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A type I error consists of rejecting the null hypothesis H₀ when it is true.

A type II error involves not rejecting H₀ when it is false.

A test statistic is a function of the sample data used as a basis for deciding whether H₀ should be rejected. The selected test statistic should discriminate effectively between the two hypotheses. That is, values of the statistic that tend to result when H₀ is true should be quite different from those typically observed when H₀ is not true.

Usually, you would like for a type I error to be very small (highly unlikely). In this case, when the alternative hypothesis is \({H_a}:\mu < 5\), the type I error is deciding that water is safe when it is not- this can affect a lot of people and it is a grave error. The type II errors says that the water is unsafe when it is safe, this error is not as serious as the first there are no such consequences.

In the second case, when \({H_a}:\mu > 5\), the type II error is now that the water is safe while it is not, which is the more serious case. As mentioned in the beginning, it is better to choose that the type I error is more serious so that we can control the error(explicitly).