I would like to know what statistical tests are used to make sure the data is good.

Statistical tests that I am aware of are used to compare data sets. For these engineering tests, there are no data sets to compare. You do the test, average the break strength, and that's it. However, sometimes the data is all over the place and the variances are large.

Is there a test that concludes, "I am 95% confident that the break strength is X."?

And if it is lower than 95% we should increase the sample size?

Thank you!