Reject or accept the null?

[Lilybird86]

In a hypothesis test, the alternative hypothesis is that the mean is greater than 11. If the sampling error is 3 And the sample mean is 6, do we:

accept the null
Reject the null
Cannot reject the null

why is my answer accept the null wrong? Wouldn’t the null be < or equal to 11. And wouldn’t the values be 3-9 which is leads than 11? Help please

 

[Harry_the_cat]

Maybe if you post the whole question we could help.

 

[Dr.Peterson]

What have you been taught about the conclusion of a hypothesis test?

Commonly it is emphasized that we never "accept" the null'; rather, we "fail to reject" the null (your last option above). So it's not that your reasoning about the data is wrong, but that your wording is wrong.

Here is a good explanation: https://www.thoughtco.com/fail-to-reject-in-a-hypothesis-test-3126424 . As is said there, "It is important to note that a failure to reject does not mean that the null hypothesis is true—only that the test did not prove it to be false."

Here is another: https://blog.minitab.com/blog/under...ans-say-failure-to-reject-the-null-hypothesis . "Replacing "failure to reject" with "accept" would be wrong."