Let X be a single observation form the uniform distribution:
f(x) is a piece wise function where f(x)= $\frac{1}{\theta}$ if $0<x<\theta$ and $0$ otherwise.
Suppose we use (X, 1.5X) as a confidence interval for $\theta$. What is the confidence level.
I thought I could backwards engineer this by letting $X = x- z_\frac{\alpha}{2} \frac{\sigma}{\sqrt n}$ and $1.5X = x+ z_\frac{\alpha}{2} \frac{\sigma}{\sqrt n}$ but it doesn't work out, how do I go about this question?
I don't know what the link ("Question is here") has to do with the question you've written. Here is what the link states:
But here is an approach to answer the question you wrote. The confidence interval (X,(3/2)X) will only include $\theta$ if $(3/2)X \geq \theta$. That probability is
$$\int_{\frac{\theta }{\frac{3}{2}}}^{\theta } \frac{1}{\theta } \, dx=1/3$$
So the confidence level is (approximately) 33.3%.