Type I and Type II Error

#1
Let {X1, X2, ..., X25} be a random sample of 25 observations from a normal population havingmean μ and variance 2. Define the null hypothesis H0 : μ = 0 and the alternative hypothesisH1 : μ > 0. Consider the following decision rule:
reject H0 if X' > 0.5accept H0 if X' ≤ 0.5
a.) Calculate the probability of making a type I error.
b.) Calculate the probability of making a type II error when in fact μ = 0.2.


what I got till now is
z=(X'-µ)(/sqrt(n))
z=.5/sqrt(2)
X'=z*(Sqrt(2/25))+0
.... any ideas ???

thank you so much
 

hlsmith

Omega Contributor
#2
what I got till now is
z=(X'-µ)(/sqrt(n))
z=.5/sqrt(2)
X'=z*(Sqrt(2/25))+0
.... any ideas ???

thank you so much

I can't quite make out your response. However, you know what your level of significance is (>0.05), so you should be able to incorporate that into your equation.
 
#3
the level of significance is not given?? I could however assume 0.05 but then there is no room left for a calculation of type I error...since If I impose lvl sign I indirectly set alpha ???
 

Dason

Ambassador to the humans
#4
However, you know what your level of significance is (>0.05), so you should be able to incorporate that into your equation.
Ignore this (sorry hlsmith).

You're given the cutoff and asked to determine the type I error rate (the "level of significance").