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Hi! My name is Kody Amour, and I make free math videos on YouTube. My goal is to provide free open-access online college math lecture series on YouTube using free open-access resources. I rely on generous donations and ad revenue - a special thanks to everyone who helped this channel grow. **Please only give if you have the financial ability to do so.** Support this Amour Learning channel directly on Patreon: / amourlearning ------------------------------------------------------------------------------------------------------------------- Credit to all of the authors of all of the resources below that greatly helped influence this video. My newer videos are much more original than these videos. Free open-access online math textbooks: https://aimath.org/textbooks/approved... My favorite number theory textbooks: Number Theory: In Context and Interactive by Dr. Karl-Dieter Crisman: http://math.gordon.edu/ntic/ Elementary Number Theory: Primes, Congruences, and Secrets by Dr. William Stein: https://wstein.org/ent/ A Computational Introduction to Number Theory and Algebra by Dr. Victor Shoup: https://shoup.net/ntb/ My favorite programming language: SageMath (which in my view is categorically more productive than Python, R, Mathematica, Matlab, Maple, Magma, etc - if you're using any of these and they aren't working out, consider switching to Sage): https://www.sagemath.org/ A free in-depth tutorial for SageMath: https://doc.sagemath.org/html/en/tuto... Learn LaTeX in 30 minutes: https://www.overleaf.com/learn/latex/... ------------------------------------------------------------------------------------------------------------------- My favorite math/science YouTube channels that I absolutely love (in no particular order): Zach Star: / @zachstar Numberphile: / @numberphile 3Blue1Brown: / @3blue1brown MIT OpenCourseWare: / @mitocw Khan Academy: / @khanacademy PBS Infinite Series: / @pbsinfiniteseries Lex Fridman: / lexfridman Studies often compare two groups. For example, researchers are interested in the effect aspirin has in preventing heart attacks. Over the last few years, newspapers and magazines have reported various aspirin studies involving two groups. Typically, one group is given aspirin and the other group is given a placebo. Then, the heart attack rate is studied over several years. There are other situations that deal with the comparison of two groups. For example, studies compare various diet and exercise programs. Politicians compare the proportion of individuals from different income brackets who might vote for them. Students are interested in whether SAT or GRE preparatory courses really help raise their scores. You have learned to conduct hypothesis tests on single means and single proportions. You will expand upon that in this chapter. You will compare two means or two proportions to each other. The general procedure is still the same, just expanded. To compare two means or two proportions, you work with two groups. The groups are classified either as independent or matched pairs. Independent groups consist of two samples that are independent, that is, sample values selected from one population are not related in any way to sample values selected from the other population. Support The Show On Patreon: / kodyamour ------------------------------------------------------------------------------------------------------------------- My name is Kody Amour, and I provide online math lectures to the public. My aim is to provide content that attends to a sound, productive conceptual understanding. Basically, I want to make sense, and I want my videos to be coherent with each other. If you think that these videos have helped you, please consider supporting this channel by subscribing, and please consider donating to this cause via Patreon! Website: http://amourlearning.org/ Facebook: / amourlearning Twitter: / kodyamour Udemy: https://www.udemy.com/user/kodyamour/ Linkedin: / kodyamour