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.

• ( h_0 ): the food is safe.
• ( h_a ): the food is not safe.

is the following an example of a type i or type ii error?
the sample suggests that the food is safe, but it actually is not safe.
a. type i
b. type ii

Explanation:

Step1: Recall Type I and Type II error definitions

Type I error: Reject \(H_0\) when \(H_0\) is true. Type II error: Fail to reject \(H_0\) when \(H_0\) is false.

Step2: Analyze the given situation

Here, \(H_0\): The food is safe (null hypothesis). The sample suggests the food is safe (fail to reject \(H_0\)), but the food is actually not safe (\(H_0\) is false).

Answer:

B. Type II