Pop’s Popcorn, Inc. needs to determine the optimum power and time settings for their new licorice-flavored microwave popcorn. They want to find a combination of power and time that delivers high- quality popcorn with less than 10% of the kernels left unpopped, on average—a value that their market research says is demanded by their customers. Their research department experiments with several settings and determines that power 9 at 4 minutes is optimum. Their tests confirm that this setting meets the less than 10% requirement. They change the instructions on the box and promote a new money back guarantee of less than 10% unpopped kernels.
a) If, in fact, the setting results in more than 10% kernels unpopped, what kind of error have they made? What will the consequence be for the company?
b) To reduce the risk of making an error, the president ( Pop himself) tells them to test 8 more bags of popcorn (selected at random) at the specified setting. They find the following percentage of unpopped kernels:
7, 13.2, 10, 6, 7.8, 2.8, 2.2, 5.2.
Does this provide evidence that the setting meets their goal of less than 10% unpopped? Explain.