Question

For each situation described, indicate whether it makes more sense to use a relatively large significance level (such as \(\alpha=0.10\) ) or a relatively small significance level (such as \(\alpha=0.01\) ). Testing a new drug with potentially dangerous side effects to see if it is significantly better than the drug currently in use. If it is found to be more effective, it will be prescribed to millions of people.

Short answer

It is more appropriate to use a relatively small significance level, such as \(\alpha = 0.01\), to minimize the risk of falsely declaring the new drug as more effective.

Step-by-step solution

Understanding the context

In this situation, we are testing a new drug with potentially dangerous side effects to know if it is significantly better than the currently used drug. If we find it more effective, it will be prescribed to millions of people.

Interpreting significance level

A significance level (\(\alpha\)) is the probability of rejecting the null hypothesis when it is actually true. Therefore, a larger \(\alpha\) means a greater chance of wrongly rejecting the null hypothesis (Type I error). In the context of this experiment, it would mean a greater chance of concluding that the new drug is more effective when it actually isn't.

Conclusion

Considering the stakes, including dangerous side effects and the drug potentially being prescribed to millions of people, a Type I error could have serious consequences. Consequently, it is better to use a relatively small \(\alpha\) (such as \(\alpha = 0.01\)). The lower \(\alpha\) reduces the chance of falsely concluding that the new drug is more effective, therefore minimizing the risk of prescribing an ineffective or potentially harmful drug to millions of people.