I claim the IQ score of CFA candidates not less than 125, may be because I think highly of you folks. You come to me and say I don’t think so, I will run a hypothesis test to check.
H0: IQ >= 125, Ha: IQ < 125
I think the null should be what you want to negate.
H0: IQ <125 One tailed test; Therefore Ha: >=125
I like the kamran’s example…it hits right on the head.
Our Hypothesis says x=0.4. Now how significantly is it close to 0.4.
So the sample will help us establish wheather the we had it 95% of the times, indicated by t-stat which in essence, measures whether the std deviation was less than 5%. A high t-stat indicates that it is pretty significant that the null is negated OR Ha is right OR ==> we can easily reject the null.
However when no as significant we may have to give up rejecting null and confirm sadly that H0"IA<125.
Please correct me if wrong