Suppose that for a particular hypothesis test, the consequences of a Type I error are not very serious, but there are serious co
nsequences associated with making a Type II error. Would you want to carry out the test using a small significance level α (such as 0.01) or a larger significance level (such as 0.10)? Explain the reason for your choice.
We want to reduce type II error we carry out the test using a larger significance level (such as 0.10) and not a small significance level α (such as 0.01).
Step-by-step explanation:
Type I error
Rejecting the null hypothesis when it is in fact true is called a Type I error.
It is denoted by alpha, α that is the significance level.
Lower values of alpha make it harder to reject the null hypothesis, so choosing lower values for alpha can reduce the probability of a Type I error.
It is given that the consequences of a Type I error are not very serious, but there are serious consequences associated with making a Type II error.
Type II error
This is the error when we fail to reject a false null hypothesis or accept a null hypothesis when it is true.
Higher values of alpha makes it easier to reject the null hypothesis.
So choosing higher values for alpha can reduce the probability of a type II error.
The consequence here is that if the null hypothesis is true, increasing the value of alpha makes it more likely that we make a Type I error.
Since, we want to reduce type II error we carry out the test using a larger significance level (such as 0.10) and not a small significance level α (such as 0.01).
This will increase type I error but that is okay since we do not have serious consequences for it.
