Hypothesis testing is based ona) minimizing the type I error b) minimizing the type II errorc) minimizing the sum of type I and type II errorsd) none of these
Question
Hypothesis testing is based ona) minimizing the type I error b) minimizing the type II errorc) minimizing the sum of type I and type II errorsd) none of these
Solution
Hypothesis testing is based on c) minimizing the sum of type I and type II errors.
Here's why:
In hypothesis testing, we aim to make the best decision based on the data we have. However, there's always a chance of making an error - either rejecting a true null hypothesis (Type I error) or failing to reject a false null hypothesis (Type II error).
While we would ideally like to minimize both types of errors, in practice, there's often a trade-off between the two. Reducing the probability of one type of error often increases the probability of the other type of error.
Therefore, the best approach is to try to minimize the sum of the two types of errors. This is often done by choosing a significance level (the probability of a Type I error) that balances the risks associated with both types of errors.
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