If the sampling distribution is really centred on mu, then how likely is my X-bar?

Mathematically, we assume the null hypothesis is true unless we have evidence against it. But, either the null or the alternative could be our claim.

Steps in traditional method

Worked example. Our X-bar is pretty far out, so we think it’s more likely that the sampling distribution is really centred on some other number than 29.1.

There is always some probability of making an error in hypothesis testing.

It’s easier to reject H0 with the same evidence on a one-tailed test, so don’t go there unless you are really sure the other side is logically impossible.

Example of a right-tailed test. We think our plant food could have increased production, or made no difference. We don’t think it could possibly have made things worse.

Steps in the P-value method of hypothesis testing.

The same example, but this time using the P-value method.

The summary statement (step 5) is not creative writing – these four are all you will ever need.

We can narrow in closer and closer around the hypothesized value, but we can never be certain that it is exactly, precisely correct. That is why we never “support” or “accept” the null hypothesis – we only “fail to reject” it.