whether use t test or z test My null hypothesis are there is no difference between number of farmers insured and district wise performance of crop insurance during 2018-19 my question is that i have a secondary data on number of farmers insured (Population) in 2018 and 2019 which test i will apply to test the hypothesis whether t test or z test. I know the standard deviation and variance of population and size of population is greater than 30
t-test or z-test: assume normality or s≈σ? Let's say I have a large sample ($n&gt;30$) with mean $\bar{X}$ and standard deviation $S$. I can calculate only: $T=\frac{\bar{X}-\mu}{S/\sqrt{n}}$.  If I want to use t-test for a hypothesis, then I have to assume normality of the population. If I want to use z-test for a hypothesis, then I have to assume that $\boldsymbol{s\approx\sigma}$.  What is the less important assumption? What test should I do? Should I do t-test, z-test or doesn't matter?
Find the number of dissimilar terms in the expansion of $$\bigg(x+\frac{1}{x}+x^2+\frac{1}{x^2} \bigg)^{20}$$  Could someone give me some hint to proceed in this question. I used $x+1/x=t$ and wrote expansion as $(t^2+t-2)^{20}$ but even this does not convey much information. Please help. Shortest distance between $2$ lines with direction vectors Let L1 be the line passing through the point $P_1=(−11, 10, −1)$ with direction vector $\vec d_1=\begin{bmatrix}−2\\ 3\\ −1\end{bmatrix}t$, and let $L_2$ be the line passing through the point $P_2=(−8, 9, 10)$ with direction vector $\vec d_2=\begin{bmatrix}−1\\ 3\\1\end{bmatrix}t$. Find the shortest distance, $d$, between these two lines, and find a point $Q_1$ on $L_1$ and a point $Q_2$ on $L_2$ so that $d(Q_1,Q_2) = d$.   I dont really understand how to properly approach this question, how do i start? Determine if Term has Grandparent/Great-Grandparent Can you triple-boot safely? Hyperref - Token not allowed Possible Duplicate:          The following code:  \subsection{The classes $\mathcal{L}(\gamma)$}   generates the errors:  Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref)                removing `math shift' on input line 1938.   Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref)                removing `\gamma' on input line 1938.   Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref)                removing `math shift' on input line 1938.   What do I have to do to keep \gamma in the subsection, so that it is also listed in the table of contents? How to suppress Terminated message after killing in bash? What is the best way to remove accents (normalize) in a Python unicode string? why is the output of the following code coming to be zero? Evaluating $\int \frac{1}{{x^4+1}} dx$ I am trying to evaluate the integral  $$\int \frac{1}{1+x^4} \mathrm dx.$$  The integrand $\frac{1}{1+x^4}$ is a rational function (quotient of two polynomials), so I could solve the integral if I can find the partial fraction of $\frac{1}{1+x^4}$. But I failed to factorize $1+x^4$.   Any other methods are also wellcome. I've heard that you need to get a Mac if you want to develop iPhone apps. Is this true?   Is it possible to develop iPhone apps using Linux? If yes, what do I need and where do I download the necessary tools? I need to round the edges of this object.  The bottom edges are going to be rounded in conjunction with another object, so, I guess, this should be left out right now.  I tried using the bevel tool (and a bevel modifier) on an edge (series of Blender edges), but I got the problems you see on the images. When selecting all edges, the bevel doesn't know any limit and isn't applied symmetrically.  When selecting only the edges shown (or only the other ones), I can't proceed with the rest of the bevel, and strange little artifacts appear.  FYI: The top surface is derived from an icosphere.    Without the subdivision shown above, a stair comes into existence (bad):    Whole object: How to draw a return arrow from node-3 to node-1 Does time pass fastest in isolated, resting space? While it is fairly established that both fast movement and the presence of gravity make time pass slower as compared to a system at rest / free of gravity, does that mean that there is no way for time to pass faster than in vacuum, or does general relativity also have "faster" metrics?  To be more precise, is there any frame into which one could go for a while, and on returning to vacuum less time would have passed there? How do you do a deep copy of an object in .NET? I want a true deep copy. In Java, this was easy, but how do you do it in C#? Moment of inertia: why $\mathrm{dI}=r^2\mathrm{dm}$ instead of $\mathrm{dI}=m\mathrm{dr^2}$? Why are there $|G/G'|$ 1-dimensional representations of $G$? Let $G'$ be the derived subgroup of a finite group $G$.   We have a correspondence $\{\mathrm{reps \ of \ G/G'}\} \longleftrightarrow \{\mathrm{reps \ of \ G \ with \ kernel \ containing \ G' }\} $  If we restrict to 1-dimensional reps, we get:  $\{\mathrm{1\ dimensional \ reps \ of \ G/G'}\} \longleftrightarrow \{\mathrm{1 \ dimensional \ reps \ of \ G \ with \ kernel \ containing \ G' }\} $  Now my notes say that there are $|G/G'|$ 1-dimensional reps of $G$. Since there are $|G/G'|$ 1-dimensional reps of $G/G'$, this must mean that all 1-dimensional reps of $G$ have kernel containing $G'$. Why is this so?  Thanks Calculate probability (area) under the overlapping area of two normal distributions How can I sanitize user input with PHP? Is there a catchall function somewhere that works well for sanitizing user input for SQL injection and XSS attacks, while still allowing certain types of HTML tags? MD5 Hash outputs not produced Are there any hash outputs not produced by the MD5 hash function? I need to use it as a placeholder for an empty hash while comparing two hashes. Not getting edit's +2 rep after reaching 2k rep After reaching 2k rep , I'm not receiving  +2 rep per edit. Why?