You have the following sample draw X = {34,28,50,102,18,39,90,71,140,19,89,55} of a random variable $X_i$ assume to be iid with finite means and variances. Test $H_o: \mu = 50$ against a one-sided alternative at the 5% level: present the test statistic and its distribution properties, the critical value and the p-value. Prove your claims about the distribution.
I computed the 99% confidence interval (my professor calls the 'asymptotic bands'), by calculating the standard error and what not.
I'm pretty sure I need to use the t-distribution, but while looking this up online, it seems to be for random draws from normal distributions with unknown variances. I'm only assuming a mean, and I know nothing about the distribution of $X_i$.
Can I just say it must asymptotically converge to a standard normal and look up $t_{11,.05}$?