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 to see whether taking a vitamin supplement each day has significant health benefits. There are no (known) harmful side effects of the supplement.

Short answer

Use a relatively large significance level (such as \(\alpha=0.10\)).

Step-by-step solution

- Understand the context of the test

The experiment in question tests whether taking a daily vitamin supplement significantly improves health, with no known harmful side effects. So the cost of making a mistake (false positive) is not high and the cost of missing a true positive (false negative) could be high, since people could miss on potential health benefits.

Step 2- Decide on the appropriate significance level

In this setting, it may make more sense to use a higher significance level such as \(\alpha = 0.10\). This is because the risk of a false positive (deciding that the vitamin has health benefits when it does not) is not very harmful, but missing a true positive effect (deciding that the vitamin does not have health benefits when it does) could prevent people from experiencing potential health benefits.