# Thread: type i and ii error

1. ## type i and ii error

I have an exponential population. A single observation is used to test the null hypothesis that the mean waiting time is p = 10 against the alternative hypothesis that p does not equal 10. If null is rejected if and only if observed value is < 8 or > 12, find probability of type I error

I'm clueless...any help is appreciated

2. write down your density and what this p is.

3. it doesn't specify a specific density. Also I was using p in place of theta. Sorry, I should have clarified.

Don't I have to use the normal approximation to an exponential? And, if so, is this just the same equation as the normal approximation for Poisson?

4. still
some people write an exponential density as

$e^{-x/p}/p$ while others use $pe^{-px}$

5. It's the latter one

6. $\alpha=\int_0^8f(x)dx+\int_{12}^{\infty}f(x)dx$

and I use the first density.

7. ## Umpt

Are you conversant with the concept of uniformly most powerful test?it works and i get it to be 1.0135