$$H_0:\mu=0 \quad\quad H_1:\mu>0 $$
we assume the distribution of the sample is Gaussian.
If $p$-value is very big, sample mean very small, we still accept null hypothesis.
Isn't it counterintuitive? Why are we still using it?
E.g. $x_1,x_2,\ldots,x_n$, sample mean is $-5$, variance is known as 1.
$$H_0:\mu=0 \quad\quad H_1:\mu>0 $$ It's easy to see that $p$-value is very big, but we still accept mu = 0. But actually it is very intuitive that $\mu$ is less than 0 or at least not equal to zero?