5 votes
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Hypothesis test, finding p-value

I think the Central Limit Theorem is a poor approximation here for 5 samples. The exact probability is $P(T \ge t) = P(5T \ge 4) = P(5T = 5) + P(5T = 4) = \frac{1}{2^5} (\binom{5}{0} + \binom{5}{1}) = ...
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  • 81.6k
4 votes

What is an equivalent of Student's t-test for exponential distribution?

I'll put an idea for a two-sided hypothesis test here, but a study of power/optimality of the test is more work. We use the exponential pdf parametrisation $f_{\theta}(x)=\theta^{-1}e^{-x/\theta}$. ...
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  • 8,616
3 votes
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Finding the upper bound of a critical region

$P(\min \{X_1,\dots,X_n \}<k | H_0) \ne P(X_1<k;X_2<k;...;X_n<k|H_0)$. The event $\min \{X_1,\dots,X_n \}<k$ is the event at least one of $X_i < k$. What you have right now is the ...
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  • 718
1 vote

Hypothesis test, finding p-value

$ H_{0}: X \sim \mathcal{N}( 0,5;\ \ 5\cdot 0,5 \cdot (1-0,5))= \mathcal{N}(0,5;\ \ 1,25).$ $ p-value = P(\{X >0,8\}) = 1 - P(\{Z\leq \frac{0,8-0,5}{\sqrt{1,25}}\}) = 1 -\phi(0,2683)= 0,3942.$
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  • 19

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