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Choosing between $z$-test and $t$-test Background: I'm giving a presentation to colleagues at work on hypothesis testing, and understand most of it fine but there's one aspect that I'm tying myself up in knots trying to understand as well as explain it to others.  This is what I think I know (please correct if wrong!)   Statistics that would be normal if variance was known, follow a $t$-distribution if the variance is unknown CLT (Central Limit Theorem): The sampling distribution of the sample mean is approximately normal for sufficiently large $n$ (could be $30$, could be up to $300$ for highly skewed distributions) The $t$-distribution can be considered Normal for degrees of freedom $&gt; 30$   You use the $z$-test if:   Population normal and variance known (for any sample size) Population normal, variance unknown and $n&gt;30$ (due to CLT) Population binomial, $np&gt;10$, $nq&gt;10$   You use the $t$-test if:   Population normal, variance unknown and $n&lt;30$ No knowledge about population or variance and $n&lt;30$, but sample data looks normal / passes tests etc so population can be assumed normal   So I'm left with:    For samples $&gt;30$ and $&lt;\approx 300$(?), no knowledge about population and variance known / unknown.   So my questions are:   At what sample size can you assume (where no knowledge about population distribution or variance) that the sampling distribution of the mean is normal (i.e. CLT has kicked in) when the sampling distribution looks non-normal? I know that some distributions need $n&gt;300$, but some resources seem to say use the $z$-test whenever $n&gt;30$... For the cases I'm unsure about, I presume I look at the data for normality. Now, if the sample data does looks normal do I use the $z$-test (since assume population normal, and since $n&gt;30$)? What about where the sample data for cases I'm uncertain about don't look normal? Are there any circumstances where you'd still use a $t$-test or $z$-test or do you always look to transform / use non-parametric tests? I know that, due to CLT, at some value of $n$ the sampling distribution of the mean will approximate to normal but the sample data won't tell me what that value of $n$ is; the sample data could be non-normal whilst the sample mean follows a normal / $t$.  Are there cases where you'd be transforming / using a non-parametric test when in fact the sampling distribution of the mean was normal / $t$ but you couldn't tell? List of feature engineering techniques Is there any resource with a list of feature engineering techniques? A mapping of type of data, model and feature engineering technique would be a gold mine. How to determine if .NET code is running in an ASP.NET process? I have an instance of a general purpose class that will be executed both under ASP.NET and a stand alone program. This code is sensative to the process where it is being run - that is, there are certin methods that should not called if running under ASP.NET. How do you determine if the code is executing in an ASP.NET process?  The solution I am currently using is answered below.    I wish someone would add a comment as to why this question has gotten downvoted and/or propose a better way to ask it! I can only assume at least some folks have looked at the question and said "what an idiot, ASP.NET code is .NET code". Story about a deadly alien creature on another planet that has some chemical in its body that makes it faster Does installing and using Wine open up your Linux platform to Windows viruses? Just wondering if installing Wine might open up a fairly solid Linux desktop to the world of Windows viruses.  Any confirmed reports about that?  Would you then install a Windows antivirus product under Wine? Printing reverse of any String without using any predefined function? Let $A\neq I$ be a $5\times5$ matrix with real entries such that the sum of the entries in each row of $A$ is $1$. Then the sum of all the entries in $A^3$ is  1)$\space 3$ $\qquad $2)$\space 15$ $\qquad$ 3)$\space 5$ $\qquad$ 4)$\space 125$  Solution:  The answer is $5$ if $A = I$, but for $A \neq I$,  I found that vectors $\begin{pmatrix} 1\\ 1\\ 1\\ 1\\ 1\\ \end{pmatrix}$ and  $\begin{pmatrix} -1\\ -1\\ -1\\ -1\\ -1\\ \end{pmatrix}$  are eigen vectors for the matrix $A$ corresponding to eigen value $1$. From here, I dont know how to proceed, please help me solve the question..and if there are mistakes in my argument, please tell me.. Give moderators the option to select a deletion reason when removing posts When should I use # and = in ASP.NET controls? Functions Which are non differentiable on a Given Set. One thing that made me curious while watching a football game on TV was the numbers that appear on the ground. For instance, there's a "1st &amp; 10" beside one team, but there was a "3rd &amp; 6" a few minutes prior (and I think it was beside the other team). What do these numbers mean? How to scale a tikzpicture including texts? It seems that the scale option scales only the length of lines, but not the size of texts. For instance, 1 and true and not scaled in the following code.  \begin{tikzpicture}[thick, scale=0.6] \draw [dashed] (1,12) -- (11,12); \node[above] at (4,11) {1}; \node[above] at (8,11) {true}; \end{tikzpicture}   Could anyone tell me how to scale everything together within a tikzpicture? Thank you very much!  PS: It is a picture in a presentation with Beamer. how can I show this question : function Let $f\colon\mathbb R\to\mathbb R$ defined by  $$f(x)=a_1\sin x+a_2\sin2x+a_3\sin3x+\cdots+a_n\sin nx,$$ for some values $a_1,a_2,a_3,\cdots,a_n\in\mathbb R.$ Prove that $$ |f(x)|\le|\sin x|\quad \forall x\in \mathbb{R}$$ implies: $$|a_1+2a_2+3a_3+\cdots+na_n|\le1$$ Retrieving Current Location and Zip using Geolocation Button Let $G$ be  a group and $H$ be a subgroup of $G$ of index $2$ .Then show that if $a,b\notin H$ then $ab\in H$.   $a,b\notin H\implies aH,bH\neq H\implies $ $aH=bH$  since $H$ has only two distinct left cosets in $G$.  $\implies a^{-1}b\in H$  How to show that $ab\in H$ from here? What is the integral of 0? How to use wc and piping to find how many files and directories are in a certain directory? How can I use word counter (wc) and piping to count how many files or directories are in the /usr/bin directory? Using different delimiters in sed commands and range addresses My phone was just stolen an hour or so ago. Are there any options for tracking? What role does "spontaneously symmetry breaking" played in the "Higgs Mechanism"? In talking about Higgs mechanism, the first part is always some introduction to the concept of spontaneously  symmetry breaking (SSB), some people saying that Higgs mechanism is the results of SSB of local gauge symmetry, some people says that we can formulate Higgs mechanism in a gauge invariant way, some people also says that we need only a non-zero vaccum expectation value... I am confused about this different or maybe same point of views.  In this post:  , the most highly voted answer, I still can't feel how SSB worked in Higgs mechanism. It seem that the validity of last part, the appearance of a mass term for $A$, is guaranteed if we have a non-zero equilibrium value $\phi_0$ to expand around. I do not see that the requirement that the phase of the field $\phi$ need to be fixed at some particular value to generate mass term. Thus it seems to me it is not true that SSB is really indispensable for Higgs mechanism.  To put it simply:  The spontanously breaking of what is attributed to Higgs mechanism?   local gauge symmetry global symmetry, since breaking of a "gauge symmetry" should not have any effect on physics. In higgs mechanism, the really broken symmetry is a global one. Mathematically, it is similar in looking as fixing a gauge, but one should not think it as a spontanously breakdown of local gauge symmetry. other.   Is SSB really indispensable for Higgs mechanism?    yes, Higgs mechanism is relied on the SSB of some symmetry (above question), the other approches of description eventually has spontanously broke some symmetry. No, the SSB is just one way to describe Higgs mechanism (or even not a complete way), what is really need is the non-zero vaccum expectation value, for example in the linked post the requirement for the mass term to occur is to have some non-zero expectation value of $\phi$ to expand around, we do not need the phase of the field to be fixed, thus the symmetry is not broken. Other.   some reference materials:    States that SSB of local gauge symmetry is impossible.  in the abstract states that:       gauge symmetries merely reflect a redundancy in the state description   and therefore the spontaneous breaking can not be an essential   ingredient. Indeed, as already shown by Higgs and Kibble, the   mechanism can be explained in terms of gauge invariant variables,   without invoking spontaneous symmetry breaking     In the introduction it says:      In particular, we emphasize that global U(1) phase rotation symmetry,   and not gauge symmetry, is spontaneously violated, and show that the   BCS wave function is, contrary to claims in the literature, fully   gauge invariant