Can I resample two datasets and then perform a t-test?

I have two datasets with 35 points each. I know that both are pulled from normal distributions with equal variances. A two-sample t-test indicates they have the same mean, but the p-value is close to my alpha.

1. Knowing they are normal with equal variances, would it make sense to just create normal distributions with the relative sample means, draw say 1,000 points from each, and then perform a two-sample t-test?

2. Would it be fruitful to do this, ie could I expect to learn anything new?

• A nonsignificant result in a two-sample t-test does not indicate they have the same mean. It indicates that there is not enough evidence to rule out the possibility that they have the same mean. – brendan Oct 22 at 15:57
• I look forward to less and less wieldy sentences as my understanding grows – user12686018 Oct 25 at 1:46
• It is definitely one of the risks of most technical fields! – brendan Oct 25 at 9:20

• Those first two words are important. Why do you want to do this, just to get from $p=0.51$ to $p=0.49?$ – Dave Oct 22 at 1:11