Refer to the situation described in Exercise 77. Suppose the store has recently adopted a standard policy on shipment quality: If the overall shipment contains no more than 5% mislabeled hats, it should be considered “good” (that is, it is of acceptable quality). More than 5% mislabeled hats and the shipment will be considered “bad” and sent back to the supplier. The shipping and receiving manager will have just one sample of 20 hats to check.
In Exercise 77
The Fred Meyer store in Portland has just received a large shipment of fitted baseball caps from Gradient Sporting Goods. In previous orders, a number of the hat sizes have been mislabeled. Because of this, the shipping and receiving manager plans to randomly check 20 of the hats in the current shipment. If 10% of the hats in the current shipment are mislabeled, how likely is it that the sample of 20 will have?
a. Suppose the manager uses the following decision rule: If the sample has one or more mislabeled hats, send back the entire shipment. Suppose this test is applied to a “good” shipment (specifically, one in which exactly 5% of the hats are mislabeled). How likely is it that the store will send back the shipment?
b. Where should the cut off for test results is set in the sample of 20 in order to ensure that you have no more than a 1% chance of making the mistake of sending back a “good” (that is, a 5% mislabeled) shipment?