Can Positive Values of Observations imply Population Positive Mean? Suppose that we have N-observations for a random variable $V$ from a population:
$$\{v_1,\;\ldots,\;v_N\}$$
, and all of the observations is positive: $v_i>0\quad \forall i=1,\;\ldots,\;N$.
Here, assume that the observations are "randomly sampled" (i.i.d.)
I think, from the positive values of observations, it is reasonable to guess that the population mean $\mathbb{E}[V]$ is also positive because the observations may represent the population distribution due to the random sampling assumption.
But, I am also skeptical about whether a statement for data can imply a statement for a population.
So, is it possible to derive $\mathbb{E}[V]>0$ from $v_i>0\quad \forall i=1,\;\ldots,N$?
In other words, can we mathematically prove the following implication?
$$v_i>0\quad \forall i=1,\;\ldots,N \quad \Longrightarrow \quad \mathbb{E}[V]>0$$
(Note that I am not asking an inference question. I want to know whether we can prove that under the random sampling assumption.)

You can't prove it, but you can calculate a confidence interval for the population mean given the sample. This requires an assumption on the population distribution.
More information is required for a better answer
