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10.2.5 The following data are recorded in Statistical Methods for Research Workers by R A_ Fisher (Hafner Press, New York; 1922), and show the classifications of 38...

Question

10.2.5 The following data are recorded in Statistical Methods for Research Workers by R A_ Fisher (Hafner Press, New York; 1922), and show the classifications of 3883 Scottish children by gender (X) and hair color (Y)_= fair 592 544= red 119 97= medium 849 677= dark 504 451= jet black 36 14X =m X =fIs there any evidence for a relationship between hair color and gender? (b) Plot the appropriate bar chart(s) (c) Record the residuals and relate these to the results in parts and (b). What do you con

10.2.5 The following data are recorded in Statistical Methods for Research Workers by R A_ Fisher (Hafner Press, New York; 1922), and show the classifications of 3883 Scottish children by gender (X) and hair color (Y)_ = fair 592 544 = red 119 97 = medium 849 677 = dark 504 451 = jet black 36 14 X =m X =f Is there any evidence for a relationship between hair color and gender? (b) Plot the appropriate bar chart(s) (c) Record the residuals and relate these to the results in parts and (b). What do you conclude about the size of any deviation from independence?



Answers

Explore provide two data sets from "Graphs in Statistical Analysis," by $F .$ J. Anscombe, the American Statistician, Vol. $27 .$ For each exercise,a. Construct a scatterplot. b. Find the value of the linear correlation coefficient $r$, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. c. Identify the feature of the data that would be missed if part (b) was completed without constructing the scatterplot.$$\begin{array}{l|c|c|c|c|c|c|c|c|c|c|c}\hline x & 10 & 8 & 13 & 9 & 11 & 14 & 6 & 4 & 12 & 7 & 5 \\\hline y & 9.14 & 8.14 & 8.74 & 8.77 & 9.26 & 8.10 & 6.13 & 3.10 & 9.13 & 7.26 & 4.74 \\\hline\end{array}$$

Another to solve the nutrition, we have been assumed that small piece. It was too small to be. Not. We have The value are cute too. Is it was two X 1- and everyone Square and be one Plus X 2- and squired by Np Doom. And it was a bren Petri. We have a value as speaker physical stood. We need you excellent. Next to the extreme. Now since Cuban equals two empty square next week was to do and be and 21 minus speed, we get the value. That's too and this one less extra divided by two and two X one plus X two. Bless X three. Thank you. Hope you read it.

In problem that nine. We're going to be comparing a passenger ideal age in years with that given age group. And so this data shows six age groups and, ah, different ideal age. Is that they specifying And we're going to do a side by side box, but showing the six groups. So to do that, we have to select the deter the six age groups. And then you sat the box blood from thes battle. And as you can see here for the difference categories, the as you move from category two category, the ideal age increases. So that is what they display suggests that the display suggest that as you increase as you move from one category to the other, the age the ideal is increases. So this is the smallest for 18 to 24 the largest is for 65 plus. Now they're going to use this side, and then we're going to perform on analysis of variance to test the clean that they deal. Age is not the same for all age groups and they get to use offer. It's zero point 05 Okay, So to perform the analysis of brands, we go to data tub and data analysis and then select the and now another single factor. Then why deter? You have to select the palace, then make sure it's group by columns on the liberals in the fast room and I'll phase European 05 Ben with me. Make sure that we have output close to our deter. See, So then you press OK. And here the results for the analysis of lions. So we need to look at what decision has to be made based on these values. And we focused on the P value. So the P value is 1.5 substantially, probably getting 12 while there level of significance asked by 0.5 So this tells us that the P value is smaller than the level of significant Alfa, and in that case, we reject the night. But this is of and we are we because we can conclude that from the given sample, the mean ideal age is not the same for all age groups. So there are some differences from it group to a group when it comes to the ideal age. Then in part c of the question, we're going to be looking at what can cook conclusions we can draw from the results. Here. You find that when you're young, you tend tohave a smaller ideal age. And when you old, you have a large idea. So as you grow older, your ideal age seems to be also increasing. Then, in part d of the question, we're going to explain how this box plots drone demonstrate the results pond in Part B, where we tested the analysis of violence, using the analyst with various technique. So we see that ideal ages. The difference from age group is group things that means do not line up horizontally. Uh, if this means, or if this box puts oh well, it within one horizontal line, then would say that the ideal age I would not be affected by the each group.

To solve this equation, we have to We have been given, Yeah, I could not Friedman suitable David Right now, the total of the frequencies dr you don't know sequences Is Double 2, 3, 6 1. No, we have to draw Not far. Which is called according to the handyman. Which is this. It is this is one. You're not playing time. This is for 19 1995. There's just one light. This is for the community Mr01, 3 and 25 9 million. And this is for not donna European two or 3 months. Thank you.

Here we have a data set featuring a series of X Y coordinates. We are going to use what we know about regression and hypothesis, testing and correlation to determine whether or not there is in fact, a linear correlation here and whether or not that correlation is significant so you can see up top the table that we have that we're working with. You can go ahead and insert that into a graphing calculator. Doing that, you would get a scatter plot that looks something like this so you can see that it's actually not on linear. And if you also within your graphing calculator, go ahead and do your linear regression T test, you'll find that you have that. We have a correlation of coefficient, which is our equal to 0.81 0.816 So that might lead us to believe that there's actually a strong linear correlation here. But given the scatter plot that we have, we see that it's not, in fact, linear at all. So for part C here, where it's asking what would have been missed if we had not first graft a scatter plot, it would have been missed that are coefficient of correlation is actually in in an air. We shouldn't be using that to determine the relationship between our X Y data here. We should actually instead probably be using R squared, which is the coefficient of determination. And looking at your test results on your graphing calculator, you'll see that we have in our square 0.667 which is much less than our coefficient of correlation. Um, so in the case where we don't graph at first, we may miss this entirely and erroneously conclude that we have strong correlation within our data.


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