Question

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. h0: the food is safe. ha: the food is not safe based on the hypotheses above, is the following statement a type i or type ii error? the sample suggests that the food is safe, but it actually is not safe.

Answer 1

The statement "the sample suggests that the food is safe, but it actually is not safe" is an example of a Type II error.

A Type II error occurs when the null hypothesis (in this case, that the food is safe) is not rejected, even though it is false (in this case, the food is actually not safe). In other words, the inspector has failed to identify a problem with the food when there actually is one.

On the other hand, a Type I error would occur if the inspector falsely concludes that the food is not safe when it actually is safe, i.e. rejecting the null hypothesis when it is true.