# Interpreting wording for formulating hypothesis testing

I've been presented with paired data for individuals' weights before and after a dieting program (paired t-test problem).

The question being asked is "test the hypothesis that the dieting program is effective." Does this wording relate to the null hypothesis or the alternative?

Below is the Minitab output for the paired t-test assuming that the null hypothesis is that there is no change. The descriptive statistics show that the mean weight before the dieting program (180 lbs.) is greater than the mean weight after the dieting program (170 lbs.).

Let mu1 = population mean before and mu2 = population mean after the dieting program. As can be seen in the Minitab output, I ran the paired t-test with following hypotheses...

 Null hypothesis: mu of difference = 0

Alt. hypothesis: mu of difference > 0


Where "mu of difference" = mu1 - mu2. Have I interpreted "test the hypothesis that the dieting program is effective" correctly?

• Please add the [self-study] tag & read its wiki. – gung - Reinstate Monica Oct 29 '15 at 2:41
• In view of the two conflicting answers, it's apparent that you should justify your choice of null & alternative hypotheses with reference to the context. Where does the burden of proof lie? What does "effective" mean? – Scortchi - Reinstate Monica Oct 29 '15 at 10:25
• I've added Minitab output to show the descriptive statistics to make the problem more clear. – clafo094 Oct 30 '15 at 20:30

Looks like you're on the right track. When you say "Does this wording relate to the null hypothesis or the alternative?" I'm not quite sure what you mean. You're testing the effectiveness of the dieting program. So you're correct by saying the null hypothesis is that it has no effect. However, it's a little tricky with the alternative hypothesis. It's (usually) bad practice to only check for one tail when testing effectiveness like this. Most of the times, you want to check both tails, because then you'll detect if the drug is really ineffective (i.e. they gain a lot of weight while on the dieting program). If you just check for one tail like you did, and they do gain a lot of weight, the stat test won't show you that as being significant.

"the hypothesis that the dieting program is effective."

That is the null hypothesis!!

So does "effective" mean:

1. No weight loss
2. Some weight loss
3. A weight gain?

Obviously you want (2).

The alternative would thus be no weight loss or a weight gain.

rb612's point was that you might want to test that the result was statistically significantly different than 0. Which is a good idea, but it isn't what the problem is asking for.

• This is incorrect. The null hypothesis in such a case is that there is no effect. The alternative hypothesis is that there is an effect. – Cliff AB Dec 25 '15 at 18:59