I learnt that a p-value lower than the alpha value of 0.05 leads us to reject the null hypothesis and vice versa. It seems to be the opposite for critical values. What then, is this critical value - how is it calculated and what does it signify?
I am unable to understand what exactly is critical value.My question here is why do we fail to reject a null hypothesis when the test statistic is within the range of critical value.  What i am trying to ask is what is the property of the critical value that makes the hypothesized value to fall within the range implied by the critical value.  Thanks in advance
What was Dumbledore's original wand made of? Some fields like Economics and Maths have their work in progress published as "working papers" with notes like "work in progress, do not cite or quote without the author's permission."Sometimes they upload these to their own websites or to their universities websites. I don't see much of this going on in my own field (sociology). I have heard from people that are afraid of having their work scooped or that fear that work published in this way will not be considered as "unpublished" by journals and conferences.  What are the advantages of making work in progress available in this way? Integrate $$\displaystyle \int_{0}^{\pi}{\frac{x\cos{x}}{1+\sin^{2}{x}}dx}$$ Suppose $f(x)$ is linear i.e. $f(x + y) = f(x) +f(y) $ and monotone on $[-\infty, +\infty]$, then $f(x) = ax$, a real.  We know $f(0)=0$, and if one assumes differentiability it is quite easy.      But how does monotone make up for differentiability? For an infinite line charge, $E$ falls off with $1/r$; for an infinite sheet of charge it's independent of r! The infinitesimal contributions to $E$ fall off with $1/r^2$, so why doesn't the total $E$ fall off the same way for the infinite line and sheet charges? During Order of the Phoenix, Voldemort tries his best to lure Harry to the Ministry so that Harry retrieves the prophecy for him. In the aftermath, while Harry follows Bellatrix towards the exit, he raises a valid question:  ”Why couldn’t he (Voldemort) come and get it (the prophecy) himself?”  This is a valid question, the prophecy is labeled as referring to the Dark Lord and maybe Harry Potter. Only those mentioned can retrieve the prophecy, so Voldemort should have been able to get it, assuming he is the Dark Lord of the prophecy. Bellatrix gives a good answer:  “Get it himself?” shrieked Bellatrix on a cackle of mad laughter. “The Dark Lord, walk into the Ministry of Magic, when they are so sweetly ignoring his return? The Dark Lord, reveal himself to the Aurors, when at the moment they are wasting their time on my dear cousin?”  Despite the cackle of mad laughter, the reasoning is sound, Voldemort didn't want to reveal himself. Yet he does exactly that when he appears in the Ministry and is seen by the Minister himself, and he exposes himself for no gain. Bellatrix may or may not have been able to escape without his help, but he couldn't know that before he came, and his other followers that were captured were freed again a few months later, so it wouldn't have mattered much, he would have freed her, too. So why did he go to the Ministry and reveal himself? Invert Color Ramp in QGIS How to 'sum' a standard deviation? I have a monthly average for a value and a standard deviation corresponding to that average. I am now computing the annual average as the sum of monthly averages, how can I represent the standard deviation for the summed average ?  For example considering output from a wind farm:  Month        MWh     StdDev January      927     333  February     1234    250 March        1032    301 April        876     204 May          865     165 June         750     263 July         780     280 August       690     98 September    730     76 October      821     240 November     803     178 December     850     250   We can say that in the average year the wind farm produces 10,358 MWh, but what is the standard deviation corresponding to this figure ? Unable to mount NTFS external hard drive How to create an OD road distance matrix in QGIS? I'm looking for the steps required to produce an origin-destination (OD) cost matrix.  What I'm looking for is a matrix of road distances. The distance matrix tool only produces euclidian distances. The QGIS Roadgraph plugin produces the shortest road distance from one origin to N destinations. What I need is a file containing distances from all origins to the N closest destinations. I have a lot of origins so repeating the analyses with Roadgraph is not an option. Thanks again.  I'm looking for a step-by-step description, starting from scratch (ie, with my 3 shapefiles: origins, destinations, road network). virtual methods I am learning P&amp;S's Introduction of quantum field theory. My teacher said that if the mass of neutrino is exactly 0, then we should not observe any right-handed neutrinos and left-handed anti-neutrinos according to Weyl's theory. It is because $$ \left( i\gamma^\mu \partial_\mu - m \right) \psi = \left( \begin{array}{cc} -m &amp;  i\left(\partial_0 + \vec\sigma \cdot \vec\nabla\right) \\ i\left(\partial_0 - \vec\sigma \cdot \vec\nabla\right) &amp; -m \end{array} \right) \left( \begin{array}{c} \psi_L \\ \psi_R \end{array} \right) =0. $$  If we set m=0, then we will have:  \begin{align} i\left(\partial_0 - \vec\sigma \cdot \vec\nabla\right) \psi_L &amp;= 0; \\ i\left(\partial_0 + \vec\sigma \cdot \vec\nabla\right) \psi_R &amp;= 0. \end{align}  And if these formulas can describe neutrinos we must conclude that there are two types of neutrinos.  