There are two types of professional wrestlers: "babyfaces" ("good guys") and "heels" ("bad guys"). between any pair of professional wrestlers, there may or may not be a rivalry. suppose we have n professional wrestlers and we have a list of r pairs of wrestlers for which there are rivalries. give an o. n c r/-time algo- rithm that determines whether it is possible to designate some of the wrestlers as babyfaces and the remainder as heels such that each rivalry is between a babyface and a heel. if it is possible to perform such a designation, your algorithm should produce it.

An information technology analyst believes that they are losing customers on their website who find the checkout and purchase system too complicated. she adds a one-click feature to the website to make it easier, but finds that only about 99% of the customers are using it. she decides to launch an ad awareness campaign to tell customers about the new feature in the hope of increasing the percentage. she doesn't see much of a difference, so she hires a consultant to her. the consultant selects a random sample of recent purchases, tests the hypothesis that the ads produced no change against the alternative that the percent who use the one-click feature is now greater than 99%, and finds a p-value of 0.240.24. what conclusion is appropriate?