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Chapter 6 Solutions
Chapter 6 Solutions

... 6.56. (a) For Ha : µ > µ0 , the P-value is P(Z > 1.34) = 0.0901. (b) For Ha : µ < µ0 , the P-value is P(Z < 1.34) = 0.9099. (c) For Ha : µ = µ0 , the P-value is 2P(Z > 1.34) = 2(0.0901) = 0.1802. 6.57. (a) For Ha : µ > µ0 , the P-value is P(Z > −1.73) = 0.9582. (b) For Ha : µ < µ0 , the P-value is ...
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... since the sum of i.i.d. exponential random variables has a Gamma distribution (not considered in this course). In the first case, the exact probability (to 4 d.p.) is 0.4162 (compared to the estimate 0.4176). In the second case, the exact probability (to 4 d.p.) is 0.6835 (compared to the estimate 0 ...
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... Quotas were not representative of population (they were based on 1940s census data which under-represented urban population) Stopped polling too soon ...
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... was 1.25 ± 0.4 ms-1.” “A kilometer downwind the concentration of the pollutant was 14 ppm, with 95% confidence interval (7, 27).” We are given a point estimate and an interval estimate, and once again the information is—at least in an informal, intuitive way—easy to understand. Each of these stateme ...
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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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