A question from my class: Ask students whether they are vegetarian. Of n=25 students, y=0 answered "yes". For testing Ho: p=0.5 and Ha: p <> 0.5. Show that the likelihood ratio statistic equals 34.7.
I have tried SEVERAL ways to calculate this and I am getting nothing near 34.7. In the notes, the test statistic is calculated by -2(L(po) - L(p1)). However, when I calculate this, I am getting 6.24.
PLEASE HELP!
$$ LR = -2\ln\left[\frac{\sup_{\theta\in\Theta_0} \mathcal L(\theta)}{\sup_{\theta\in\Theta_1} \mathcal L(\theta)}\right]. $$ Note that $\mathcal L(\theta)=(1-\theta)^{25}$, $\Theta_0=\{0.5\}$, $\Theta_1=[0,1]\setminus\{0.5\}$, and $$\sup_{\theta\in\Theta_1}(1-\theta)^{25}=\sup_{\theta \neq 0.5}(1-\theta)^{25}=1$$ since for $\theta=0$ this probability attaines maximum value. So $$ LR=-2\ln (1-0.5)^{25} = -50 \ln 0.5 = 34,657359028. $$