# Hypothesis Testing

1. Dec 1, 2009

### cse63146

1. The problem statement, all variables and given/known data

Let X have a binomial distribution with the number of trails n = 10 and with p either 0.25 or 0.5. The simple null hypothesis p = 0.5 is rejected and the alternate hypothesis p = 0.25 is accepted if the observed value of X1, a random sample of size 1, is less than or equal to 3. Find the significance level and the power of the test.

2. Relevant equations

3. The attempt at a solution

I believe that the power function is P(X<3) = P(Bin(10,0.25) < 3) and the significane leve would be $$= \alpha = P_{H_0}(_{10}C_i 0.5^{10}0.5^{10-i}<3) = 0.171875$$

Is this correct?