Null Hypothesis

I appreciate everyone's help. Just the language of statistics is challenging. Is the following true or false.....after finding the t-statistic, this number is compared to the one in the t-chart. If the t-number is greater than or equal to the number in the chart, then the test is significant and the null hypothesis is rejected. I stated that it was false because the conclusion is that the test is significant, but the comparative numbers lead us to "fail to reject the null hypothesis." Am I right? Please help.


TS Contributor
If a test is significant, you do reject the null hypothesis. If it is not significant, you fail to reject the null hypothesis. You cannot prove the null.

Think of it like a jury trial. A person is presumed to be innocent (null hypothesis). If the evidence is significant, the null hypothesis of innocence is rejected and the person is found guilty. If the evidence is not significant, we fail to reject the null hypothesis. This is why a person is not declared innocent, but is found not guilty. You cannot prove the person is innocent (null hypothesis).