Hypothesis testing framing I wanted to ask you for the advice. I am doing some stats exercise and apparently, I cannot get the zero and alternative hypothesis correct. For example, 'At the .01 significance level, can bank management conclude that younger customers use the ATMs more than senior customers?' I thought that the zero hypothesis is that younger customers use the ATMs more or equal to than senior citizens while alternative that less. But the answer sheet says that it's another way around. Do I need to always reverse the question? What would be your advice?
 A: It seems that the context of this question is traditional frequentist hypothesis testing, and I will answer relative to that. (There are other frameworks for
statistical decision-making that might take different approaches.)
To "conclude at the 1% level that young customers use ATMs more than senior
customers" $(\mu_y > \mu_s)$ means that we reject the null hypothesis $H_0: \mu_y \le \mu_s$ in favor of the alternative hypothesis $H_a: \mu_y > \mu_s.$
If the study is well-planned, there will have been an earlier power computation to
determine the necessary sample sizes of the youth and senior groups (typically the same for both groups). 
The idea is to take into account the assumed variability in ATM usage within the 
two groups and the difference in usage between groups that would be of practical importance.
Then the sample size would be chosen
so that, if the actual difference in usage is some particular number $\Delta = \mu_y - \mu_s$ or greater, then there is reasonable probability, say 90% or 95% or even 99%, that $H_0$ will be
rejected.
Sometimes, one distinguishes between the 'research hypothesis' $(H_a)$ and
the 'null hypothesis' $(H_0).$ Often the null hypothesis is the unremarkable
one of the two and the alternative hypothesis would be more interesting.
Perhaps if $H_0$ is rejected in favor of $H_a,$ then more attention will be
paid to the needs of young ATM customers in the future (types of transactions available, locations of ATMs, incentives to use ATMs, etc.)
Also, remember that the null hypothesis must always contain an $=$-sign --- whether as $\mu_y \le \mu_s$ (here), or as $\mu_y = \mu_s$ or $\mu_y \ge \mu_s$ (in other situations). This is because the $=$-sign in the null hypothesis determines
the 'null distribution' for performing the test (determining the critical value
for a test at the 1% significance level or computing the P-value).
