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Estimating the population mean when the population variance is
Estimating the population mean when the population variance is

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... 17 You are taking a multiple-choice test that has 8 questions. Each of the questions has 5 choices, with one correct choice per question. If you select one of these options per question and leave nothing blank, in how many ways can you answer the questions? ...
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... Using a only person’s horoscope, a professional astrologer can correctly predict which of three personality charts applies to that person with probability 1/3. Another example: A (unbiased) jury assume a person is not guilty until proven innocent. ...
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< 1 ... 215 216 217 218 219 220 221 222 223 ... 269 >

Foundations of statistics

Foundations of statistics is the usual name for the epistemological debate in statistics over how one should conduct inductive inference from data. Among the issues considered in statistical inference are the question of Bayesian inference versus frequentist inference, the distinction between Fisher's ""significance testing"" and Neyman-Pearson ""hypothesis testing"", and whether the likelihood principle should be followed. Some of these issues have been debated for up to 200 years without resolution.Bandyopadhyay & Forster describe four statistical paradigms: ""(1) classical statistics or error statistics, (ii) Bayesian statistics, (iii) likelihood-based statistics, and (iv) the Akaikean-Information Criterion-based statistics"".Savage's text Foundations of Statistics has been cited over 10000 times on Google Scholar. It tells the following.It is unanimously agreed that statistics depends somehow on probability. But, as to what probability is and how it is connected with statistics, there has seldom been such complete disagreement and breakdown of communication since the Tower of Babel. Doubtless, much of the disagreement is merely terminological and would disappear under sufficiently sharp analysis.
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