After you have completed the statistical analysis and decided to reject or fail to reject the Null hypothesis, you need to state your conclusion about the claim. To get the correct wording, you need to recall which hypothesis was the claim.
If the claim was the null, then your conclusion is about whether there was sufficient evidence to reject the claim. Remember, we can never prove the null to be true, but failing to reject it is the next best thing. So, it is not correct to say, “Accept the Null.”
Think of the criminal court analogy: we never officially say the defendant is innocent. If the prosecutor does not provide us sufficient evidence to convict, we say the defendant is not guilty.
If the claim is the alternative hypothesis, your conclusion can be whether there was sufficient evidence to support (prove) the alternative is true.
Again in the criminal court analogy, if the prosecutor presents sufficient evidence, we reject the Null hypothesis that the defendant is innocent and declare the defendant Guilty.
Use the following table to help you make a good conclusion.
The best way to state the conclusion is to include the significance level of the test and a bit about the claim itself.
For example, if the claim was the alternative that the mean score on a test was greater than 85, and your decision was to Reject then Null, then you could conclude:
“At the 5% significance level, there is sufficient evidence to support the claim that the mean score on the test was greater than 85.”
The reason you should include the significance level is that the decision, and thus the conclusion, could be different if the significance level was not 5%.
If you are curious why we say “Fail to Reject the Null” instead of “Accept the Null,” this short video might be of interest: Here