Question

FDA food contamination guidelines allow for pineapple juice to contain up to 15% mold and still be shipped out. In practice, it is assumed that pineapple juice is okay to be shipped out; a batch is only discarded if there is statistically significant evidence that it contains more than the allowed amount of mold.

(a) Write the appropriate null and alternative hypotheses for this approach to the situation.

(b) Which of the following is the consequence of making a type I error?

• A batch of pineapple juice meets the guidelines, but is discarded.

• A batch of pineapple juice fails to meet the guidelines, but is shipped out.

• A batch of pineapple juice meets the guidelines, and is shipped out.

• A batch of pineapple juice fails to meet the guidelines, and is discarded.

(c) Which of the following is the consequence of making a type II error?

• A batch of pineapple juice meets the guidelines, but is discarded.

• A batch of pineapple juice fails to meet the guidelines, but is shipped out.

• A batch of pineapple juice meets the guidelines, and is shipped out.

• A batch of pineapple juice fails to meet the guidelines, and is discarded.

(d) Which level of significance (α) minimizes the probability that a batch of pineapple juice gets shipped out when it fails to meet the guidelines?

0.1 0.05 0.01

Answer 1