1. Remember that we want to find support for what we think is true about the world (H1) when we perform a hypothesis test.  Despite all your lifetime efforts to avoid rejection, we do want to reject H0.

2. The decision should tell what you do with H0.  You either “reject H0” or you “cannot reject H0”.  You should also include a numerical comparison that explains the decision.  This comparison may relate a test statistic to a critical value(s) or it can relate a p-value to the significance level (alpha).

3. The interpretation tells us whether the evidence in the sample supports or does not support H1.  If we reject H0, then we have strong evidence in support of H1 (recall that we’ve given H0 the benefit of the doubt and required an unusual test statistic from the sample—think of it as an outlier—before we can say H0 is wrong).  If we cannot reject H0, then we do not have strong evidence to demonstrate H1.  Be sure that you don’t write “H1” in your sentence.  Tell people what you learned about the real situation.

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Remember that we can only come up with strong evidence for H1 when we do a hypothesis test.  The best we can do for H0 is present weak evidence for H0, so we always say that we "have" or "do not have" strong evidence for H1.

To see the importance of making H1 what the decision maker is true, consider the following experiment.

You run a company that produces batteries.  A major industrial customer wants to include your batteries with its product, if your batteries have long lives (let's say the average life is greater than 750 hours).  You want to convince this customer that indeed your batter do last longer than 750 hours.   If we make H1 what you want to demonstrate, we will have the hypotheses labeled A below.  If you do the opposite you will have hypotheses labeled B (you can think of the first hypothesis in B as mu greater than or equal to 750 hours).

A     H0: mu = 750 hours                                    B     H0: mu = 750 hours
        H1: mu > 750 hours                                           H1: mu < 750 hours

Now.  Assume that you use set A and reject H0.  Interpret the decision.
 
 
 
 

Now. Assume that you use set B and cannot reject H0.  Interpret this decision.
 

Now consider both interpretations.  Does either statement say your batteries are short-lived (not long-lived)?
                                                      Which of these statements would be better to tell the customer?
                                                        Does your answer to the last question make it better to make H0 or H1 what you think is true?