# type i and ii error

• February 25th 2010, 07:47 PM
noles2188
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
• February 25th 2010, 08:21 PM
matheagle
write down your density and what this p is.
• February 25th 2010, 09:20 PM
noles2188
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?
• February 25th 2010, 09:29 PM
matheagle
still
some people write an exponential density as

$e^{-x/p}/p$ while others use $pe^{-px}$
• February 25th 2010, 09:40 PM
noles2188
It's the latter one
• February 25th 2010, 09:46 PM
matheagle
$\alpha=\int_0^8f(x)dx+\int_{12}^{\infty}f(x)dx$

and I use the first density.
• February 25th 2010, 10:43 PM
markotti
Umpt
Are you conversant with the concept of uniformly most powerful test?it works and i get it to be 1.0135