Finding the null and alternative hypothesis for this problem **Question** > The BEG Company operates service centers in various cities where customers can call to get answers to questions about their bills. > > Previous studies indicate that the distribution of time required for each call is normally distributed, with a mean $\mu=540$ seconds. > > Company officials have selected a random sample of $50$ calls and wish to determine whether the mean call time will be improved after a training program given to call center employees. **My Solution** $$H_0:\mu \ge 540, \ H_1:\mu < 540$$ However, this answer is wrong. I do not understand this question, I would highly appreciate if someone could explain it further on how to find out the null and alternative hypothesis for this question.

Your answer is mathematically perfectly correct.

* $H_0$ - the status quo or even an adversary effect - in your case: $\mu$ stays the same or worsens
* $H_1$ - the **claim** that something has changed - in your case: $\mu$ got better



Unfortunately there are also textbooks around (and corresponding teachers/lecturers) who seem to systematically exchange $H_0$ and $H_1$.

The idea of the hypothesis testing is to find enough statistical evidence that $H_0$ - the status quo - is improbable (here the significance level $\alpha$ comes into play).

This is considered to be achieved, if the test statistic delivers a value that is rather improbable **under the assumption that $H_0$ is true**.