Food inspectors inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test with the following hypotheses. \( \mathrm{H}_{0} \) : the food is safe \( \mathrm{H}_{\mathrm{a}} \) : the food is not safe The following is an example of what type of error? The sample suggests that the food is not safe, but it actually is safe. Otype I type II not an error

This scenario is an example of a type I error. In hypothesis testing, a type I error occurs when the null hypothesis (\( \mathrm{H}_{0} \)) is rejected when it is actually true. Here, the inspectors conclude that the food is unsafe based on the sample results, but in reality, the food is safe. It's like crying wolf when there’s no wolf—imagine the surprise at the dinner table when everyone is worried over nothing! On the flip side, type II errors occur when the null hypothesis is not rejected when it should be, meaning unsafe food is labeled as safe. This would be akin to saying nothing is wrong when, in fact, there might be a sneaky food-borne villain lurking! Balancing these errors is critical to ensure food safety.