A cosmetics firm uses two different ship-ping companies. Shipper A is more expensive, but managers believe that fewer shipments get damaged than when shipped the current shipper used by the firm, Shipper B. To compare the shippers, the company devised the following comparison. The next 450 shipments to outlet stores were randomly assigned to Shipper A or to Shipper B. Upon receipt, an agent at the store reported whether the shipment had suffered noticeable damages. Because shipping with Shipper A is more expensive, a financial calculation showed that Shipper A needs to have at least 10% fewer damaged shipments than Shipper B for Shipper A to improve profits.
(a) How would you randomly assign the shipments to Shipper A or to Shipper B?
(b) Does the data show that shipping with Shipper A exceeds the needed threshold by a statistically significant amount?
(c) Is there a statistically significant difference between the damage rates?