# Repeated testing to increase confidence?

I want to know if the population mean equals some value $m$. For this puporse, I am using a one-sample t-test.

The null-hypothesis of the one-sample t-test is that the difference between population mean $\mu$ and given value $m$ is different using the sample mean $\overline{x}$.

Doing the t-test onces using a random sample gives me a t-test statistic and some p-value. The p-value might or might not be significant (p<0.05), depending on the random sample.

In order to be more confident about the test, wouldn't it be useful to repeat it several times? For instance, I could draw 100 random samples, perform for each sample the t-test and then report summary statistics for the t-test statistics and p-values. If all p-values are below 0.05 then I would be much more confident that I can safely reject the null hypothesis.

However, I have never seen somone doing this kind of repeated testing. Is this approach not valid?