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

H_a: the food is not safe

The following is an example of what type of error?

The sample suggests that the food is safe, but it actually is not safe.

• type I
• type II
• not an error

Answer 1

SOLUTION

For solving the problem first we need a general awareness about the Type I error and Type II error.

Type I error : It is an error occured when the rejection of null hypothesis when it is true. That is the null hypothesis is actually true but we reject it. This kind of error is called Type I error.

Type II error : This type of error occured when we fail to reject the false null hypothesis as the result of a test procedure. That is the error when we accept a null hypothesis but the alternative hypothesis is true.

Now let us consider the given problem. The hypothesis are

H₀: The food is safe

H_a:The food is not safe.

And given that the sample suggest that the fodd is safe (that is we accept the null hypothesis), but it actually is not safe (that is the null hypothesis is false or the alternative hypothesis is true).

So from above definitions we can conclude that the error occured is Type II error.