The owner of Get-A-Away Travel has recently surveyed a random sample of 337 customers to determine whether the mean age of the agency's customers is over 20. The appropriate hypotheses are Upper H 0: muequals20, Upper H Subscript a Baseline : mu greater than 20. If he concludes the mean age is over 20 when it is not, he makes a error. If he concludes the mean age is not over 20 when it is, he makes a error.

On this case we want to test if the mean age of the agency's customers is over 20, so the system of hypothesis would be:

Null hypothesis:

Alternative hypothesis:

If he concludes the mean age is over 20 when it is not, he makes a type I error . If he concludes the mean age is not over 20 when it is, he makes a Type II error error.

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".  

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".  

Type I error, also known as a “false positive” is the error of rejecting a null  hypothesis when it is actually true. Can be interpreted as the error of no reject an  alternative hypothesis when the results can be  attributed not to the reality.  

Type II error, also known as a "false negative" is the error of not rejecting a null  hypothesis when the alternative hypothesis is the true. Can be interpreted as the error of failing to accept an alternative hypothesis when we don't have enough statistical power.  

Solution to the problem

On this case we want to test if the mean age of the agency's customers is over 20, so the system of hypothesis would be:

Null hypothesis:

Alternative hypothesis:

If he concludes the mean age is over 20 when it is not, he makes a type I error . If he concludes the mean age is not over 20 when it is, he makes a Type II error error.