Basically I am asked if people over age $35$ spend more money on average than people less or equal to age $35$ with significane level $0.05$.
And I have a sample of the population that I can use for my hypothesis testing.
What I tried to do:
-I stated my null hypothesis that the averages are the same (no difference between them).
-I chose my test statistic to be the difference between the averages.
Then did the bootstrap with a confidence interval of $95\%$.
And the results I got showed that $0$ is in my confidence interval, so I accepted the null hypothesis(NOTE: I am not sure of this decision, does having zero in my confidence interval mean I can accept the null hypothesis OR does it mean I just can't reject it and it may still be true or false?).
and by that I answered no to the question.
A little confusion after I have finished:(Which probably occurred because my NOTE above).
Looking at my visualization, I had more values in the negative side of the graph (less than $0$), when I took the difference between Average of older people minus the average of younger people (Average of how much they spend) in my bootstraps, which makes me want to say that the Average of younger people is bigger than the older people, but that won't work here because I need to have the required significance level and not just work with my intuition.
And so I hesitated and came here to ask, is my work legitimate? did I miss something important that led to my weird conclusion?
I would appreciate any feedback about my work, and I'm open for any nice and better ideas than mine to try them out.
Thanks in advance!
One never accepts the null hypothesis, one just fails to reject it with a conclusion that you have no statistically significant evidence that the averages are different.