My confusions are:   It is known that the mass of neutrino is not 0, therefore there are chances (depending on the mass) to find right-handed neutrinos and left-handed anti-neutrinos. But we don't. If I accept that there are only these two types of neutrinos (right-handed anti-neutrinos and left-handed neutrinos), this property of neutrino causes the parity violation, so parity violation must relate to angular momentum and therefore spinor space. Am I write? Are there any reasons why neutrino is so weird that is has mass but still has helicity + Or - 1. This goes against with what I have learned that only when a particle  moves at the speed of light can its spin aligned with its momentum. Preface:  An axis plotted with  is usually using the current math font for its ticklabels. But if they are overwritten by e.g. xticklabels={-8,-6,...,8} then the current text font is used. Also an axis label ylabel={Y} would be in text font unless put explicitly in math mode ylabel={$Y$}. However it would be nice, if  one hadn't to do so.   Question:  I'm aiming to ensure that pgfplots always uses the current math font. But please assume that the classic font commands like \rmfamily are screwed up by the corporate design I'm supposed to use, e.g. assume: \renewcommand{\rmdefault}{\sfdefault}  It works if I explicitly define a font  \newcommand{\pgfmathfont}{\fontfamily{pxfonts}\selectfont}   and pass it to pgfplots together with assume math mode=true:  \begin{axis}[ font = \pgfmathfont,  tick label style={/pgf/number format/assume math mode=true} ]   But it requires that I insert the name of the current math font. How can I do that automatically? How to get the currently used math font to insert it into the macro?    MWE  \documentclass{beamer}  \usetheme{Warsaw} \usefonttheme{professionalfonts} \usepackage{pxfonts} \usepackage{pgfplots}  % screwed up by Corporate Design \renewcommand{\rmdefault}{\sfdefault}  % I'd like this line to be generic! \newcommand{\pgfmathfont}{\fontfamily{pxfonts}\selectfont} %           put current math font here   X  \begin{document}  \begin{frame}  This is a basic equation:    \[ x + y = 42\]  \begin{tikzpicture}     \begin{axis}[ %   font = \rmfamily, % makes no sense here     font = \pgfmathfont,      xlabel={$x$-label: I want to be in math font!},     ylabel={Y},     xtick={-4,-3,...,4},     xticklabels={-8,-6,...,8}, %   xticklabels={$-8$,$-6$,...,$8$}, % does not work     tick label style={/pgf/number format/assume math mode=true}     ]      \addplot {x^2};      \end{axis} \end{tikzpicture}  \end{frame}  \end{document}     Everything related to  is no option at all!  Thank you! I have modeled a simple pocket watch in Blender. Every time I import it into Unity3D, regardless of whether I export it from Blender as an FBX or 3ds file, it always comes out missing faces! Why is this happening? I have never had problems importing models into Unity3D like this before.  Blender Screenshot    Unity Screenshots     It seems to me that different faces appear when I rotate it differently. How can I prevent this? Thanks! Replace a string in a text file using a shell script not working properly I have a text file containing this:  0 0 -1 0 1 0 0 0 0 -1 0 0 1.5 0.0 1.0 1   and I want to replace the 1.0 to 2.0 so that it becomes:  0 0 -1 0 1 0 0 0 0 -1 0 0 1.5 0.0 2.0 1   so I use this command:  sed -i 's/'1.0'/'2.0'/g' /home/user1/file1.txt   or this:  sed -i 's/1.0/2.0/g' /home/user1/file1.txt   but this is the result that appears and I don't know how to fix this:  0 0 -2.0 2.0 0 0 0 -2.0 0 1.5 0.0 2.0 1 How to extend the background of an image? $X/{\sim}$ is Hausdorff if and only if $\sim$ is closed in $X \times X$ Careers ads break the Android app Clicking any Careers (or Jobs) ad in the Android app feed results in an instant crash for the Android App version 1.0.89. What happens to a Devil when its alignment is forcibly changed? According to PHB 122, in the section entitled Alignment in the Multiverse, for most creatures, "alignment is a moral choice." Myth says good-aligned gods created the races that are free to choose to be evil (they have free will), while evil-aligned gods created the races that are very inclined towards evil, since they were born to serve the evil god in the first place.  However, there are some types of creatures -- like devils -- which embody an alignment in its essence:     Alignment in the Multiverse, PHB 122      A devil does not choose to be lawful evil, and it doesn't tend toward lawful evil, but rather it is lawful evil in its essence. If it somehow ceased to be lawful evil, it would cease to be a devil.   My first thought was to not take this reading literally. The text could have meant that a neutral evil devil "isn't really a devil," but really, it's still a devil. It's a bit like imagining a guitarist who loses both hands. The loss of some part of a person's essence makes them not the same person anymore.  However, keeping my attention on it, I'm finding this text more and more difficult to interpret. If a devil "is lawful evil in its essence" then what does it mean when "it would cease to be a devil"? What happens to a devil when its alignment is forcibly changed?  There are , and a devil can be subject to some of them. How to change Status Bar text color in iOS