Suppose $X_1,…, X_n$ (where n is large) are modeled as iid normal. The T statistic is calculated to be $−1.7$.
Do we have enough evidence to reject $H_0:μ≥0$ at the $5\%$ level?
I am wondering wow the t statistic give us information regarding whether to reject or not.
If n is large, you don't need a $T$ statistic, because a $Z$ statistic will do the job. A one-sided hypothesis test at $\alpha = 0.05$ has a critical $Z = 1.645$. So yes.
If $n$ were small, you would need a $T$ statistic, and the critical value would depend on $n$, but in general would be larger than the critical $z$ value. So if it wasn't enough to reject with $Z$, it definitely would not be enough to reject with $T$.