1. ## Hypothesis testing

A product has strengths distributed by $~N(40,1.15)$. A modification has been made to the process in such a way that the mean strength cannot be reduced but it is not certain it will lead to any effective increase in mean strength.

Where $\bar{x}=40.844; n=9$

ii. Carry out an appropriate one-sided test of the hypothesis that $\mu=\mu_{0}=40$ with the assumption that $\sigma=1.15$.

Would the appropriate alternativehypothesis be $H_{a}:\mu>40$?

And would I just check if the estimated mean falls within $40+1.645(1.15)$?

2. ## Re: Hypothesis testing

Hey MathJack.

You are correct in that the alternative would be looking at > 40 and not != or <.

I think you should test the alternative first before the null in this case. To get this down pat you will have to actually derive the distribution from first principles using probability distributions but I would test the alternative first as a guide of what the proper evaluation is likely to be.

This is one of the things about one sided tests and usually all the first principle stuff is covered in upper undergraduate or graduate statistical inference.