# Hypothesis Testing

• Dec 1st 2009, 06:42 PM
statmajor
Hypothesis Testing
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.

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

Is this correct?
• Dec 1st 2009, 10:45 PM
matheagle
You said .... is less than or equal to 3, but you only summed less than
And you don't even say what your i is.

$\displaystyle \alpha=\sum_{i=0}^3 {10\choose i} (.5)^{10}$
• Dec 2nd 2009, 07:00 AM
statmajor
$\displaystyle \alpha=\sum_{i=0}^3 {10\choose i} (.5)^{10} = 0.171875$

I just forgot the equal part (and Sigma), but I have included the '3' in my calculation to calculate alpha.

Is my power function P(X<=3) = P(Bin(10,0.25) < =3) correct?