# How to use the null hypothesis in hypothesis testing — draw a conclusion

This may be an odd question, but am learning about hypothesis testing and having a hard time with the logic of it, especially getting comfortable with how to draw a conclusion from the null hypothesis!

For example, here is an example question: Test the hypothesis that the mean weight of North Americans is at least 175lbs. The mean of weights of 100 sampled people is 178lbs, with a sample standard deviation of 8lbs. What can we conclude?

Here are the steps I understand:

-Define the null hypothesis: The average weight of North Americans is less than (<) 175lbs. (Alternative hypothesis: The average weight of North Americans is at least (>=) 175lbs.)

-Assume the null hypothesis to be true.

-Find the Z-score associated with some significance interval (let's say, 95%; which for a two-tailed test, Z-score would be -1.96,1.96)

-Calculate the Z-score for the problem: $\frac{(Sample Mean - Hypothesis Mean)}{(Standard Deviation)}$ --> $\frac{(178 - 175)}{(8/\sqrt{100})} \approx 3.75$

Here is where I have a hard time drawing a conclusion. I've drawn out the normal curve and marked the confidence interval boundaries and z-score, but have a hard time with how these are used to either accept/reject the null hypothesis.

Here the null hypothesis assumes the average weight of North Americans is less than (<) 175 lbs. What does this mean for where the z-score lies in comparison to the significance interval? What if my null/alternative hypothesis were switched; then how would this effect the conclusion (as the calculations would be the same)?!

Sorry if these are basic questions, I'm having a hard time getting comfortable with the pattern of logic here, even by drawing out.

Any insights are greatly appreciated. Thanks for your time!

• This doesn't appear to be clearly distinct from your earlier question with a very similar title: stats.stackexchange.com/questions/321430/… ... please edit to avoid any repetition of the earlier question (if something is unclear in what you meant to ask in the earlier question, clarify that earlier question). Here you should clearly distinguish what you're asking now from what you asked before -- how is this a distinct question? What is it asking that is NOT part of the earlier question... ctd – Glen_b Jan 8 '18 at 2:31
• ctd... Given that the general thought process is explained there you'll need to be more specific about where your difficulties occur. – Glen_b Jan 8 '18 at 2:33