Finding the null and alternative hypothesis for this problem

Question

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.

Answer 1

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.

Answer 2

You are giving two alternative hypothesis which are

• $H_0$: the mean call time will be worsened after a training program given to call center employees.
• $H_1$: the mean call time will be improved after a training program given to call center employees.

The null hypothesis is that the training has no effect on the duration of a call.

Answer 3

The correct hypotheses are: $$\begin{align} H_0: \ \mu=540 \\ H_1: \ \mu <540 \end{align}.$$ Interpretation: The problem states "mean=540 seconds", so is the null hypothesis. To improve mean call time implies to decrease the mean call time by more efficient work of the call center operators.