# If the difference in means doesn't fall in the 95% CI but 0 does, what to do?

A question regarding bootstrap confidence intervals. If the hypothesis is comparing two means (e.g. the difference in calorie intake between males and females), should the value 0 be used or the difference in means be used to refer to at the end when we compare it to the 95% confidence interval.

In my instance the difference in mean ($\bar{x_1}$ - $\bar{x_2}$) did not fall in the 95% confidence interval. Suppose the value 0 (since the hypothesis is $\bar{x_1}$ - $\bar{x_2}$ = 0) lies within the 95% confidence interval.

Should we reject the null hypothesis?

• It's very strange that the difference of your two samples doesn't fall in the confidence interval for the difference. Are you sure about it? As @grldsndrs said, I'm afraid you might have get confused with different differences or intervals. – Pere Oct 26 '16 at 10:19

## 1 Answer

If you are comparing two means, and you make the assumption that their difference is 0 ( Null Hypothesis ), if 0 ends up being in your confidence interval, you should fail to reject the Null Hypothesis that their difference is 0.

It seems you are getting confused about the difference of the sample means and the hypothesized difference of the means.