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Hypothesis testing assesses whether data are inconsistent with a given hypothesis (usually a null hypothesis of no effect).
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Inferences about $\mu$ based on the sum of two dependent normal RVs
Given:
$X \sim \mathcal{N}(\mu, \sigma^2)$
$Y|X=x \sim \mathcal{N}(0, (\theta x)^2)$
$Z = X + Y$
I want to be able to make hypothesis tests or confidence intervals for $\mu$ using $Z$ and known $\th …