Question

Suppose that for a particular hypothesis test, the consequences of a Type I error are very serious. Would you want to carry out the test using a small significance level \(\alpha\) (such as 0.01 ) or a larger significance level (such as 0.10 )? Explain the reason for your choice.

Short answer

Given the serious consequences of a Type I error, it would be better to carry out the test using a small significance level (such as 0.01) to minimize the risk of committing a Type I error.

Step-by-step solution

Understanding Type I Errors

A Type I error occurs when the null hypothesis is true but it is rejected. It is often considered a 'false positive.' The consequences of a Type I error can be serious, depending on the context of the test.

Understanding Significance Level

The significance level (\(\alpha\)) is the probability of rejecting the null hypothesis when it is true. Therefore, a smaller value of \(\alpha\) decreases the chance of a Type I error.

Making the Decision

Given the serious consequences of a Type I error in this case, it would be preferable to choose a small significance level, such as 0.01, to minimize the risk of a Type I error.