Thread: 'Universal' Formula for finding the probablilty of a Type 1 Error

1. 'Universal' Formula for finding the probablilty of a Type 1 Error

Hi!
I'm an AP stats student and I'm fortunate enough to have an EXTREMELY incompetent teacher (a bit of sarcasm there) so I was wondering if anyone could properly explain how to find the probability of getting a Type 1 Error... this seems to be an area that few text books explain thoroughly... although mine explains how to find a Type 2 quite thoroughly. Go figure.

If anyone even has time to write only the formula that would be more than enough!!

Thanks!!

2. Originally Posted by agoelz13
Hi!
I'm an AP stats student and I'm fortunate enough to have an EXTREMELY incompetent teacher (a bit of sarcasm there) so I was wondering if anyone could properly explain how to find the probability of getting a Type 1 Error... this seems to be an area that few text books explain thoroughly... although mine explains how to find a Type 2 quite thoroughly. Go figure.

If anyone even has time to write only the formula that would be more than enough!!

Thanks!!
This is the formula: Pr(reject H0 | H0 true).

The best way is to read examples like this one: http://www.mathhelpforum.com/math-he...e-i-error.html

I'm sure a search of these forums will uncover other examples.

3. Umm... ok I think I need the in-depth explanation because unfortunately that formula as well as the other examples I've found aren't making sense to me... perhaps it would be easier to explain with a problem?:

You have an SRS of size n= 9 from a normal distribution with $\displaystyle \sigma = 1$. You wish to test

$\displaystyle \, H_O \,: \mu = 0$

$\displaystyle \, H_O\,: \mu > 0$

You decide to reject $\displaystyle \,H_O\,$ if $\displaystyle \bar{x} > 0$ and to accept $\displaystyle \,H_O\,$ otherwise.

(a) Find the probability of a type 1 error

(b) Find the probability of a type 2 error when $\displaystyle \mu = 0.3$

(c) Find the probability of a type 2 error when $\displaystyle \mu = 1$

4. Originally Posted by agoelz13
Umm... ok I think I need the in-depth explanation because unfortunately that formula as well as the other examples I've found aren't making sense to me... perhaps it would be easier to explain with a problem?:

You have an SRS of size n= 9 from a normal distribution with $\displaystyle \sigma = 1$. You wish to test

$\displaystyle \, H_O \,: \mu = 0$

$\displaystyle \, H_O\,: \mu > 0$

You decide to reject $\displaystyle \,H_O\,$ if $\displaystyle \bar{x} > 0$ and to accept $\displaystyle \,H_O\,$ otherwise.

(a) Find the probability of a type 1 error

(b) Find the probability of a type 2 error when $\displaystyle \mu = 0.3$

(c) Find the probability of a type 2 error when $\displaystyle \mu = 1$
(a) Calculate $\displaystyle \Pr( \text{Reject} \, H_0 \, | \, H_0 \, \text{true}) = \Pr\left(\overline{X} > 0 {\color{white}\frac{.}{.}} | \, \overline{X}\right.$ ~ Normal $\displaystyle \left.\left(\mu = 0, \sigma = \frac{1}{\sqrt{9}}\right)\right)$.