# Testing for unknown proportion

1. Apr 17, 2007

### EvLer

1. The problem statement, all variables and given/known data
for testing Ho : p = 0.2 vs H1: p > 0.2 when will the power of Rao score test be larger:
1. alpha = 0.05 n = 10
2. alpha = 0.01 n = 10

2. Relevant equations
Rao score test: reject Ho when |sqrt(n)*(p' - po)/sqrt(po (1-po)| > z(alpha)

po in this case = 0.2 and p' is estimated proportion from the given data.
z comes from N(0,1)

power is defined as 1 - Beta, where Beta is the prob. of making type II error in testing hypothesis, i.e. accepting Ho when H1 is true

3. The attempt at a solution
I think (2) since with higher alpha it is easier to reject Ho, but I am a bit doubtful on this.
Thanks.