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Hypothesis Testing and the Method of Indirect Proof

"The clinching proof of my reasoning is that Iwill cut anyone who argues further into dogmeat."
-- Attributed to Sir Geoffery de Tourneville, ca 1350 A.D.

MAT 203: Geometry for Middle and Elementary School Teachers (3)
Prerequisites: admission to a certification program in elementary or middle school and MAT 201 and 202 with a combined grade point of 2.5 in the two courses. The course emphasizes conceptual understanding and communication of geometric topics, and developing elementary geometric proofs through problem solving and technology. Topics include angles, lines, circles, polygons, polyhedra, congruency and similarity, trigonometry, and non-Euclidean geometry.

de Branges, L.

Misuse of statistics - Wikipedia

What is the distribution of the product of sample observations from the uniform (0, 1) random?

In 2000, the Clay Mathematics Institute () offered a $1 million prize () for proof of the Riemann hypothesis. Interestingly, of the Riemann hypothesis (e.g., by using a computer to actually find a zero off the ), does not earn the $1 million award.

You may marvel at the roundabout procedure whereby a researcher tests a null hypothesis that is believed to be untrue in the hope of rejecting it and thereby accepting the alternative hypothesis that is believed to be true. On reflection, you may recall a similar procedure taught in plane geometry and algebra the method of indirect proof. This method consists of listing all possible answers or solutions to a problem and showing that all but one is contrary to known fact or lead to an absurdity. By a process of elimination, the one that is not contrary to known fact or absurd must be true. The success of the method of indirect proof depends on listing all possibilities and finding a contradiction for all but one. The comparable procedure in testing a null hypothesis consists of formulating the null and alternative hypotheses so that they exhaust all the possibilities concerning a population parameter. A sample is obtained from the population, and appropriate statistics, such as the sample mean and standard deviation, are computed. If it is highly improbable that the obtained value of the sample mean would have occurred if the null hypothesis were true, then the null hypothesis must be considered a poor prediction of the population mean and should be rejected in favor of the alternative hypothesis.

Statistical hypothesis testing - Wikipedia

There is one important difference between the method of indirect proof and null hypothesis testing. In indirect proof, a possibility is rejected only if it is found to lead to a contradiction to known fact or is absurd. In hypothesis testing, the null hypothesis is rejected if they obtained value of a sample mean is very unlikely if the null hypothesis is indeed true. It follows that null hypothesis testing, unlike the method of indirect proof, does not provide incontrovertible proof because the null hypothesis is rejected because of the occurrence of an event that is improbable but not impossible.

In statistics terminology, the students in the study are the sample and the larger group they represent (i.e., all statistics students on a graduate management degree) is called the population. Given that the sample of statistics students in the study are representative of a larger population of statistics students, you can use hypothesis testing to understand whether any differences or effects discovered in the study exist in the population. In layman's terms, hypothesis testing is used to establish whether a research hypothesis extends beyond those individuals examined in a single study.

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The main thrust of the site is to explain various topics in statistical analysis such as the linear model, hypothesis testing, and central limit theorem">

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common ancestor hypothesis - Scientific American

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For example, ever since the Web entered the popular consciousness, observers have noted that it puts information at your fingertips but tends to keep wisdom out of reach.

History of the efficient markets hypothesis ..

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Statistics - definition of statistics by The Free Dictionary

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