be lower when the maximum weight squatted increases.

In problem five, We have assembled data between brain volume on the I Q scores. We have 123 45 We have five sample data. We will make the scatter blood. Then we will make a conclusion about another coalition we can constructed here the X variable, which is the first variable brain volume in Centimeter Cube and the I variable. The ICO scores on a test. No units. We will construct. We will start by the brain volume. The brain volume minimum value off assemble, assemble data is 10 thousands and 29 then and the maximum is 10 thousands. 1000 and 40 1347 which means we can start by 1000. Here the X axis And in the boy, for example, 1350 we go a step off 50. If we have here 1000. This means we have here to thousands. Sorry. Meet no 10,000. Of course. 100 then. And we have here, for example. And here and we have in middle a small step off 50 And in the y axis we have the minimum value is 93 on the maximum is 113. Then we can start the Y axis by 19 and going a step off. Five. 95 then? Yeah. 100. 105. And we have here. But on the and 10. 115. This is our graph. Then we can construct the bear points. The first is 100 1000, 173. 1, 173 is something like here. And we have one on one as a school. Something back here. This is the first point. Second point is that 67 67 is something like here and 23. And the three is something like here. Then 347. Something like here and 94. You just here 29. We have 29 here, for example. And 97 seven is something like here. Finally, the fifth point is at 204 here on 113. 113 is here on the authority. This is the points. This is the scatter plot of the points. We can see that there is no religion between the brain volume on Dick. We can express it by a line that best fits all the points. You can see that there is here a point that is for from the four points. And if we want to construct a line like this, we'll get this point as for enough and so on. Then there is no correlation or every year, no correlation or Rainier correlation between the two variables, and this is the final answer off our problem.

We want to construct a confidence interval about the population, mean you for a sample, the sample mean expire equals 4.76 sample size and equals 20 sample standard deviation S equals 2.297 And confidence level 90%. To start off with, let's identify the T score needed to compute this interval to find this T score, we need to know the degree of freedom 19 And the confidence level .9. We can use a tea table which maps for these two variables the direct T score needed in this case T C equals 1.7 to 9. Next let's calculate the margin of error. E. Given by the formula. The left equals two times as of a root and plugging in these three variables for this problem we obtain equals 1.25. Finally we can compute the margin of error or rather the confidence interval from that margin of error using X bar minus is less than you. Is that the next plus? E plugging in? Our expert in R. E Gives 3.51 is less than meal is less than 6.01. Finally, we can interpret this to mean that we can say with 90 confidence that the mean is between 35.1 3.51 and 6.01. Yeah.


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