Question

How can type 1 and type 2 errors be minimized?

Answer 1

Hint: When the null hypothesis$\left( {{H}_{0}}:\mu ={{\mu }_{0}} \right)$ is true and we reject it, we make a type 1 error. When the null hypothesis is false and we fail to reject it, you make a type 2 error. We express the method of minimizing error by their level of significance in hypothesis tests.

Complete step by step solution:
The probability of a type 1 error (rejecting a true null hypothesis) can be minimized by picking a smaller level of significance α before doing a test (requiring a smaller p-value for rejecting ${{H}_{0}}$).
Once the level of significance is set, the probability of a type 2 error (failing to reject a false null hypothesis) can be minimized either by picking a larger sample size or by choosing a "threshold" alternative value of the parameter in question that is further from the null value. This threshold alternative value is the value you assume about the parameter when computing the probability of a type 2 error.

Note:
As We conduct your hypothesis tests, consider the risks of making type 1 and type 2 errors. If the consequences of making one type of error are more severe or costly than making the other type of error, then choose a level of significance and a power for the test that will reflect the relative severity of those consequences.