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Hypothesis testing assesses whether data are inconsistent with a given hypothesis (usually a null hypothesis of no effect).

3 votes
1 answer
9k views

Hypothesis testing for parameter of uniform distribution

I'm solving the following exercise from Larry Wasserman's book "All of Statistics". Let $X_1, \dots, X_n\sim \text{Unif}(0,\theta)$ and let $Y = \max{X_1,\dots,X_n}$. We want to test $H_0: \theta …
12 votes
2 answers
2k views

Two definitions of p-value: how to prove their equivalence?

I'm reading through Larry Wasserman's book, All of Statistics, and currently about p-values (page 187). Let me first introduce some definitions (I quote): Definition 1 The power function of a test wi …
1 vote
0 answers
96 views

bootstrapping for a parameter estimation

At the moment I'm studying bootstrap and I want to do some examples to get a feeling for it. Suppose I generate the following data: set.seed(10) data <- rnorm(1000,1,3) number <- min(data[data <= 0.9 …