Finding the p_value from a hypothesis testing

Question

I understand that we have a rejection region when all the values of theta are less than 3, such that R={T(X)< c} with c = -z_alpha.

I can get the sample mean from the three values: x_bar = 3.29, as well as the sample standard deviation 0.1752 and I have mu = 3.

I tried to work this out but I can't use z_alpha in the probability statement since i don't have the confidence level.

Answer 1

T - statistic $= min(x_1,x_2,x_3) = 3.11$

$\mu = 3$

Standard deviation $=\sqrt{\frac{0.11^2+.3^2+.46^2}{2}} = 0.396043$

p value $= \frac{statistic - \mu}{\sigma} = \frac{3.11-3}{0.396043} = 0.277748\approx 0.281$