Question

A business claims that the mean time that customers wait for service is at most 5.9 minutes. Write the null and alternative hypotheses and note which is the claim.

Answer 1

The hypothesis test is a tool that allows you to test the probability of occurrence of a given event, for this two possible scenarios are formulated, the alternative hypothesis that is the one posed by the researcher or that has thrown the investigation, and the null hypothesis that is the opposite scenario to which you want to try.

In this case, as the company affirms that the average duration of the waiting time for customers t is at most 5.9 minutes, that is,
`t \leq  5.9`, this will be the alternative hypothesis, the one that will be demonstrated, So the null hypothesis is the opposite, that is, the waiting time is greater than 5.9 minutes.

Answer

`H_(0): t >5.9\\H1: t\leq 5.9`